Question

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 is the supply function of each firm?

(c) If there are currently 100 firms producing the good, what is the market supply function? What is the short-run competitive equilibrium in this market with 100 firms? What is the profit of each firm?

(d) What is the long-run competitive equilibrium price and quantity in this market?

Answer #1

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)...

Competitive Market :
The market demand is Q = 2600-100P
there are 100 identical firms in the market, each with
Total cost TC = 0.25q^2 + 20q + 16
Marginal cost MC = 0.5q + 20
P = market price
Q = market output
q = output of individual firm
A. calculate the market equilibrium price and output.
B. Calculate a firm's profit or loss at the market
equilibrium

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.

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.

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...

The total cost function for each firm in a perfectly competitive
industry is TC(y)=100+8y^2 . Market demand is q=2000-(market price)
.
Find: the long run equilibrium firm quantity (y), market
quantity (q), amount of firms, and price.

Consider the market for good Q. The inverse demand function is
p(Q) = 24 – 2Q, where p denotes the price of good Q. The production
costs of the representative firm are C(Q) = 4Q. In addition,
production causes environmental damage of D(Q) = 12Q.
a) Determine the socially optimal output level Q*. Discuss the
optimality condition and illustrate your solution in a
diagram.
b) Assume that there is no government intervention. Calculate the
market equilibrium in the case of...

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....

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...

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