monopoly practice problems

8/10/2019 Monopoly Practice Problems

1/4

Microeconomics I

Assignment 3

Due on: October 20, 2014 (before 2:30 PM)To be submitted to Mr. Manhar (TA)

1. Suppose there is only one farmer in a village who owns all the available land andproduces rice for the entire local market. His total costs are given by T C = 5Q . The

market demand curve for rice is p = 25 Q . The farmer is free to decide the selling

price and quantity of rice.

(a) Determine the prot maximizing levels of price and quantity. Also, calculate

prots at this output.

(b) Calculate social welfare.

Now government carries out a radical land reform as a result of which almost every-

body in this village becomes a producer of rice. However, there is only one unlucky

villager who could not be provided with land (due to limited availability) and has no

choice but to remain a buyer, luckily the only one in the market. But our egalitarian

government compensates him with a good amount of money. The money is so good

that a strong income effect raises his individual demand curve to the level of previous

market demand curve.

So in effect, the village market faces the same market demand as before, but with

only one buyer and many identical producers whose cost conditions are given by

T C = 5Q .

The buyer being the only one, enjoys the power to decide the buying price and

quantity and his objective is to attain maximum consumer surplus.


2/4

IGIDR 2014 Microeconomics I, Assignment 3

(c) Determine the optimal price and quantity for the entire market.

(d) Calculate social welfare and comment on the efficiency of this market.

4+3+4+4=15

2. There are two consumers who have utility functions

u 1(q 1, m 1) = 10x1 + m 1

u2(q 2, m 2) = 5x2 + m 2

The price of the m-good is one, and each consumer has a large initial wealth. Both

goods can only be consumed in non-negative amounts.

A monopolist supplies the q -good. The monopolist knows that the consumers are

of two different types, and type A has the utility function u1(.) and type B has the

utility function u2(.). However, the monopolist does not know who is of which type.

The monopolists cost function is as follows.

C (q ) =0 if q 10

if q > 10

Solve the monopolists prot maximization problem. Illustrate your answer graphi-

cally.

10

3. Consider the following. There is one rm, rm 1. There are two markets, market 1

and market 2. Firm 1 is the monopolist in both market 1 market 2. Let x and y

denote, respectively, output of rm 1 in market 1 and output of rm 1 in market 2.

The demand is innitely elastic in market 1 at p1 = 50 and the inverse demand in

market 2 is p2 = 200 y. Cost function of rm 1 is given by C 1 = (x + y ) 2

2 + F , where

F is the xed cost.

Page 2 of 4


3/4


Suppose that the government intervenes in market 1, which raises the price in market

1 to 55.

(a) Will rm 1 like such intervention?

(b) Will your answer to (a) change, if rm 1s cost function was C 1 = cx + ( d

x )y + F , where > 0?

(c) Illustrate your answers graphically.

Now, suppose that rm 1 can supply any amount of output in market 2 at price

p2 = 50 or less. However, no rm can sell a positive amount of output in market 2

at a price higher than p2 = 50.

(d) Will your answer to (a) change? Why or why not?

(e) Will your answer to (b) change? Why or why not?

8+8+3+8+8=35

4. Suppose that there is a rm, called rm 1, which is the only producer of the (perish-

able, i.e. non-durable) good x . Firm 1 survives for two periods and aims to maximize

its prot. The prevailing rate of interest is r .

The production technology of rm 1 exhibits constant returns to scale and there is no

xed cost of production. Further, rm 1s production technology remains the same

in both periods.

Market demand functions in period 1 and period 2 are given by p1 = a q 1 and

p2 = a + bq 1 q 2, respectively, where a > b > 0 and q i denotes the quantity demanded

in period i (i = 1 , 2).

If rm 1 produces x1 amount in period 1, the government imposes tax/subsidy at

the rate tx 1 on its period 2s production.

Page 3 of 4


4/4


(a) For any given t, calculate rm 1s output decisions and equilibrium prices in

period 1 and period 2. Please specify the necessary parametric restrictions to

have meaningful solutions. Can you tell us the relation between t and b, if any?

(b) Suppose that the governments objective is the maximize social welfare. What

will be the optimal t?

(c) How will your answer to (b) change, if rm 1 is a foreign rm and the market

for the good is the domestic market?

(d) Will your answer to (b) change, if rm 1 is a domestic rm and sells its output

in a foreign countrys market?

10+10+10+10=40

Page 4 of 4

monopoly practice problems

Documents