The wholesale market for Gala apples is perfectly competitive
consisting of identical individual producers with cost function C =
200 + q2 where q is a firm’s number of crates of apples supplied.
The current market price is P = $50 per crate q. Market demand for
Gala apples is QD = 8,000 – 100P.
a. Find a typical firm’s supply function and the quantity a
supplier produces at the $50 price.
b. Find the market quantity demanded at price $50.
c. Calculate the profit/loss for a supplier and show
graphically the situation (for a firm and in the
market).
d. Explain how this market will adjust to a long-run
equilibrium. Find/calculate the long-run
equilibrium market price, quantity, and a firm’s profits.
(Assume market demand remains constant but that the number of
(identical) firms can increase/decrease, i.e., firms can enter/exit
the market.) Show the long-run equilibrium graphically for a firm
and in the market.
e. At the long-run equilibrium, how many firms exist in the
market and how much does each supply?
f. Show on producer surplus and consumer surplus on your
market graph above. Using these concepts, explain why we say that
the competitive market output maximizes the economic welfare of
suppliers and demanders.
(10 points) A firm’s production function is q = 10KL with per
unit input prices for labor w = 3 and
capital r = 2. Support your answers with a graph of
isoquant-isocosts.
a.
Calculatetheleast-costinputcombinationofLandKtoproduce60unitsofoutput.
b. Suppose the wage decreases to $2. How does this affect
input use holding constant output at 60? c. What are the total
costs of producing the two output levels in parts (a) and
(b)?