Joshua owns a small boat and catches lobster off the coast o

Joshua owns a small boat and catches lobster off the coast of Maine. His weekly cost function is T C(q) = 40 + 5q + 5q 2 . He sells his lobsters to the local wholesaler at the market price p (in dollars).

(a) Find Joshua’s short-run supply function for lobsters. (Hint in this case short-run marginal cost is the same as long-run marginal cost.)

(b) Find Joshua’s long-run supply function for lobsters.

(c) Find Joshua’s shutdown price and Joshua’s breakeven price (the price at which profit equals zero).

(d) Suppose the market price is $30, calculate his profit. What will Joshua do in the long run? Explain.

Solution

(a) Joshua’s short-run supply function for lobsters is his marginal cost function. MC = 5 + 10q. Since AVC = 5 + 5q

and it is minimum at AVC = 5, Supply function is MC = P = 5 + 10q or q = 0.1P - 0.5

(b) Joshua’s long-run supply function for lobsters is same as its short-run supply function at q = 0.1P - 0.5 because

in this case short-run marginal cost is the same as long-run marginal cost

(c) Joshua’s shutdown price is any price below 5 because the minimum price needed is its minimum AVC which is

$5. Joshua’s breakeven price is the price at which profit equals zero. Profit is 0 when P = ATC

This happens when P = mininum ATC

ATC = 40/q + 5 + 5q and its minimum when ATC \'(q) = 0

-40/q^2 + 5 = 0

q^2 = 8 and q = 2.82 and price = 40/2.82 + 5 + 5*2.82 = 33.28

(d) Suppose the market price is $30, his quantity is 2.82 and his profit (30 - 33.28)*2.82 = -9.25. Joshua will not

produce and leave in the long run because he is a incurring a loss.