Question

Use the information below to answer the following questions. The information in the table below depicts the total demand for premium channel digital cable TV subscriptions in a small urban market. Assume that each digital cable TV operator pays a fixed cost of $100,000 (per year) to provide premium digital channels in the market area and that the marginal cost of providing the premium channel service to a household is zero. Table 16-1 Quantity 0 3,000 6,000 9,000 12,000 15,000 18,000 Price (per year) $120 $100 $ 80 $ 60 $ 40 $ 20 $ 0

Answer 1

1. The table below has been expanded to fill revenue, cost and profit (in case of 1 player). Explanation follows

Quantity 0 3000 6000 9000 Price 120 100 Revenue 0 300000 Profit -100000 200000 80 380000 480000 540000 Cost 100000 100000 100000 100000 100000 100000 100000 60 440000 380000 12000 40 480000 15000 20 200000 300000 0 18000 0 - 100000

Revenue is price*quantity
Cost is fixed at 100000
Profit is revenue-cost.

As we can see, profit is maximum when quantity=9000 and price is $60.

Hence option B ($60) is correct.

2. The same table, but now in case of 2 players, is shown below.

Quantity 0 3000 6000 9000 Price 120 100 Profit -200000 Revenue 0 300000 480000 540000 100000 80 Cost 200000 200000 200000 200000 200000 200000 200000 280000 340000 60 12000 40 480000 280000 15000 20 100000 300000 0 18000 0 -200000

As we can see, now also the profit is being maximized at price 60 and quantity 9000. So,

Option B is correct.

3. The total profit, as shown in part B, is 340000. So, each will make

340000/2=170000.

Hence, option A is correct.

4. If the channels are not able to collude, it means both will try to maximize their individual profit. They will keep trying to increase their profit until such a situation arises where neither can move from current situation and improve their profit (nash equilibria). Lets see how this will happen.

This will happen at a point where none of them can increase their profit by moving.

Lets say both firms are at price 100 initially, The total profit is 100000 and both get 50000. Now one firm drops the price to 80. The firm now gets 380000 and the other gets zero. So the other will also move there and both will get 140000. Then again one of them has an incentive of moving to 60 as there that firm will get 440000, but then the other firm will also move there and both will get 140000. This keeps happening till price is 40 and quantity is 12000. At this price there is ni point in going to 20 as then the profits for each will drop. So this point is the Nash equilibria.

Hence, correct answer is D-12000.

5. As already shown in part 4, the price will be 40, Hence, correct option is A-40.