Question

Suppose a monopoly firm can produce any level of output it wishes at constant marginal (and average) cost of GH¢5 per unit. Assume the monopoly sells its goods in two different markets separated by some distance. The demand curve in the first market is given by Q1 = 55 - P1.

The demand function in the second market is given by Q2 = 70 - 2P2

i. If the monopolist can maintain the separation between the two markets, what level of output should be produced in each market, and what price will prevail in each market? What are total profits in this situation?


ii. Assume that the monopolists follows the two-part tariffs pricing
[ T(q) = a + pq ] policy , what is the maximum entry fee that must be charged?

iii. How much profit will the firm make?

Answer 1

Solution:

Let $q_1$ and $q_2$ production volumes in the two indicated markets.

$$\begin{cases} {55-q_1=2(q_1+q_2)}\\{70-2q_2=2(q_1+q_2)} \end{cases}$$

$$\begin {cases} {3q_1+2q_2=55}\\{1q_1+4q_2=70} \end{cases}$$

$$\begin{cases} q_1=10\\q_2=12.5 \end{cases}$$

Then

$$\begin{cases} p_1=45\\p_2=29.25\end{cases}$$

$$Pr=45\times 10+29.25\times12.5 - (10+12.5)\times 5=703.125$$

If the monopolists follows the two-part tariffs pricing T(q) = a + pq policy then entrance fee a

$$a=(12.5-10)\times(45-29.25)=39.375$$

$$Pr=39,375+22.5\times45-22.5\times5=939.375$$