Question

Consider a publicly available technology of producing a good that is characterized by the variable cost function VC(Q) = 1/2(Q^2) and fixed costs FC = 2 for a firm that operates the technology. In the short run, fixed costs are unavoidable. In the long run, fixed costs are avoidable and it is free for any firm outside of the market to enter, should it want to. In the short run, the set of firms in the market is fixed. The market demand curve is given by demand function, Q^D (P) = 40 − 20P

a) In short run market equilibrium, what is the equilibrium price and quantity? What is the profit level of each producer?

b) Suppose market demand increases to Q^D(P) = 120 − 20P . Determine the new short run competitive equilibrium (state the new equilibrium price, the aggregate quantity supplied and demanded, how much each producer is producing, and the profit level of each producer).

c) In the long run, there is free entry, and so the number of firms will adjust so that in the competitive equilibrium, firm profits are zero. Subject to the new demand function, what is the long run competitive equilibrium price level? How many firms are there in the market? How much is each firm producing?

d) In the long run equilibrium, calculate aggregate surplus. In addition calculate producer surplus and consumer surplus.

e) Suppose as social planners, we dictate that relative to the long run equilibrium, all firms must each produce one additional unit of the good, which is then consumed by the consumers. What happens to aggregate surplus?

Answer #1

Consider a publicly available technology of producing a good
that is characterized by the variable
cost function V C (Q) = 1 Q2 and fixed costs F C = 2 for a firm
that operates the technology. In 2
the short run, fixed costs are unavoidable. In the long run,
fixed costs are avoidable and it is free for any firm outside of
the market to enter, should it want to. In the short run, the set
of firms in...

Consider a publicly available technology of producing a good
that is characterized by the variable cost function VC (Q) =
(1/2)Q2 and fixed costs FC = 2 for a firm that operates
the technology. In the short run, fixed costs are unavoidable. In
the long run, fixed costs are avoidable and it is free for any firm
outside of the market to enter, should it want to. In the short
run, the set of firms in the market is fixed....

1). The market demand function for a good is given by Q = D(p) =
800 − 50p. For each firm that produces the good the total cost
function is TC(Q) = 4Q+( Q2/2) . Recall that this means
that the marginal cost is MC(Q) = 4 + Q. Assume that firms are
price takers.
(a) What is the efficient scale of production and the minimum of
average cost for each firm?
Hint: Graph the average cost curve first.
(b)...

Consider a perfectly competitive market with demand Q=1,000-4P.
The marginal cost for each firm in the market is constant at
MC=4.
Determine the competitive equilibrium price and quantity.
.
Graph demand, supply, and the equilibrium found in part A).
Determine consumer surplus, producer surplus, and total
surplus.
Is consumer surplus or producer surplus equal to zero? Why or
why not?
Is this question representative of a long or short-run
perfectly competitive market? How do you know?

The market demand function for a good is given by Q = D(p) = 800
− 50p. For each firm that produces the good the total cost function
is TC(Q) = 4Q+ Q^2/2 . Recall that this means that the marginal
cost is MC(Q) = 4 + Q. Assume that firms are price takers.
(a) What is the efficient scale of production and the minimum of
average cost for each firm? Hint: Graph the average cost curve
first.
(b) What...

Suppose that the technology to produce surfboards is according
to the cost function C(q) = 4 + 5q + .25q2 where 4 is the sunk
fixed cost firms have to incur to enter into this market. Market
demand for surfboards is given by: Q = 1550 - 10P. Surfboard
producers are price takers, in other words they take the market
price as given. a) Find a surfboard producer’s short-run supply
curve. (Hint: start with profit maximization of a single firm)....

The long run cost function for each (identical) firm in a
perfectly competitive market is C(q) =
q1.5 + 16q0.5 with long run
marginal cost given by LMC = 1.5q0.5 +
8q-0.5, where q is a firm’s
output. The market demand curve is Q = 1600 –
2p, where Q is the total output of all
firms and p is the price of output.
(a) Find the long run average cost curve for the firm. Find the
price of output and the amount of output...

3: For each (identical) firm in a perfectly competitive market
the long-run cost function is C(q) = q1.5 + 16q0.5 with long run
marginal cost being LMC = 1.5q0.5 + 8q-0.5, where q = firm’s
output. Market demand curve: Q = 1600 – 2p, where Q = total output
of all firms, and p = price of output. (a) For the firm find the
long run average cost curve , as well as the price of output and
the amount...

2. Suppose a representative firm producing in a perfectly
competitive industry has the following cost function: C(q) = q2 +
8q + 36 a. Solve for the firm’s average cost function. b. At what
level of q is average cost minimized (i.e. what is the minimum
efficient scale for the firm)? What is the value of average cost at
this level of q? c. Suppose all firms in this industry are
identical and the demand function for this industry is...

Given an aggregate demand function Q( p) = 54
− 2 p and a cost function for each firm of
C(q) = 3q^ 3+ 29. (Hint: we must
have q ≥ 0, so when you look at the roots, pick the non-
negative one.)
(a) Suppose there are 36 firms. Setup and solve the firm profit
maximization problem. Then solve for the price, quantity, and
profits for each individual firm and aggregate equilibrium
quantity, given that the number of firms...

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