Question

typical perfect competitive firm in the coffee market is given by the The cost curve for a following 1284qi + 2q% TC The market demand curve for coffee is given by the following P 84 2q (a) i) Find the long ru and quantity, output for each firm, the number of firms in the industry and the level of producer and consumer surplus. Show your answer in a clear well-labelled diagram (ii) What is the value of own price elasticity of demand at the market equilibrium? Is demand elastic or inelastic? (5 marks) competitive equilibrium. That is, identify the equilibrium price n (b) i) Assume now that the government imposes a specific tax of 8 on sellers. Find the new market equilibrium. That is, identify the equilibrium price and quantity, output for each firm, the number of firms in the industry and the deadweight loss associated with the tax (ii) Show the outcome for individual firms in market equilibrium in a separate well labelled diagram (5 marks) well labelled diagram. Also, show the a

Answer 1

TC 128 4q+2q, P - 84 -2q

(a) (i) Each firm maximizes its profits as follows:

pq 128 4q 2q p-4 4q 0 q 4

In the long run, each firm makes zero profit. Substituting the value of quantity in the profit function:

4 0-p p 28 128 4 -2( p2 +8p- 1008 0 4 4 4.

At this price, each firm produces 6 units.

At this price, the market demand is:

28-84 2Q Q-28

Hence, there are 5 firms in the market with 4 producing 6 units each and one producing 4 units.

In the long run equilibrium, each firm makes zero profit, hence, producer surplus is zero.

Consumer surplus can be calculated using the following diagram of the demand curve and the equilibrium price:

-80 -60 40 20 40 60 0 20

Consumer surplus is the area below the demnd curve and above the price line. It is 1/2* 28 * (84 - 28) = 784

(ii) Price elasticity of demand is calculated as follows:

a P 28 e = dP 28 2 II l

Since the elasticity lies between 0 and -1, demand is inelastic.

(b) (i) Each firm maximizes its profits as follows:

Tp 128 4q 2q -8 p-4 4 0 q p-4 4

Substituting this value in the profit function and putting it equal to zero:

4 0-p)136 4 p 29.2 -2( p2 +8p- 1088 o 4 4 4.

At this price,each firm sells 6.3 units.

Demand at this price is:

29.2-84 20 Q-27.4

Hence, there are 5 firms in the market, with 4 selling 6.3 units each and one selling 2.2 units.

Deadweight loss is the loss of efficiency in the market due to the tax. It is: 1/2 * (28 - 27.4) * (29.2 - 28) = 0.36

(ii) The following image shows the output for individual firms at the calculated price

-80 -60 40 20 40 60 20

The upward sloping curve is the supply curve for individual firms.

Market equilibrium is illustrated in the following image:

-80 -60 40 (27.4, 29.2) 20 60 0 40 80 20