manager

• A person who directs resorces to achieve a stated goal.
• direct efforts of others, delegate tasks within an organization
• A person who directs resorces to achieve a stated goal.
• purchase inputs to be used in the production of goods and services such as the output of a firm are in charge of making other decisions, such as product price or quality.

Resources

anything used to prodeuce a good ore service or, more generally, to achieve a goal.

What scarcity means

Scarcity means that making one chioce you give up to another.

managerial economics

the study of how direct scarce resources in the way that most efficiently achieves a managerial goal.

Managerial economics focses on how managers allocate their scarse resources.

scarce resources

• People
• Skills
• Office equipment
• Warehouses (magazzini, depositi)
• Machinery
• Raw materials

economic profits

total revenue - total opportunity cost

• The cost of the explicit (or accounting) and implicit resources that are foregone when a decision is made. 
• The cost of an alternative that must be forgone in order to pursue a certain action. Put another way, the benefits you could have received by taking an alternative action.
• Example: The opportunity cost of going to college is the money you would have earned if you worked instead. On the one hand, you lose four years of salary while getting your degree; on the other hand, you hope to earn more during your career, thanks to your education, to offset the lost wages.
• The difference in return between a chosen investment and one that is necessarily passed up. Say youinvest in a stock and it returns a paltry 2% over the year. In placing your money in the stock, you gave up the opportunity of another investment - say, a risk-free government bond yielding 6%. In this situation, your opportunity costs are 4% (6% - 2%).

Accounting profits

• The amount of money taken in from sales (total revenue, or price times quantity sold: TR=P*Q) - the dollar cost of producing goods ore services.
• Accounting profits tend to be higher than economic profits as they omit certain implicit costs, such as opportunity costs.

explicit (or accounting) cost

A business expense that is easily identified and accounted for. Explicit costs represent clear, obvious cash outflows from a business that reduce its bottom-line profitability.

implicit cost

A cost that is represented by lost opportunity in the use of a company's own resources, excluding cash.

present value

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net present value

The present value of the income stream generated by a project - the current cost of the project.

profit maximization

maximizing the value of the firm, which is the present value of current and future profits.

marginal benefit

The change in total benefits arising from a change in the managerial control variable Q.

Additional benefit that arises by sing an additional unit of the managerial control variable.

marginal cost

The change in total costs arising from a change in the managerial control variable Q.

The additional cost incurred by using an additional unit of the managerial variable

marignal net benefits of Q MNB(Q)

The change in the net benefit that arise from a one-unit change in Q.

MNB(Q) = MB(Q) - MC(Q)

market demand curve

A curve indicating the total quantity of a good all consumers are willing and able to purchase at each possible price, holding the prices of related good, income, advertising, and other variables constant.

demand shifters

Income (Normal and inferior good)

Prices of related goods (substitutes and complements)

Advertising and consumers tastes

Population

Consumer expectations

normal good

A good for which an increase (decrease) in income leads to an increase (decrease) in the demand for that good.

Examples:steak, airline travel, designer jeans.

inferior good

A good for which an increase (decrease) in income leads to a decrease (increase) in the demand for that good.

Examples: Bologna bus travel, "generic" jeans.

substitutes

Goods for which an increase (decrease) in the price of one good leads to an increase (decrease) in the demand for the other good.

Examples: Coke and Pepsi, chicken and beef, cars and trucks, raincoats and umbrella.

complements

Goods for which an increase (decrease) in the price of one good leads to a decrease (increase) in the demand for the other good.

Examples: Computer software and Computer, Beer and pretzels, food and clothes.

consumer surplus

The value consumers get from a good but do not have to pay for.

Is the area bove the price paid for a good, but below the demand curve.

market supply curve

A curve indicating the total quantity of a good that all producers in a competitive market would produce at each price, holding input prices, technology, and other variables affecting supply constant.

excise tax

Tax on each unit of output sold, where the tax revenue is collected from te supplier.

ad valorem tax

"According to the value". Percentage tax used by governments agencies. (example: sales tax = tasse di vendita)

supply function

A function that decribes how much of a good will be produced at alternative prices of that good, alternative input prices, and alternative values of other variables affecting supply.

supply curve

the amount producers will be willing to produce at a given price.

the price firms would have to receive to be willing to produce an additional unit of good.

shortage of the good

There is not enough of the good to satisfy all consumers willing to purchase it at that price. Price rises.

Producers are willing to produce less at the lower price.

Consumers wish to purchase more at the lower price.

surplus of the good

Firms are producing more than they can sell at that price. Price lowers.

market equilibrium

The interaction of supply and demand determines a competitive price, such that there is neither sortage nor a surplus of the good:

demand curve=supply curve

-> equilibrium price and equilibrium quantity

price ceiling

• The maximum legal price that can be charged in a market.
• Results in a shortage
• Price ceilings discriminate against those who havea high opportunity cost of time and do not like to wait in lines (first come, first served).

Full economic price

The dollar amount paid to a firm under a price ceiling, plus the nonpecuniary price.

price floor

• The minimum legal price that can be charged in a market.
• Example: minimum wage.
• Results in a surplus.
• Sometimes government agree to purchase the surplus. (Many agriculturale products)

elasticity

A measure of the responsiveness of one variable to changes in another variable; the percentage change in one variale that arises due to a given percentage.

EG,S=(%deltaG)/(%deltaS)=(dG/dS)*(S/G)

Relationship between G and S

• EG,S > 0, then S and G are directly related
• EG,S < 0, then S and G are inversl< related
• EG,S = 0, then S and G are unrelated

How responsive G is to change in S

• |EG,S| > 1, (larger denominator) then a small percentage changein S will lead to a relatively large percentage change in G.
• |EG,S| < 1, (smaller denominator) then a given percentage change in S will lead to a relatively small percentage change in G

own price elasticity

A measure of te responsivenesss of quantity demanded of a good to a change in the price of that good; the percentage change in quantity demanded divided by the percentage change in the price of the goood. 

It is always a negative number!

• |EQx,Px| > 1 or MR > 0, elastic demand -> increase (decrease) in price leads to decrease (increase) in total revenue. 
• |EQx,Px| < 1 or MR < 0, inelastic demand -> increase (decrease) in price leads to an increase (decrease) in total revenue.
• |EQx,Px| = 1 or MR=0, unit elastic demand -> Total revenue is maximized at the point where demand is unitary elastic.

Conceptually, the qantity consumed of a good is relatively responsive to a change in price of the good when demand is elastic and relatively unresponsive to changes in price when demand is inelastic. Howerver, when demand is elastic, a price increase will reduce consumption considerably.

• Perfectly elastic (EQx,Px=-infinity) -> demand curve is a horizontal line in graph P(Q)
• Perfectly inelastic (EQx,Px=0= -> demand curve is a vertical line in graph P(Q). Consumers do not respond at all to to changes in price.

3 factors affecting own price elasticity magnitude

• Available substitutes: the more subsitutes available, the more elast the demand.Implication:demand for broadly commodities (ex food) tends to be more inelastic than the demand for specific commodities (ex beef).
• Time: Demand tends to be more inelatic in the short term than in the long term; time allows consumers to seek out available substitutes.The more times consumers have to react to a price change, the more elastic the demand for the good.
• Expenditure Share: Goods that comprise a small share of consumer's budgets tend to be more inelastic than goods for which consumer spend large portions of their incomes.

cross price elasticity

A measure of the responsiveness of the demand for a good to changes in the price of a related good: the percentage change in the qantity demanded of one good divided by the percentage change in the price of a related good.

• If EQx,Py > 0 then X and Y are substitutes
• If EQx,Py < 0 then X and Y are complements

income elasticiy

A measure of the responsiveness of the demand for a good to changes in consumers income; the percentage change in quantity demanded divided by the percentage change in income

• If EQx,M > 0, then X is a normal good
• If EQx,M < 0, then X is an inferior good

elasticities of logarithmic demand functions

corresponds to the coefficient of the considered demand shifter.

least squares regression

The line that minimizes the sum of squared deviations between the line and the actual data points

Regression Analysis (RA)

for estimating demand function (non solo)

RA: standard error of each estimated coefficient

measure of how much each estimated coefficient would vary in regression based on the same underlying true demand relation, but with different observations. 

σâ, σ^b

RA: Confidence intervals

Given a parameter estimate, its standard error, and the iid normal assumption, the manager can construct upper and lower bounds on the true value of the estimated coefficient by onstructing a 95%  confidence interval.

Rule of thumb:   â±2σâ    and    ^b±2σ^b

RA: t-statistic

Evaluating statistical significance of estimated coefficient

The ratio of the value of a parameter estimate to the standard error of the parameter estimate:

tâ=â/σâ

Rule of thumb for using t-statistik: When the absolute value of t-statistic is ≥ 2, the manager can be 95% confident that the true value of the underlying parameter in the regression is not zero.

reason: when the absoulute value of the t-statistic is large, the standard error of the parameter estimate is small relative to the absolute value of the parameter estimate. Thus, one can be more confident that, given a different sample data drawn from the true model, the new parameter estimate will be in the same ballpark.

RA: R-square

Evaluating the overall fit of the regression line

Multiple R, R-square and Adjusted R-square provide diagnostics that indicate how well the regression line explains the sample of observations of the dependent variable.

The R-square (or coefficient of determination) tells the fraction of the total variation in the dependent variable that is explained by the regression.

R²=SS_reg/SS_tot

SS=sum of squared errors

A data set has values y_i, each of which has an associated modelled value f_i (also sometimes referred to as ŷ_i). Here, the values y_i are called the observed values and the modelled values f_i  are sometimes called the predicted values.

SStot=Somma(yi-ymedio)²

SSreg=Somma(fi-ymedio)²

Range: 0≤R2≤1

The closer the R-square is to 1, the better the overall fit of the estimated regression equation to the actual data.

Drawbacks: 

• subjective measure of goodness of fit.
• It cannot decrease when additional explanatory variables are included in the regression -> sometimes the R-square is very close to 1 merely because the number of observations is small relatively to the number of estimated parameters.

For this reason, many researchers use the adjusted R-square given by:

Radj²=1-(1-R²)*(n-1)/(n-k-1)

Where n is the total number of observations and k the number of estimted coefficients.

RA: F-statistic

Evaluating the overall fit of the regression line

• Measure of goodness of fit, that hasn't the drawback of the subjectiveness.
• The F-statistics provides a measure of the total variation explained by the regression relative to the total unexplained variation. The greater the F-statistic, the better the overall fir of the regression line through the actual data.
• The statistical properties are known, thus one can objectively determine the statistical significance of any reported F-value.
• The lower the significance of the F-statistic, the more confident you can be of the overall fit of the regression equation. Regression that have F-statistics with significance values ≤ 5% are generally considered significant.

statistically significant

• In statistics, a result is called "statistically significant" if it is unlikely to have occurred by chance.
• A result that was found to be statistically significant is also called a positive result; conversely, a result that is not unlikely under the null hypothesis is called a negative result or a null result.

consumer opportunities

The possible goods and services consumer can aofford to conume.

Consumer preferences

The goods and services consumers actually consume.

consumer preference oredring proprties

• Completeness: consumer is capable of expressing a preference for, or indifference among, all bundles.
• rThe consuemr views the products under consideration as "goods" instead of "bads".More is bette:
• Diminishing Marginal Rate of Substitution: As a consumer obtains more of good X, the amount of good Y he is willing to give up to obtin another unit of good X decreases. -> Indifference curves are convex from the origin.
• Transititity: For any three bundles A, B, and C, if A>B and B>C, then A>C. If  A~B and B~C then A~C.

more is better + transitivity: 

• indifference curves do not intersect one another.
• The consumer will not get caught in a perpetual cycle of indecision.

indifference curve

A curve that defines the combinations of two goods that give a consumer the same level of satisfaction.

• Curves farther from the origin imply higher levels of satisfaction than curves closer to the origin.
• Every bundle on curve III is preferred to those on curve II, and every bundle on indifference curve II is preferred to those on curve I. The three indifference curve are convex and do not cross. 

marginal rate of substitution (MRS)

The rate at which a consumer is willing to substitute one good and still mantain the same level of satisfaction.

Absolute value of the slope of an indifference curve.

budget set (or opportunity set)

The bundles of goods a consumer can afford.

PxX+PyY ≤ M

bundle line

The bundels of goods that exhaust a consumer's income.

PxX+PyY = M

market rate of substitution

The rate at which one good may be traded for another in the market slope of the budget line.

It is the slope of the budget line -Px/Py

consumer equilibrium

The equilibrium consumption bundle is the affordable bundle that yields the greatest satisfaction to the consumer. The equilibrium refers to the fact that the consumer has no incentive to change to a different affordable bundle once this point is reached.

Occurs at MRS=Px/Py

Substitution effect

The movement along a given indifference curve that results from the change in relative prices of goods, holding real income constant.

Income effect

The movement frome one indifference curve to another that results from the change in real income caused by price change.

spot exchange

An informal relationship between a buyer and a seller in which in which neither party is obligated to adhere to specific terms for exchange.

Advantage:

• the input manufacturer specializes in what it does best: producing inputs
• avoids contract costs
• avoids costs of vertical integration.

Disadvantage:

• possible hold-up problem
• Often used when inputs are standardized

contract

A formal relationship between a buyer and a seller that obligates the buyer and seller to exchange at terms specified in  legal document.

By acquiring inputs with contracts, the purchasing firm enjoys the benefit of specializing in what it does best, because the other fir actually produces the inputs the purchasing firm needs.

Advantages:

• This method of obtaining inputs works well when it is relatively easy to write a contract that describes the characteristics of the inputs needed
• reduces opportunism
• avoids skiming on specialized investments.

Disadvantage:

• costly to write: it takes time, and often legal fees, to draw up a contract
• also it can be difficult to cover all the contingencies that could occur in the future. Thus, in complex environments, contracts will necessarily be incomplete.

vertical integration

A situation where a firm produces the inputs required to make its final product.

Advantages:

• reduces opportunism
• avoids contracting costs
• avoiding underinvestment

Disadvantages:

• Lost specialization 
• may increase organizational costs.

transaction costs

Costs associated with acquiring an input thtat are in excess of the amount paid to the input supplier.

Includes:

• searching for the supplier costs
• costs of negotiating the price. (opportunity costs of time, legal fees...)
• other required investments or expenditures

specialized investment

def, types, implications

An expenditure that must be made to allow two parties to exchage but has little or no value in any alternative use. 

Investment in a parricular exchange that cannot be recovered in another trading relationship.

relationship-specific cost

A type of exchange that occurs when the parties to a transaction have made specialized investments.

The two parties are tied together because of the specific investemtn made to facilitate exchange between them.

types of secialized investments

• Site specifity: when buyer and seller of an input must locate their plants close to each other to be able to engage in exchange (for ex electric power powerplants locate close to coal mine). Cost of builings = SI
• Physical-Asset specifity: the capital equipment needed to produce an input is designed to meet the needs of a particularbuyer and cannot be readily adapted to produce inputs needed by other buyers. (for example the lawn mower engines required special machines)
• Dedicated Assets: Investments made by a firm that allow it to exchange with a particular buyer. 
• Human Capital: specialized skills that workers must learn to work for a particulary firm -> if these skills are not useful or transferable to other employers -> specialized investment.

implications of specialized investments

Specialized costs increase transaction costs:

• Costly bargaining: each side employs negotiators to obtain a more favorable price; parties may behave strategically to enhance their bargaining positions (Ultimatum, ..).
• Underinvestment: the level of the specialized investment is lower than the iptimal level cause the prudent behaviors in case somthing goes wrong. (ex ->buying cheaper machine to sell)
• Opportunism and the hold-up problem: The buyer or the seller may attempt to capitalize the "sunk" nature of the investment by engaging in opportunism.
• hold up: one's a firm make a specialized investment, the other partymmay attempt to rob it of its investment by taking advantage of the investment sunk nature. (esempio del controllo qualità)

the principal-agent problem

occurs when the principal (ex owne/managerr) of the firm cannot observe the effort of the agent (ex manager/workers).

Problem: Principal cannot determine whether a bad outcome was the result of the agent'slow effort or due to bad luck.

• Manager's must recognize the existence of the principal-agent problem and devise plans to align the interest of workers with that of the firm
• Shareholders must create plans to align the interest of the manager with those of the shareholders.

forces that disciploine managers

• Internal Incentives
• Incentive constracts
• Stock options, year-end bonuses
• External incentives
• Personal Reputation
• Potential for takeovers (the purchase of one company by another -> rischio sostituzione)

Solution to the Manager-Worker 

• Profit sharing: Mechanism used to enhance worker's efforts that involves making the worker's compensation dependent on the underlying profitability of the firm.
• Advantage: it reduces the incentive to produce low quality products
• Revenue sharing: Mechanism used to enhance worker's effort that involves linking compensation to the underlying revenues of the firm (tips (mance) and sales commissions). Useful when worker productivity is related to revenues rather than to costs. 
• Problem: they do not provide an incentive for workers to minimize costs (esempio del cameriere che per aver più mancia dà porzioni più grandi).
• Advantage: it reduces the incentive to produce low quality products
• Piece rates: (es sarte pagate pro jeans). 
• Potential problem: the effort must be expended in quality control.
• Time clocks and spot checks: 
• Time clocks to control when workers arrive and when they depart from job. But they do not control effort.
• More useful -> Spot cheks: controlli casuali del manager, che può controllare sia presenza che sforzo.
• Advantage: reduced cost of monitoring workers.
• Disadvantege: They must occur frequently and they must entail some penalty.

market structure

Factors that affect managerial decisions, including:

• the number of firms competing in a market
• the relative size of firms
• technological and cost considerations
• demand conditions
• the ease with which firms can enter or exit the industry.

four firm concentration ratio

The fraction of total industry sales generated by the four largest firms in the industry

• the more c4 -> 0: the less concentrated the industry
•  the more c4 -> 1: the more concentrated the industry

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Herfindahl-Hirschman index (HHI)

Rothschild index

A measure of the sensitivity to price of a product group as a whole relative to the sensitivity of the quantity demanded of a single firm to a change in its price.

R = ET/EF     0≤R≤1

where ET is the elasticity of demand for the total market and EF is the elasticity of demand for the individual firm’s product.

• R=1: the individual firm faces a demand curve with the same sensitivity to price as the market demand curve
• R->0, the firm’s price sensitivity is much greater than the market’s. With many identical firms, R->0

Lerner index

A measure of the difference between price and marginal cost as a fraction of the product's price.

L=(P-MC)/P=-1/Ed    0≤L≤1

Ed: elasticity of demand of the firm.

The interpretation of this mathematical relationship is that a firm which is maximizing profits will never operate along the inelastic portion of its demand curve.

• Higher numbers implies greater market power.
• For a perfectly competitive firm (where P=MC), L=0; such a firm has no market power.

integration and merger activity

uniting productive resources. Can occur through a merger. Can occur during the formation of a firm.

Types:

• Vertical: Various stages in the production of a product are integrated in one firm. Vertical integration reduces transaction costs. vertical merger is the integration of two or more firms that produce components for a single product.
• Horizontal: Production of similar products is merged into one firm. 
• Advantages: 
• Savings from economies of scale and scope (socially beneficial)
• Increased market power (social cost)
• Conglomerate: Production of unrelated products is merged into a single firm. Unclear why this is observed. Scarcity of superior managerial talent? Improved cash flows (should not matter if capital markets work well)?

perfect Competition

• Many firms, each of which is small relative to the entire market.
• Firms have acsess to the same technologie and produce similar products.
• Perfect information on both sides of market.
• No transaction costs.
• Free entry and exit -> in the long run firms earn zero profits. (firms are "price takers", P=MR)
• Firms do not have market power -> no individual firm has perceptible impact on the market price, quantity, or quality of the product produced in the market.
• Firm demand curve = market Price.
• Both concentration ratio and Rotschild index tend to be close to zero.

Monopolistic competition

• Many firms and consumers.
• Each firm produces a product that is slightly different from products produced by other firms.
• Example: Restaurant in city with many fodd estabilishments.
• Firms have some role over the market price (but market power is limited). Because by raising the price, some consumers will remain loyal to the firm due to a preference for the particular characteristics of its product. But some other costumer will switch to another firm.
• Level of sales depends on the price a firm set.
• Maximize profits: MR=MC.
• Firms often spend considerable sums on advertisin.
• Free entry and exit impacts profitability.
• Concentration measures are close to zero; Rotschield index is greater than zero (product differentiation).
• The good: product variety
• The bad to society: P>MC and Excess capacity (unexploited economies of scale)
• The ugly to managers: P=ATC > minimum of average costs -> zero profits in the long run

Oligopoly

• A few large firms tend to dominate the market.
• Examples airline, aerospace markets.
• Products may be either identical ore differentiated.
• When one firm in an oligopolistic market changes its price or marketing strategy, not only its own profits but the profits of other firm in the industry are affected (mutual interdipendence).
• The mutual interdipendence gives rise to strategic interactionamong the firms.
• Higliy concentrated markets.

Monopoly

• A firm that is the sole producer of a good or service in the relevant market.
• Examples: most utility companies are the sole providers of electricity and natural gas in a given city.
• There is a tendency for seller to capitalize on the monopoly position by restricting output and charging a price above MC. Consumer cannot switch to another producer in the face of higher prices.
• There is extreme concentration and the Rotschid index is unity

cost complementaries

exist when the MC of producing one output is reduced when output of another product is increased.

comparative advertising

A form of advertising where a firm attempts to incerase the demand for its brand by differentiating its product because of its brands.

brand equity

The additional value added to a product because of its brand

niche marketing

A marketing strategy where goods and services are tailored to meet the needs of a particular segment of the market.

green marketing

A form of niche marketing where firms target products toward consumers who are concerned abou environmental issues.

brand myopic

A manager or a company that rests on a brand's past laureals instead of focusing on emerging industry trends or changes in consumers preferences.

sweezy oligopoly

An industry in which:

• there are few firms serving many consumers
• firms produce differentiated products
• each firm believes rivals will respond to a price reduction but will not follow a price increase
• Barriers to entry exist
• key feature: price-rifidity
• profit maximization: MRs=MC

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• The kinked-shaped marginal revenue curve implies that there is a range over which changes in marginal cost do not affect the profit-maximizing level of output. (This is in contrast with competitive, monopolistically competitive and monopolistic firms)
• The frims have an incentive not to change their pricing behaviour provided marginal costs remain in a given range.
• Firms do not want to change their prices because of the effect of price changes on the behavoiur of the other firms in the market.
• Sweezy model has been criticized because it offers no explanation of how the industry settles on the initial price that generates the kink in each firm's demand curve.

Cournot oligopoly

An industry in which:

• there are few firms serving many consumers
• firms produce either differentiated or homogeneous products
• each firm believes rivals will hold their output constant if it changes its output (the output of rivals is viewed as given or fixed)
• Barriers to entry exist
• Industry output is lower than the socially efficient level. This inefficiency arises because the equilibrium price exceeds marginal cost. But when the number of firms is arbitrarily large, the equilibrium price in a homogeneous product Carnout market is arbitraly close to marginal cost, and industry output approximate that under perfect competition.

homogeneous product

Each firm's MR depends on the output produced by the other firm.

Firm 1’s best-response (or reaction) function is a schedule summarizing the amount of Q1 firm 1 should produce in order to maximize its profits for each quantity of Q2 produced by firm 2.

Since the products are substitutes, an increase in firm 2’s output leads to a decrease in the profit- maximizing amount of firm 1’s product.

To find a firm’s best-response function, equate its marginal revenue to marginal cost and solve for its output as a function of its rival’s output.

Cournot equilibrium

A situation in which neither firm has an incentive to change its output given the other firm's output.

The two firm’s best-response functions intersect.

isoprofit curve

A function that defines the combinations of outputs produced by all firms that yield a given firm the same level of profits.

Isoprofit curves that lie closer to firm 1's monopoly output Q1M are associated with higher profits fot that firm.

The isoprofit curves reach their peak where they intersect the firm's reaction function.

The isoprofit curves do not intersect one another

To maximize profits a firm should push its isoprofits curve as far as possible until it is just tangential to the given output of the other firm.

Graphycally isoprofit curves of the other firms are the mirror image of those for the first firm.

Carnout equilibrium

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Change in marginal costs

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Reduction in marginal costs leads to an increase in output of the same firm and a decline in the other firm's output -> the first firm enjoys a larger market share due to its improved cost situation.

Collusion

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Collusion leads to a price that exceeds MC, an output below the socially optimal level, and a deadweight loss. However the colluding firms enjoy higher profits than they would earn if they competed as Carnout oligopolists.

best-response (or reaction) function

A function that defines the profit maximizing level of output for a firm given output levels of another firm.

Q1=r(Q2)

collusion

Whenever a market is dominated by only few firms, firms can benefit at the expense of consumers by "agreeing" to restrict output or, equivalently, to charge higher prices.

Stackelberg oligopoly

An industry in which:

• there are few firms serving a large number of consumers
• firms produce either differentiated or homogeneous products
• A single firm chooses an output before rivals select their outputs
• all other firms (the followers) take the leader's output as given and select outputs that maximize profits given the leader
• since the price exceeds marginal cost, industry output is below socially efficient level -> deadweight loss (but lower than in monopoly)
• The leader chooses he point on the follower's reaction curve that corresponds to the highest level of profits.
• The leaders profit are higher than they would be in Cournot equilibrium and the followers profit are lower than in Cournot equilibrium.

Bertrand oligopoly

An industry in which:

• there are few firms serving many consumers
• firms produce identical products at a constant marginal cost
• firms compete in price and react optimally to competitors' prices. Each firm independently sets its price in order to maximize profits (price is each firms’ control variable).
• Consumers have perfect information and there are no transaction costs
• barriers to entry exist
• For the view point of the manager, BO is undesiderable: it leads to zero economic profits even if there are only two firm in the market.
• From the view point of consumers, BO is desiderable: it leads to prescisely the same outcome as a perfectly competitive market.

Bertrand equilibrium

Firms set P1=P2=MC

Comparing the 4 oligopoly model

• total market output:B>S>C
• price: C>S>B
• profits: B -> lowest profits. Optimal decision and profits vary depending on the type if oligopolistic interaction that exist in the market

contestable market

• A market in which all firms have access to the same technology
• Consumers respond quickly to price changes
• Existing firms cannot respond quickly to entry by lowering their prices
• there are no sunk costs

Implications

• Threat of entry disciplines firms already in the market
• Incumbents (already existing firm in the market) have no market power over the consumer, even if there is only a single incumbent (a monopolist)

sunk costs

• sunk costs are retrospective (past) costs that have already been incurred and cannot be recovered. Sunk costs are sometimes contrasted with prospective costs, which are future costs that may be incurred or changed if an action is taken.
• Costi che non puoi recuperare uscendo dal mercato.
• A cost that is forever lost after it has been paid

simultaneous-move game

Game in which each player makes decisions without knowledge of the other players' decisions.

sequential-move game

Game in which one player makes a move after observing the other player's move.

one-shot game

the underlying game is played more than once.

repeate game

the underlaying game is played more than once.

GT: strategy

Decision rule that describes the actions a player wil take at each decision point.

normal-form game

A representation of a game indicating the players, their possible strategies, ad the payoffs resulting from alternative strategies.

simulateous-move, one shot games

• optimal strategy is only easy to determine, if there is a dominant strategy. If you have one, play it!
• In absence of a dominant scenario: 
• Use secure strategy. 
• Better: look at the game from your rival's perspective. If you rival has a dominant strategy, anticipate that he will play it.
• Managerial Application:
• Optimal Managerial decisions in a Bertrand oligopoly: each firm's best strategy is to charge a low price, regardless of the other firm's choice. The outcomeis that both firms charge low prices and earn profits of zero.
• Collusion would be that both firm agree to charge the higer prices in order to get more profit. But: Collusion is illegal in the USA; there is no incentive to keep the promise.
• Advertising and Quality decisions
• Coordination decision
• Not all games are games of conflict.
• Communication can help solve coordination problems.
• Sequential moves can help solve coordination problems.
• Examples:Industry standards (size of CDs) or National standards (electric current, traffic laws)
• Nash bargaining 
• generally there are multiple nash equilibria -> this leads to inefficiencies when the parties fail to coordinate on an equilibrium.

dominant strategy

A strategy that results in the highest payoff to a player regardless of the opponent's action

secure strategy

A strategy that guarantees the highest payoff given the worst possible scenario.

Has two shortcomings:

• It is a very conservative strategy and should be considered only if you have a good reason to be extremely averse to risk.
• It does not take into account the optimal decisions of your rival and thus may prevent you from earning a significant higher payoff.

Nash equilibrium

A condition describing a set of strategies in which no player can improve her payoff by unilaterally changing her own strategy, given the other players' strategies.

mixed (randomized) strategy

A strategy whereby a player randomizes over two or more avaiable actions in order to keep rivals from being able to predict his action.

Useful in games where no pure strategy Nash equilibrium exists.

infinitely repeated games

A game that is played over and over again forever and in which players receive payoffs during each play of the game.

trigger strategy

A strategy that is contigent on the past play of a game and in which some particular past action "triggers" a differnt action by aplayer.

Collusive outcome can be sustained in the infinitely repeated game with the following trigger strategy:"Cooperate provided no player ever cheated in the past. If any cheats, punish the player by choosing the one-shot Nash equilibrium strategy forever after"

extensive-form game

A representation of a game that summarizes the players, the information available to them at each stage, the strategies available to them, the sequence of moves, and the payoffs resulting from alternative strategies

subgame perfect equilibrium

A condition describing a set of strategies that consitutes a Nash equilibrium and allows no player to improve his own payoff at any stage of the game by changing strategies. It involves only credible threats.

prodction function

A function that defines the maximum amount of output that can be produced with a given set of inputs.

Q=F(K,L)

K= capital, L=Labour

fixed factors of production

The inputs the manager cannot adjust in the short run.

variable factors of production

The inputs a manager can adjust to alter production.

short run

The time frame in which there are fixed factors of production.

long run 

the horizon over which the manager can adjust all factors of production

total product

The maximum level of output that can be produced with a given amount of inputs.

average product

• A measure of the output produced per unit of input.
• AP=Q/LL
• APK=Q/K

marginal prduct

• The change in total output attributable to the last unit of an input.
• MP=ΔQ/ΔLL
• MPK=ΔQ/ΔK
• MP<0: the last unit of input reduced the total product

Marginal returns

• Ingreasing marginal returns: range of inoput usage over which marginal product increases.
• Decreasing (diminishing) marginal returns: range of inoput usage over which marginal product declines.
• Negative marginal returns: range of inoput usage over which marginal product is negative.[image]
• Principle: As the usage of an input increases, marginal roduct initially increases (increasing marginal returns), then begin to decline (decreasing marginal returns), and eventually becomes negative (negative marginal returns)

guiding the production process

Manager should ensure that:

• the firm operates on the production function
• Aligning incentives to induce maximum worker effort
• the firm uses the correct level of inputs (=firm operates at the right point on the production function)
• Principle: To maximize profits, a manager should use inputs at levels at which the marginal benefit equals the marginal cost, then:
• When labour or capital vary in the short run, a manager will hire
• labor until the value of marginal product of labour equals the wage: VMPL=P*MPL=w
• captial until the value of marginal product of capital equals the rental rate: VMPK=P*MPK=r

value maringal product

• The value of the output produced by the last unit of an input. 
• VMP=P*MPLL
• VMPK=P*MPK
• P=Prezzo a cui  puoi vendere l'aumento in output.

linear production function

• A production function that assumes a perfect linear relationship between all inputs  and total output.
• Capital and Labour are perfect substitutes
• Q=aK+bL
• MRTS=b/a

[image]

• Inbuts are substituted at constant rate, independent of the input levels employed.

Leontief production function

• A production function that assumes that inputs are used in fixed proportion.
• There is no input substitution along isoquants.
• Capital and Labour are perfect complements
• Q=min(bK,cL)
• There is no MRTS, because there is no substitution alon an isoquant.

[image]

Cobb-Douglas production function

• A production that assumes some degree of substitutability among inputs.
• Q=KLαβ
• Diminishing MRTS (meno usi di un input, più devi usare dell'altro per avere lo stesso output)[image]

Isoquant

• The combinations of input (K,L) that yield the producer the same level of output.
• The shape o an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.
• Move away from the origin = increasing output
• Move along isoquants = Substituting one input for another.
• For most production function relations, the isoquants lie somewhere between the perfect substitute and fixed-proportion cases -> rate of substitution will change along an isoquant.

Marginal rate of technical substitution MRTS

The rate at which two inputs are substituted while maintaining the same output level.

It corresponds to the absolute value of the slope of the isoquant.

MRTSKL=MPL/MPK

law of diminishing marginal rate of technical substitution

A peoperty of a function stating that as less of one input is used, increasing amounts of another input must be employed to produce the same level of output.

Isocost line

• A line that represents the combinations of inputs that will cost the producer the same amount of money.
• wL+rK=C <-> K=C/r-w/r*L[image]
• Isocost farther from origin = higher costs
• Changes in input prices = change in the slope

cost minimization

[image]

• The cost minimization happens where:
• slope of isoquants=slope of isocosts
• MRTSKL=w/r
• MPL/w=MPK/r
• Example: if MPL/w>MPK/r firm should substituting away from capital and toward labor.

Optimal input substitution

To minimize the cost of producing a given level of output, the firm shoul use less of an input and more of other inputs when an input's price rises.

[image]

cost function

The cost to the firm of producing isoquant Q: C(Q)

fixed costs FC

Costs that do not change with changes in output

include the costs of fixed inputs used in the production.

variable costs VC(Q)

Costs that change with changes in output

incude the costs of inputs that vary with output

short-run cost function

A function that defines the minimum possible cost of producing each output level when variable factors are employed in the cost-minimizing fashion.

total costs TC(Q) or C(Q)

C(Q)=FC+VC

[image]

average fixed cost AFC

Fixed costs divided by the number of units of output

AFC=FC/Q

average variable costs AVC

Variable costs divided by the number of units of ouput

AVC=VC(Q)/Q

Marignal (incremental) cost

The cost of producing an additional unit of output, that is the change attributable to the last unit of output.

MC=ΔC/ΔQ

average total cost ATC

ATC=C(Q)/Q=AVC+AFC

Relations among costs

[image]

MC intersects ATC abd AVC at their minimum points. This implies that when MC is above an AC, AC is rising.

Think at the grade -> if it is above the avarage grade it increases the average grade

ATC and AVC curves get closer together as output increases. This is because the only difference in ATC and AVC is AFC.

Irrelevance of sunk costs

A decision maker should ignore sunk costs to maximize profits or minimize losses.

cubic cost function

Costs are a cubic function of output: provides a reasonable approximation to virtualy any cost function.

C(Q)=f+aQ+bQ2+cQ3

f=fixed costs

long-run costs

In the long run all costs are variable, because the manager is free to adjust the levels of all inputs

long-run average cost curve LRAC

• A curve that defines the minimum average cost producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production.
• Is the lower envelope of all the short-run average cost curves.
• LRAC lies below every point on the short-run average curves, except that it equals each short-run average cost curve at the points where the short-run average curve uses fixed costs optimally.

Economies of scale

Exist when long-run average costs decline as output is increased.

Diseconomies of scale

Exist when long-run average costs rise as output is increased.

Constant returns to scale

Exist when long-run average costs remain constant as output is increased.

multiproduct cost function

A function that defines the cost of producing a given levels of two or more types of oututs assuming all inputs are use efficiently.

Quadratic Multi-Product cost function:

C(Q1,Q2)= f+aQ1Q2+bQ12+cQ22

economies of scope

When the total cost of producing two types of outputs together is less than the total cost of producing each type of output separately.

For example when producing the things separately would require duplication of many common factors of production.

C(Q1,0)+C(0,Q2) > C(Q1,Q2)

Quadratic Multi-Product cost function? Then f>aQ1Q2

cost complementarity

When the marginal cost of producing one type of output decreases when the output of another output increases.

ΔMC1(Q1,Q2)/ΔQ2<0

Example: cow hides (pellame) and steaks 

Quadratic Multi-Product cost function? Then a<0

Realistic and complex pricing

After acquiring a substitute product:

• raise price on both products to eliminate price competition between them.
• Raise price more on the low-margin (more price elastic demand) product.
• Reposition the products so that there is less substitutability between them

After acquiring a complementary product:

• reduce price on both products to increase demand for both products
• If fixed costs are lare relative to marginal costs, capacity is fixed, and MR>MR at capacity, then set price to fill available capacity
• If promotional expenditures make demand more elastic, then reduce price when you promote the product, and vice-versa.
• Psychological biases suggests “framing” price changes as gains rather than as losses.

mean (expected value)

The expected value or average of a random variable.

The sum of the probabilities that different outcomes will occur multiplied by the resulting payoffs

E[x] = q1 x1 + q2 x2 +...+qn xn

where xi is payoff i, qi is the probability that payoff i occurs, and q1+q2+...+qn = 1.

The mean provides information about the average value of a random variable and but yields no information about the degree of risk associated with the random variable.

variance

A measure of risk.

The sum of the probabilities that different outcomes will occur multiplied by the squared deviations from the mean of the random variable.

s2 = q1 (x1- E[x])2 + q2 (x2- E[x])2 +...+qn(xn- E[x])2

High variances (standard deviations) are associated with higher degrees of risk.

Standard Deviation

square root of the variance.

risk averse

Preferring a sure amount of $M to a risky prospect with a expected value of $M

risk loving

Preferring a risky prospect with an expected value of $M to sure amount of $M

risk neutral

Indifferent between a risky prospect with an expected value of $M and a sure amount of $M

Managerial decision wit risk-adverse consumers

Product quality

Managerial tactics to induce risk-adverse consumers to try a new product:

• Lower the price of the new product below that of the existing product to compensate the consumer for the risk associated with trying the new product.(Ex: send out free samples)
• Make the consumer think that the expected quality of the new product is higher than the certain quality of the old product -> with comparison advertising.

Chain Stores

Risk adversion explains why it may be in a firm's interest to become part of a chain store instead of remaining indipendent. Example: out-of-town visitors that tipically go eat an hamburger (standardized quality) instead of risk to try a local restaurant.

Insurance

The fact that the consumers are risk adverse implies that they are willing to pay to avoid risk. This is precisely why individuals choose to buy insurance on their homes and automobiles.

Some firms give insurance to costumers through "money-back guarantees". Other sell a form of insurance.

reservation price R

The price which a consumer is indifferent between purchaising at that price and searching for a lower price

The consumer's search rule

Assumptions (premesse):

Suppose consumers face numerous stores selling identical products, but charge different prices.

The consumer wants to purchase the product at the lowest possible price, but also incurs a cost, c, to acquire price information.

There is free recall and with replacement.

[image]

• The optimal search rule is such that the consumer rejects prices above the reservation price R and accepts prices below R. 
• Stated differently, the optimal search strategy is to search for a better price when a price charged by a firm is above R and stop searching when a price below R is found.
• Consumer will search until EB(R)=c. Where EB are the expected benefits and costs

Manager point of view:

When consumers have imperfect information about prices and search costs are low, the optimal prices set will be lower than when search costs are high.

Uncertainnty and the firm

Risk aversion

• risk neutral manager -> interested in maximizing expected profits; the variance of profits does not affect their decisions. Cares noly about the expected value without considering the underlaying risk. Shareholder want this type of managers (bcs they can diversificate by purchaising shares of many different firms).
• Risk averse manager -> accept the risky project with lower expected value if it has lower risk. They will prefer the sure thing when equal expected values.

Diversification

• By investing in mutiple projects, the manager my be able to reduce risk.

Producer Search

• Similar to consumers searching for stores charging low prices.

Profit maximization

• When demand is uncertain, expected profits are maximized at the point where expected marginal revenue equals marginal cost: E[MR] = MC.

asymmetric information

• A situation when some people have better information than others.
• The people with less information may decide not to participate to the market.
• Example: Insider trading = buying and selling of stocks by persons who have privileged information about a firm.
• Problems that can arise:
• adverse selection
• moral hazard

hidden characteristics

Things one party to a transaction knows about itself, but which are unknown by the other party.

hidden action

Actions taken by one party in a relationship that cannot be observed by the other party.

adverse selection

• Situation where individuals have hidden characteristics and in which a selection process results in a pool of individuals with undesirable characteristics.
• Examples:
• Choice of medical plans.
• High-interest loans.
• Auto insurance for drivers with bad records.

moral hazard

• Situation where one party to a contract takes a hidden action that benefits him or her at the expense of another party.
• Examples:
• The principal-agent problem; Insurance companies are vulnearble to the moral hazard.
• Care taken with rental cars.
• Possible solutions:
• Incentive contracts
• Signaling

Signaling

• Attempt by an informed party to send an observable indicator of his or her hidden characteristics to an uninformed party.
• To work, the signal must not be easily mimicked by other types. 
• Example: Education.

Screening

• Attempt by an uninformed party to sort individuals according to their characteristics.
• Often accomplished through a self-selection device
• A mechanism in which informed parties are presented with a set of options, and the options they choose reveals their hidden characteristics to an uninformed party.
•   Example: Price discrimination

Auction

Potential buyers compete for the right to own a good, servis or anything of value.

Types:

• English auction
• An ascending sequential bid auction.
• Bidders observe the bids of others and decide whether or not to increase the bid.
• The item is sold to the highest bidder.
• First-price, sealed-bid auction
• An auction whereby bidders simultaneously submit bids on pieces of paper.
• The item goes to the highest bidder.
• Bidders do not know the bids of other players.
• second-price, sealed-bid auction
• The same bidding process as a first-price, sealed-bid auction.
• However, the high bidder pays the amount bid by the 2nd highest bidder.
• Dutch auction
• A descending price auction.
• The auctioneer begins with a high asking price.
• The bid decreases until one bidder is willing to pay the quoted price.
• Strategically equivalent to a first-price, sealed-bid auction. That is the optimal bids by partecipant are identical for both types of auctions.

Information structures

• Perfect information
• Each bidder knows exactly the items worth.
• Independent private values
• Bidders know their own valuation of the item, but not other bidders’ valuations.
• Bidders’ valuations do not depend on those of other bidders.
• Affiliated (or correlated) value estimates
• Bidders do not know their own valuation of the item or the valuations of others.
• Bidders use their own information to form a value estimate.
• Value estimates are affiliated: the higher a bidder’s estimate, the more likely it is that other bidders also have high value estimates.
• Common values is the special case in which the true (but unknown) value of the item is the same for all bidders.

The optimal Bidding Strategy

• A player's optimal bidding strategy in an English auction with indipendent, private valuations is to remain active unitl the price exceeds his own valuation of the object.
• In a Second-price, sealed-bid auction with independent private values, a player's optimal strategy is to his own valuation of the item. In fact, this is a dominant strategy:
• You don’t pay your own bid, so bidding less than your value only increases the chance that you don’t win.
• If you bid more than your valuation, you risk buying the item for more than it is worth to you.
• In a first-price, sealed-bid auction with independent private values, a bidder's optimal strategy is to bid less than his valuation of the item. If there are n bidders who all perceive valuations to be evenly (or uniformly) distributed between a lowest possible valuation of L and a highest possible valuation of H, then the optimal bid for a player whose own valuaion is v is given by:
• b=v-(v-L)/n
• Correlated Value estimates
• Difficult to describe because
• Bidders do not know their own valuations of the item, let alone the valuations others.
• The auction process itself may reveal information about how much the other bidders value the object.
• Optimal bidding requires that players use any information gained during the auction to update their own value estimates.
• In a common-values auction, the winner is the bidder who is the most optimistic about the true value of the item.
• To avoid the winner's curse, a bidder should revise downward his or her private estimate of the value to account for this fact.
• The winner’s curse is most pronounced in sealed-bid auctions because players do not learn anything about the other players value estimates until it is too late to act on it.

winner's curse

The bad news conveyed to the winner that his estimate of the item's value exceeds the estimates of all other bidders.

Expected Revenues in Auctions with Risk Neutral Bidders

• Independent Private Values
• English = Second Price = First Price = Dutch.
• Affiliated Value Estimates
• English > Second Price > First Price = Dutch.
• Bids are more closely linked to other players information, which mitigates players’ concerns about the winner’s curse.