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

1. Write up a producer’s cost function.

2. Determine a producer’s efficient scale of production,
Q^{e}. (Hint: We have that MC(Q^{e}) =
AC(Q^{e}), that is, at efficient scale it is necessarily
the case that marginal cost equals average cost).

3. Determine a single producer’s short run supply curve (that is, the optimal choice of output given output price, P in the situation where fixed costs are unavoidable).

4. Consider a situation where there are 10 producers in the market, all operating this technology. Determine the short run market supply curve.

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

6. 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).

7. 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?

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

9. Suppose as social planners, we dictate that all existing firms in the long run equilibrium must each produce one additional unit of the good relative to what they were already producing, which is then consumed by the consumers. We hold the number of firms in the market fixed. What happens to aggregate surplus?

I searched and found a similar problem to this with different equations for VC and FC here on Chegg Study. Please do not just copy and give me that as I noticed that the solution to the problem is incorrect. Thank you

Answer #1

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...

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...

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)....

Suppose that the market for some good is competitive and the
demand curve can be written as Qd= 200 - 4P and the supply curve
can be written as Qs= 20 + 2P
What is the equilibrium price and quantity in the market?
Suppose that every firm in the market has total costs which can
be expressed as TC= 8+10Q+5Q^2. What is the marginal
cost function of each firm?
How much will each firm produce?
How many firms are currently in...

Suppose a representative perfectly competitive firm has the
following cost function: TC = 100 + 5Q2. The short-run
market demand and supply are given by: QD = 600 - 40P
and QS = 20P. How many firms are in the market in the
short-run?

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

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...

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

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)...

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