Question

2. A perfectly competitive market where the laws of demand and supply hold is in equilibrium. Answer the following questions.

a) Assume that more sellers enter this market. The price elasticity of demand is observed to be εQd,P = 3/2. What happens to the total expenditures incurred by consumers? Explain and illustrate the change occurring in those expenditures on a graph. 2

b) Suppose now that production costs increase in this market. The price elasticity of demand is still estimated to be εQd,P = 3/2. What happens to the total expenditures incurred by consumers? Explain and illustrate the change occurring in those expenditures on a graph.

c) Suppose finally that less buyers take part in this market. The price elasticity of supply is estimated to be εQs,P = 1/4. What happens to the total revenues earned by sellers? Explain and illustrate the change occurring in those revenues on a graph.

Answer 1

2.(a)

Solution:

The price elasticity of demand is = 3/2 =1.5 , indicates that the demand is highly elastic. If price drops (increases) by 1 % point then the demand will increase (decrease) by more than 1 % point.

If we consider the total expenditure of a consumer bt TE = price times the quantity , i.e. then we can take log on both sides and then take derivative, and obtain,

The equation (1) indicated that the change in the total expenditure of the consumer is the sum of the change in price and change in quantity demand .

When more sellers enter into the market when already the market is in equilibrium, then given the demand for the commodity, supply will increase. This then will reduce the price of the commodity, which means . And according to the elasticity of demand information, it is positive 3/2 means the demand is highly elastic and .

This indicates and and

therefore we can conclude , if the price drops by 1 % point, then demand will rise by more than 1 % point, as a result, the total expenditure (TE) will rise by more than 1 % point,

in the diagram E1 is the intitial competitive market equilibrium and D1 and S1 are the initial demand and supply. AT initial equilibrium the price and quantity are p1 and q1 respectively. As more sellers enter into the market the supply curve shifts to the right given the position of the demand curve, from S1 to S2, as result the new market equilibrium occurs at point E2 with new proce p2 and quantity q2. Note that the new price is p2 < p1 and the new quantity q2 >q1. This indicates that and .

In this diagram it is clear that as price drops from p1 to p2, the TE curve shifts down, but as demand rises from q1 to q2 the TE increases from A1 to A2.

2(b)

When production cost increases then the supply curve shifts up given then demand curve and , as a result the demand falls from q1 to q2 and price rises from p1 to p2. Since the elasticity of demand is 3 / 2 , the quantity demand will fall more than proportionately. As a result, the total expenditure will go down from A1 to A2.

2 (c)

The elasticity of supply is 1/4, this means if price rises (decreases) by 1 % point the quantity supply will rise(decrease) by less than 1 % point.

The total revenue (TR) can be expressed as -

To see the effect of less buyers in the market we can take log and then take derivatives on both sides,

The equation (2) indicated that the change in the total revenue of the seller is the sum of the change in price and change in quantity demand .

When more few buyer enter into the market and when already the market is in equilibrium, then given the supply for the commodity, demand will fall. This then will reduce the price of the commodity, which means . And according to the elasticity of supply information, it is positive 1/4 means the supply is highly inelastic and .

Therefore with few buyers both the price and quantity falls. As a result the total revenue (TR) will fall as well ,

Grphically, the initial equilibrium is at E1 and as few buyers take part, the demand shifts down from D1 to D2 given the position of the supply curve S1. New equilibrium is at E2. Price falls from p1 to p2 and demand also falls from q1 to q2 at equilibrium.

The total revenue curve shifts down from TR1 to TR2 and as demand falls from q1 to q2 the total revenue falls from A1 to A2.

Therefore we can conclude with the given elasticity of the supply 1/4 , with fewer buyers the revenue of the seller will fall.