Week 13 - Firm Costs and Competition

Production function (Cobb-Douglas)

Q = A·K^β·L^(1−β)

Total factor productivity

A -> measures productivity/technology level

Total revenue (price taker)

TR(Q) = P·Q

Marginal revenue (price taker)

MR = P

Profit function

π(Q) = TR(Q) − TC(Q)

First-order condition for profit maximization

P = MC(Q*)

Second-order condition for profit maximization

d²π/dQ² < 0

Shutdown condition (short run)

Produce if P ≥ AVC(Q*)

Exit condition (long run)

Produce if P ≥ ATC(Q*)

Cost-minimization condition

MRTS = W/R

Returns to scale in Cobb-Douglas cost

Linear in Q ⇒ constant returns to scale

Competitive firm optimal output

Choose Q where P = MC(Q)

Long-run competitive equilibrium

P = minimum long-run ATC