Question

Consider the following model for the production of refined oil:

MSC = 10+0.5Q, MEC = 0.3Q, MSB = 30-0.3Q, MEB = 0

a. Based on the model, what are the price and quantity at the efficient equilibrium?

b. What is the firm's marginal profit at the efficient equilibrium quantity?

c. What is the firm's marginal profit at the competitive equilibrium quantity?

Answer 1

For socially efficient output: MSC=MSB

For competitive equilibrium output: MPC=MPB where MPC= MSC-MEC= 10+0.2Q and MPB= MSB-MEB= 30-0.3Q

Therefore socially efficient output,

10+0.5Q=30-0.3Q

Q=25 and P= 10+0.5*25= 22.5

and competitive equlibrium output.

10+0.2Q=30-0.3Q

Q=40 and P= 18

Marginal Profit for firm = marginal private benefit- marginal private cost

Case 1: efficient equilibrium

marginal profir for firm( at efficient quantity Q= 25)= 30-0.3Q-10-0.2Q= 20-0.5Q=8.5 ---- Positive marginal profit as expected

Case 2: competitive equlibrium

marginal profir for firm( at competitive quantity Q= 40)= 30-0.3Q-10-0.2Q= 20-0.5Q=0 ----- Zero marginal profit in competitve structure as expected

Good luck!!

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