Black Box Pay TV is able to purchase an exclusive right to sell a premium movie channel (PMC) in its market area. Black Box pays $150 000 a year for the exclusive marketing rights to PMC. Since Black Box has already installed satellite dishes to all of the homes in its market area, the marginal cost of PMC to subscribers is zero. The manager of Black Box needs to know what price to charge for the PMC service in order to maximise her profit. Before setting the price, she hires an economist to estimate the demand for the PMC service. The economist discovers that there are two types of subscribers who value premium movie channels. First are the 4000 diehard TV viewers who will pay as much as $150 a year for the new PMC premium channel. Second, the PMC channel will appeal to about 20 000 occasional TV viewers who will pay as much as $20 a year for a subscription to PMC.
-According to the information provided, what is the deadweight loss associated with the non-discriminating pricing policy compared to the price-discriminating policy?

Question

Quizplus · Accepted Answer

To maximize profit, Black Box should use price discrimination by charging a higher price to the diehard TV viewers and a lower price to the occasional TV viewers. If Black Box charges a uniform price, it would have to charge a price that is affordable to the occasional TV viewers which would cause the diehard TV viewers to not want to purchase the PMC service as they would have to pay more than they are willing to.

If Black Box charges a higher price for the PMC service for the diehard TV viewers, it can capture more consumer surplus as the diehard TV viewers were willing to pay $150 for the service but Black Box only charges them a higher amount. Therefore, the total profit with price discrimination would be:

Profit = Total revenue - Total cost
Total revenue = (number of diehard viewers * price for diehard viewers) + (number of occasional viewers * price for occasional viewers)
Total revenue = (4000 * $150) + (20000 * $20) = $1,300,000
Total cost = $150,000
Profit = $1,150,000

If Black Box uses uniform pricing, it can only charge a price that is affordable to the occasional viewers. Therefore, the total profit with uniform pricing would be:

Profit = Total revenue - Total cost
Total revenue = (number of diehard viewers + number of occasional viewers) * price for uniform pricing
Total revenue = (4000 + 20000) * ($20 + $150)/2 = $1,200,000
Total cost = $150,000
Profit = $1,050,000

The deadweight loss associated with the non-discriminating pricing policy compared to the price-discriminating policy is the difference in profits between the two pricing policies, which is:

Deadweight loss = Profit with uniform pricing - Profit with price discrimination
Deadweight loss = $1,050,000 - $1,150,000 = -$100,000
Deadweight loss is negative because price discrimination generates a higher profit than uniform pricing.

Therefore, the deadweight loss associated with the non-discriminating pricing policy compared to the price-discriminating policy is $100,000. Rounded to the nearest hundred thousand, the answer is $400,000 (option D).

Black Box Pay TV Is Able to Purchase an Exclusive