Question

2. Consider a competitive industry in which the market demand for the product is expressed as: P = 164 - 0.0002Q, and the industry supply of the product is expressed as:

P = 4 + 0:0003Q. The typical firm in this market has a marginal cost of MC = 4 + 1.2q

(a) Determine the equilibrium market price and output. Calculate the consumer surplus and the producer surplus at equilibrium in the industry.

(b) Determine the output of a typical firm in this industry, given your answer to part (a) above. How many firms are there in the industry?

(c) If the industry demand were to increase to P = 172 - 0.0002Q, what would the new price and output in the industry be in the short-run? What would the new output for a typical firm be? (Do not round up your answer.)

(d) If the original supply and demand (given before part a for this question) represented a long-run equilibrium condition in the market (assuming constant cost industry), would the new equilibrium in part (c) represent a new long-run equilibrium for the typical firm? Explain.

(e) Suppose the only long-run adjustment is free entry or exit of firms. To be in the long-run equilibrium with the new increased demand, how many firms would enter into or leave from the industry

Answer 1

a) The demand function of the product is P = 164-0.0002Q and supply function of industry is P =4+0.0003Q

In equilibrium, market demand = market supply which means

164-0.0002Q = 4+ 0.0003Q or , 0.0005Q = 160 or Q = 320,000

and P = 4 +0.0003*320,000 = 100

Therefore equilibrium quantity is 320,000 and equilibrium price is 100

Also total revenue or TR of industry is ,

PQ = 164Q-0.0002Q² and

marginal revenue of the firm is d(PQ)/dQ = 164-2*0.0002Q (taking derivative of either side)

                                                            = 164-0.0004Q = 164-0.0004*320000=36

Under equilibrium condition,

Marginal Revenue = Marginal cost= Average price

   Therefore consumer surplus is = Equilibrium price of the commodity- Average price of the product = 100-36 = 64

Also from supply function, we have total revenue

is PQ = 4Q +0.0003Q²

Therefore, marginal revenue is d(PQ)/dQ = 4 +0.0006Q= 4+ 192 = 196

Under equilibrium condition, marginal revenue = marginal cost = average cost

Therefore, supply price of the product is $196         

Therefore, producer surplus =   Equilibrium price of the product- Actual supply price of the product = 100-196 = -96

b) From a) supply function, we get marginal revenue = 196, Under equilibrium condition,

marginal revenue = marginal cost

or 4+1.2q = 196 or q = 192/1.2= 160

c) If demand function is changed to P= 172-0.0002Q then under equilibrium condition,

   market demand = market supply or

172-0.0002Q = 4+ 0.0003Q or, 0.0005Q = 168 or Q = 336000 which is equilibrium quantity

and equilibrium price is P= 4 +0.0003*336000 = 4+100.8 = 104.8

Also total revenue of industry from supply function, is PQ = 4Q + 0.0003Q² and

marginal revenue of the industry is d(PQ)/dQ = 4 +0.0006Q = 4+ 0.0006*336000 = 4+211.6 = 215.6

Under equilibrium condition, marginal revenue = marginal cost

Also marginal cost is MC = 4+1.2q

Therefore, 4+1.2q = 215.6 or 1.2q = 211.6 or q = 168 therefore, output of a typical firm in the market is 168

d) Equilibrium condition in the market remains same both in short run and long run Also the change in equilibrium price and quantity applies to every firm or industry under perfect competition. Therefore, new equilibrium shown in c) represent typical firm also.

e) From supply function, we have P = 4+0.0003Q

Also total revenue in this case will be, PQ = 4Q+0.0003Q² Therefore marginal revenue will be = 4+0.0006Q= 4+0.0006*320000 = 196

Therefore, 4+1.2q = 196 or q = 192/1.2 = 160

Therefore, total number of firms operating with original demand = original equilibrium quantity/output of typical firm= 320000/160 = 2000

Also total number of firms operating with increased demand = 336000/168 = 2000

therefore number of firms in industry will remain unchanged even with increased market demand.