ProblemSet_PerfectCompetition_Solutions

ECO204Y1 Y LEC0301/0401 Tutorial (2023-24) Perfect Competition (h) Find Minnie’s short-run supply curve. Solution: In the short run, Minnie produces as long as MC ≥ AV C . Her short- run supply curve is equal to MC ( Q ) from point F onward. (i) Find Minnie’s long-run supply curve. Solution: In the long run, Minnie produces as long as MC ≥ ATC . Her short-run supply curve is equal to MC ( Q ) from point E onward. Exercise 2 The canola oil industry is perfectly competitive. Every producer has the following long-run total cost function: C ( Q ) = 2 Q 3 − 15 Q 2 + 40 Q, where Q is measured in tons of canola oil. (a) Determine the long-run average total cost of producing canola oil. Solution: Recall that Average Cost = ATC ( Q ) = Total Cost Q Hence, the long-run average total cost of producing canola oil is: ATC ( Q ) = 2 Q 3 − 15 Q 2 +40 Q Q ATC ( Q ) = 2 Q 2 − 15 Q + 40 (b) What will the long-run equilibrium price of canola oil be? How many units of canola oil will each firm produce in the long run? 3

ECO204Y1 Y LEC0301/0401 Tutorial (2023-24) Perfect Competition P ( Q ) and P = MC horizontal line). We rearrange Q ( P ) to find P ( Q ) = √ 10 − Q and integrate from 0 to Q ∗ . We get: CS = (area under demand curve between 0 and Q ∗ ) − (area under P = MC horizontal line between 0 and Q ∗ ) (1) CS = Z Q ∗ 0 ( P D ( Q ) − P ∗ ) dQ − Z Q ∗ 0 ( P ∗ ) dQ = Z Q ∗ 0 ( P D ( Q ) − P ∗ ) dQ = Z 6 0 ( p 10 − Q − 2) dQ = − 2 3 (10 − Q ) 3 2 − 2 Q 6 0 = − 2 3 (10 − 6) 3 2 − 12 − − 2 3 (10 − 0) 3 2 − 0 = 1 3 20 √ 10 − 52 ≈ 3 . 75 (b) How would your answer change if the production function was Q ( L ) = L − 1? Solution: As before, rearrange Q ( L ) to get L ( Q ) = Q + 1 and solve for C ( Q ): C ( Q ) = W ∗ L ( Q ) = 1 ∗ ( Q + 1) = ( Q + 1) ATC ( Q ) = C ( Q ) Q = 1 + 1 Q MC are constant and ATC are decreasing such that 1 < 1 + 1 Q 6