Answer to Question #143890 in Finance for Mr. Dinesh Pal Singh

Question

88. Culture Extravaganza produce ballets in Boston and New York. Monthly total revenue are given by
TRB = 1,000 QB0.5
and TRN = 2,000 QN0.5
where QB is the monthly number of Boston patrons and QN is the monthly number of New York ballet attendees. Salaries of the performers are based on attendance and the firm estimates that the marginal cost is $10 per attendee in each city.
i) If Culture Extravaganza attempts to practice third-degree price discrimination, what will be the profit-maximizing prices and rates of output in each city?
ii) Will the firm earn more profit using price discrimination than if a uniform price is set? Explain.

Answer 1

Let

$TRB =1000\times QB^{0.5}$

and

$TRN = 2000\times QN^{0.5}$

i)than the condition of profit maximization

$P=MR=MC$

$TRB = 1000\times QB^{0.5}$

$TRN = 2 000\times QN^{0.5}$

$(TRB)'= (1000QB^{0.5})'=\frac{500}{\sqrt{x}}$

$\frac{500}{\sqrt{x}}=10$

x=2500

$(TRN)'= (2000QB^{0.5})'=\frac{1000}{\sqrt{x}}$

$\frac{1000}{\sqrt{x}}=10$

x=10 000

ii)Marginal costs (MS) are constant. In each market, the monopolist firm, maximizing profit when MR = MS is equal, sets a higher price (RD at which the demand for its goods is less elastic.

The word "discrimination" has a negative connotation: it is perceived as a violation of rights. But in the third degree of price discrimination, buyers often participate consciously and voluntarily, for example, buying premium products (premium alcohol or niche perfume), paying for any VIP class services, a ticket to the premiere of a play, a new collection of clothing, new digital technology (another new iPhone model, which in six months will cost much cheaper). First, at a high price, the product is purchased by those for whom image and prestige are important. When the price goes down, it's the turn of people with less purchasing power. At the same time, the quality and configuration of the product remains the same. Thus, third-degree price discrimination helps to cover the market more widely.

Third-degree price discrimination leads to a partial capture of the consumer surplus by the seller.