Question

In: Economics

Consider a competitive market for desk lamps. The demand in this market is D(P)=160-10P. There are...

Consider a competitive market for desk lamps. The demand in this market is D(P)=160-10P.

There are five firms in this market currently, each with cost function C(q)=q2/6 +24. Each firm acts competitively.

(i) What is the short-run market supply?
(ii) What is the short-run equilibrium in this market in terms of total quantity and price?

How much profit does each firm make? What is the consumer surplus?

(iii) Now suppose that free trade with the rest of the world has been allowed. The number of domestic firms is still 5. In the world market, the same desk lamps are available at price $3. What is the total quantity that consumers purchase, the quantity supplied by each domestic firm in the short-run and amount of imports? What is the consumer surplus under free trade?

(iv) Now, suppose again that there is no trade with the rest of the world.
Suppose that this is a ``constant cost’’ industry. What it the long-run equilibrium price in this market? How many firms will be in the market in the long-run equilibrium and how much will each supply?

Expert Solution

Consider a competitive market for desk lamps. The demand in this market is D(P)=160 - 10P.

There are five firms in this market currently, each with cost function C(q) = q2/6 +24. Each firm acts competitively.

(i) What is the short-run market supply?

MC = 2q/6 = q/3

q = 3MC or q = 3P. Market supply Qs = nq = 5*3P = 15P.
(ii) What is the short-run equilibrium in this market in terms of total quantity and price?

Qs = Qd

15P = 160 - 10P

P = 160/25 = 6.4 and market quantity = 15*6.4 = 96

How much profit does each firm make? What is the consumer surplus?

Each firm produces 96/5 = 19.2 units and profits are TR - TC = 19.2*6.4 - (19.2^2)/6 -24 = 37.44

(iii) Now suppose that free trade with the rest of the world has been allowed. The number of domestic firms is still 5. In the world market, the same desk lamps are available at price $3. What is the total quantity that consumers purchase,

Q = 160 - 10*3 = 130 units

the quantity supplied by each domestic firm in the short-run is q = 3P = 3*3 = 9 units

and amount of imports = 130 - 9*5 = 85 units.

What is the consumer surplus under free trade?

CS = 0.5*(16 - 3)*130 = 845

(iv) Now, suppose again that there is no trade with the rest of the world. Suppose that this is a ``constant cost’’ industry. What it the long-run equilibrium price in this market

The price is = AC = MC

(q2/6 +24)/q = q/3

q/6 + 24/q = q/3

24/q = q/6

q = 12 units

Long run price P = 12/3 = $4.

How many firms will be in the market in the long-run equilibrium

Market quantity in long run Q = 160 - 10*4 = 120 units

each firm will supply 12 units so there will be 10 firms in the long run to produce a total of 120 units.

Rahul Sunny answered 2 years ago

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