Question

Consider a perfectly competitive market where the market demand curve is p(q) = 1000-q. Suppose

there are 100 firms in the market each with a cost function c(q)
= q^{2} + 1.

(a) Determine the short-run equilibrium.

(b) Is each firm making a positive profit?

(c) Explain what will happen in the transition into the long-run equilibrium.

(d) Determine the long-run equilibrium.

Answer #1

Consider a perfectly competitive market where the market demand
curve is p(q) = 1000 − q. Suppose there are 100 firms in the market
each with a cost function c(q) = q2 + 1.
(a) Determine the short-run equilibrium. (b) Is each firm making
a positive profit?
(c) Explain what will happen in the transition into the long-run
equilibrium.
(d) Determine the long-run equilibrium.

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...

Suppose we have a perfectly competitive market where at the
equilibrium price the total market demand is 300 units. Each
individual firm in the market has a cost function C(Q) = 50 -2Q +
0.9Q^2. The number of firms this market can support in the long run
is _____?

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...

Suppose a firm operates in a perfectly competitive market where
every firm has the same cost function given by: C(q)=5q2+q+20
Suppose the market price changes. Below what price will this
firm shut down? (what is the "shut-down price").
Sandboxes are produced according to the following cost
function:
c(q) = q2 + 100
where the fixed cost of 100 represents an annual license fee the
firms pay. Every firm uses the same technology to produce sanboxes.
Recent trends have increased the...

Question 3
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...

The docking station industry is perfectly competitive. Each firm
producing the stations has long-run cost curve given by C = 400 +
20q + q2. (You may assume this is both the short-run and the
long-run cost curve.) The market demand is given by Q = 3000 – 25p.
The long-run equilibrium number of firms is _____.
(a) 20
(b) 60
(c) 75
(d) 45

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...

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)...

The docking station industry is perfectly competitive. Each firm
producing the stations has cost curve given by C = 400 + 20q + q2.
(You may assume this is both the short-run and the long-run cost
curve.) Currently, there are 50 firms producing the stations, and
the market demand is given by Q = 2000 – 25p. The long-run market
equilibrium price is?
(a) 20
(b) 60
(c) 80
(d) 40

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