The firm A&B produces high-quality widgets with a cost equal to C(qi) = 2qi. The

Question

The firm A&B produces high-quality widgets with a cost equal to C(qi) = 2qi. The demand for widgets

isQD =100P.

(a) Suppose the firm A&B is a monopolist. What is the profit-maximizing price and quantity? How

much profit does the firm collect?

(b) How much consumer surplus does the firm generate? What is the deadweight loss?

(c) Suppose consumers cannot see the differences between high- and low-quality widgets before pur- chasing them. What is the quantity sold by firm A&B if the price of low-quality widgets is $1?

(d) Suppose consumers cannot get any utility of low-quality widgets. Therefore, if they were aware and could distinguish between high- and low-quality widgets, they would purchase the high-quality widgets, regardless of the price of the low-quality widgets. How much is the firm A&B willing to pay to inform consumers about the differences between high- and low-quality widgets? How can the firm A&B achieve that?

Explanation / Answer

Ans)

QD =100P     => P = 100 - QD

Revenue, TR =(100 X QD ) - QD2

MR = d(TR) / d(QD ) = 100 – 2* QD

MC = 2

Equating MR and MC to determine the profit maximizing quantity

100 – 2* QD = 2

QD = 49

=>P =100 – 49 = 51

Profit, = PQ – 2Q

= 51*49 – 2*49

= 2401

b)

Consumer Surplus is equal to the one-half times the profit maximizing quantity, 49, times the difference between the demand intercept (the maximum price anyone is willing to pay) and the monopoly price.

CS = 0.5 X 49 X (100 – 51) = 1200.50

To calculate Dead Weight Loss, we first need Q where P =MC

100 - QD = 2

QD = 98

=>P= 2

The DWL is equal to the area below the demand curve, above the marginal cost curve, and between the quantities of 49 & 98, i.e,

DWL = [(51 – 2) X (98 – 49) ] / 2

DWL = 1200.50

c)

If the consumers cannot distinguish between the high & low quality widgets then the firms can only sell its product if it sets a price smaller or equal than $1. But since the Marginal cost is $2, there is no incentive for the firms to produce, hence the quantity sold is zero.

d)

A firm can earn a profit of $2401, if the consumers can understand the difference between high and low-quality widgets, otherwise the firm earns a profit of zero.So, the firms are willing to pay $2401 to inform the consumers about this difference. The firms can achieve this through advertising.

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