A monopoly produces a good with a network externality at a constant marginal and

Question

A monopoly produces a good with a network externality at a constant marginal and average cost of c $3. In the first period, its inverse demand curve is p- 15-1Q. In the second period, its inverse demand curve is p 15-10 unless it sells at least Q-9 units n the first pe od lf it meets or exceeds this arge then the demand curve rotates out t sels imes as many un or any given price so that s inverse den and une s p-15- The monopoly knows that it can sell no output after the second period. The monopoly's objective is to maximize the sum of its profits over the two periods For what values of would the monopoly earn a higher two-period profit by setting a lower price in the first period? If is|greater than|1.15. (round your answer to two decima,places)

Explanation / Answer

Answer:

The Marginal Cost and Average cost are given are 3 . The Demand curve in the first period is

P = 15 – Q

Hence Marginal Revenue is

MR = 15 - 3Q

Equate the marginal Revenue with the Marginal Cost

15 – 3Q = 3

3Q = 12

Q = 4

At this level price is P = 15 – Q = 15 – 4 = 11

The profit in this period is

= (11 * 4 ) – (3 * 4)

= 32

If the monopoly has to sell 9 units in this period then Price

P = 15 – 9 = 6

Profit

= (6* 9 ) – (3*9) = 27

Profit is 27

However if the firm sells 9 units in the first period then demand curve for 2nd period is

P = 15 – Q/

MC = 15 – 3Q/

MR = MC

15 – 3Q/ = 3

12 = 3Q/

Q/ = 4

Q = 4

Price = 15 – Q/ = 15 – 4 = 11

Profit = (11 – 3) * 4

            = 32

Hence will affect the decision of whether the monopoly will lower the price in the first period

The monopoly will keep the lower prices in the first period if

32 >27

> 0.843

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