Question

QUESTION 2 Suppose that a firm with market power wants to price discriminate and they decide to do so by offering quantity discounts. There are two groups of individuals in the market, males and females, with males having a more inelastic demand than females. The firm offers a price of $70 if males purchase 10 units and offers a price of $so if males purchase 50 units. These values are indicated on the graph below. Price 90 Demand Males 70 50 10 20 50 Quantity What consumer surplus do males gain by purchasing 10 units of the good for $502 b. What consumer surplus do males gain by purchasing 50 units of the good for $507 Hint: They will gain some consumer surplus but also lose some, so you should find the net gain: c. Is this quantity discount scheme incentive compatible (IC) for males? Type yes if it is IC or type no if it is not IC:

Answer 1

10 Qe А 70 B С 50 G 10. 20 50

A. If males purchase 10 units of the good for $50, then, the consumer surplus will be the area below the demand curve but above the price line at $50, at 10 units of quantity, i.e., (A + B)

Consumer Surplus (C.S.) = Area of (A + B)

C.S. = (1/2)*10*20 + (20*10)

= $(100 + 200)

= $300

B. If the males purchase 50 units of goods for $50, then some consumers who are purchasing till 20 units of goods will gain, however, consumers purchasing beyond 20 units of goods upto 50 units will actually loose in this scenario, as they have to pay more than their actual willingness to pay as per the given demand curve.

Gain in C.S. = Area (A + B + C)

= (1/2)*20*40

= $400

Loss in C.S. = Area of (G)

= (1/2)*30*50

= $750

Net Loss Consumer Surplus = Total Gain - Total Loss

= 400-750

= - $350

C. NO,

This discount scheme is not incentive compatible because the consumers are losing overall in the second case (b).