TC = FC + VC

ATC = TC/q

AFC = FC/q

AVC = VC/q

average cost is the slope of a ray from the origin to the cost curve

MC = ΔVC/Δq = ΔTC/Δq

marginal cost is the slope of the tangent line on either TC or VC

TC=FC+VC <-- short run

long run we have inputs: labor, capital and each has a cost

w-wage rate for labor

cost of labor is wL

r-rental rate for capital

cost of capital is rK

every combination of labor and capital on the isocost curve results in the same total cost

slope of curve is -(w/r)

Cost = rK + wL

Tangency condition:

slope of isocost curve (set)= slope of isoquant(quantity produced curve)

-(w/r) = -MRTS

-w/r = -MPL/MPk

w/r = MPl/MPk

substitute result of tangency condition into the production function for q

ex.) r = 15 w = 5

q = f(K,L) = K^(3/4)L^(1/4)

5/15 = derivative of f

plug result into f

(ΔC/C)/(Δq/q)

= MC(1/AC) = (MC/AC)

Eco < 1 - economies of scale

Eco > 1 diseconomies of scale

Economies of Scope

and

Product Transformation Curve

Production of 2 outputs (q,q2)

if concave, economies of scope

if convex, diseconomies of scope

advantage in producing goods jointly

Scope vs. Scale

scope is producing multiple(different) goods, scale is increasing the scale of production

1.) Price takers - many firms, no firm has a large market share (q/Q)

2.)Product Homogeniety - "standardized product" all firms produce an identical good to their competitors

3.) Free entry and exit - in the long run there exists no barriers to entering or exiting the industry

profit : ∏(q) = R(q) - C(q)

∏ - firm level profit

Profit Maximization occurs at MR = MC

(marginal revenue = marginal cost

aka when the slopes are equal, NOT when R = C

TR = P x q (price * quantity)

Average revenue(AR) = TR/q = P

MR = P

∏(q) = R(q) - C(q)

= (P*q) - C(q)[q/q])

= (P - (C(q)/q))*q

=(P-ATC(q))q

∏(q) = (P-ATC(q))q

P > ATC : profitable

P = ATC : break even (zero profit)

P < ATC : taking a loss(negative profit)

break even occurs where MC intersects ATC  

(remember P = MC) at minimum ATC

where ∏(q) = -FC

C(q) = FC + VC(q)

-FC = R(q) - (FC + VC(q))

= ....

P*q = (VC(q)/q) * q

P = VC(q)/q means 

P = AVC(q)

given of course that the firm is indifferent b/w producing and shutting down

P= MC - profit max q

p > ATC : + profit

P < ATC : -profit

AVC < P < ATC : loss in producing < FC

P < AVC : loss in producing > FC -> shut down

it is the MC curve above minimum AVC

firm supply curve: P = MC

market supply: n * MC

n = number of firms

the difference b/w price received and willingness to sell(marginal cost)

 PS = P - MC for each q

meaning with some calculus, 

PS = [P - AVC(q*)]q*

∏(q*) = PS(q*) - FC

in the long run, entering and exiting are available to firms

if ∏ >0 there will be entry

if ∏ < 0 , there will be exits

at long run equilibrium, ∏ = 0, P = ATC, P = MC, ATC = MC

PS = (P-AVC)q

∏ = PS- FC

PS = ∏ + FC

Remember, 1.) All costs are variable (TC = VC = C)

2.) Free Entry and Exit

firm at first produces Qsr at P0, but then in the long run, the firm expands production (increase in q) to Qlr (still P0). The existence of profits will cause the industry to expand however, driving the price down to p1, along the LMC curve and LAC curve until MC = AC. 

Prices fall until entry stops. This occurs at zero profit ∏ = MC = AC

what happens when firms have different costs?

the area difference between Plr and Potherfirm = economic rent.

suppose there are N firms in the market

"other firm's" profits = TR - VC - FC - Economic rent = 0

∏ = PS - FC  <-short run

in long run, no fixed costs

∏ = PS, in LR equilibrium PS = 0

in the presence of rents we have the added OPPORTUNITY COST of rent.

∏ = R(q) - C(q) - rent

= R(q) - VC - FC - rent 

remember PS = R(q) - VC

∏ = PS-rent   in LR Eq. ∏ = 0

PS = Rent