Download 1. A competitive industry is in long run equilibrium

1. A competitive industry is in long run equilibrium when a government
introduces a tax of $t per unit. Which of the following statements is
correct? Explain.
(a) The price will increase in the short run but return to its previous
level in the long run.
(b) The number of firms will fall in the long run.
(c) Price will only increase if demand elasticity is less than one.
2. In a competitive industry, there is a set of firms which produce at constant
marginal cost of 10/c per unit and zero fixed costs. The total capacity of
this group of firms is 1000 units. There is another set of firms, with
marginal cost of 20/c per unit and total capacity of 2000 units. For this
group of firms, when producing at their full capacity the average cost is
30/c per unit. The industry is originally at its long run equilibrium.
(a) Draw the long run supply curve of this industry and the short run
supply curve assuming all firms are active.
(b) After a fall in demand, there has been an initial price reduction in
the short run, followed by a price increase in the long run. Draw
demand curves before and after the fall in demand that would lead
to this situation. Explain.
(c) Consider again the initial situation and suppose the low cost firms
discover extra capacity (e.g. new oil wells) at the same marginal cost
of 10/c per unit and that in the short run this lead to a reduction
in price but in the long run the price returned to its previous level.
Draw a picture for the supply function of this industry prior and
after the change and the demand function that would explain this
situation.
3. Consider a competitive industry where all firms are identical with cost
function:
C = 200 + q2 + 10q.
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Market demand is given by:
p = 55 − Q/20
where Q denotes total industry output.
(a) Find the long run equilibrium (price, quantity and number of firms.)
(b) Suppose now the government introduces a regulation that limits the
size of firms to no more than 10 units. Will there be exit or entry of
firms? Find the new long run equilibrium.
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(c) Suppose instead that the government introduces a regulation that
forces firms to produce
no less
than 40 units. Will there be exit or
entry of firms? Find the new long run equilibrium.
(d) Compare welfare in the above two cases.
4. In the petroleum industry, extraction costs depend on the geological characteristics of oil tracts. Those tracts that are closer to the surface have
lower extraction costs than the deeper ones. Suppose there are three type
of tracts with costs of extraction c1 < c2 < c3 and annual capacity of
production q1 , q2 and q3 , respectively. There are 1000 firms of each type
which can produce up to the given capacity at the corresponding marginal
cost.
(a) Graph the aggregate supply function of the industry.
(b) Draw two demand curves that illustrate the following situation:
de-
(c) Draw two demand curves that illustrate the following situation:
de-
mand has decreased but price has not changed.
mand has decreased but total quantity has not changed.
5. An industry has two types of firms with the following cost functions:
C1
C2
2
= q2 + 50
2
= q2 + 100.
Suppose there is a total of 100 firms of type
of potential entrants of type
2.
1 and an unilimited number
(a) Graph the long run supply function for this industry.
(b) Suppose total demand is:
α
(100 − 20p) .
Calculate long run equilibrium prices for the following cases:
1, 2, 4, 6.
α =
(c) For each of the above cases, calculate the rents (excess profits) obtained by low cost firms.
6. In a competitive industry, each firm produces at constant marginal cost
c = 10 up to a capacity q̄ = 10 and cannot produce more than that.
Suppose in addition there is a fixed cost F = 100.
(a) What is the long run equilibrium price?
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(b) Suppose that due to a government regulation that limits the number of firms to 100 the equilibrium price is 40. What will the total
quantity demanded be? How much profits will the firms make? If
the interest rate is 10% and firms could sell a license to potential
entrants, how much would theses licenses sell for?
(c) Now suppose the government is considering increasing the allowed
number of firms by 10%. Due to firm lobbying, the government has
agreed that it will compensate firms exactly to offset their capital
losses. How much should the government pay each firm?
(d) If the restriction on entry where totally eliminated, how many firms
would enter the market?
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