Microeconomics Answers

1.     Assume the following for price discriminating monopolist aimed at maximizing profit. Total demand for the product of the monopolist is Q = 50-5P (P = 100-2Q)

·        Demand in Market one is Q1= 32-0.4P1(P1= 80-2.5Q1)

·        Demand in Market two is Q2= 18-0.1P2(P2= 180-10Q2)

·        Cost function is C = 50+40Q (where Q = Q1+ Q2)

a.      Find equilibrium quantities (Q1and Q2),

b.     Find equilibrium prices (P1and P2),

c.      Calculate profit (π),

d.     Calculate and Interpret elasticities (ε1 and ε2)

Suppose the inverse demand function for two Cournot dupolists is given by P= 10 – (Q1+Q2) and their cost are zero.

a) What is each firm marginal revenue?

b) What are the reaction function for the two firms

c) What are the Cournot equilibrium output

d) What is the equilibrium price?

The Cobb-Douglas production function is widely used in managerial economic and empirical analysis because it possesses several useful mathematical properties” As a manager of an organization, how you could apply Cobb-Douglas production function for decision making?

Mr. Kamal is an owner of the communication center at Y junction and uses four word processors and two typewriters to produce reports. The marginal product of a typewriter is 50 pages per day, and the marginal product of a word processor is 500 pages per day. The rental price of a typewriter is Rs.1 per day, whereas the rental price of a word processor is Rs.50 per day. Is Mr. Kamal utilizing type writers and word processors in a cost-minimizing manner? Which service process is more profitable? Type writer or word processing? Justify your answer.

Given the following data on output and inputs for ten production period

Production period Output (Q) Capital (K) Labour (L)

1 225 10 20

2 240 12 22

3 278 10 26

4 212 14 18

5 199 12 16

6 297 16 24

7 242 16 20

8 155 10 14

9 215 8 20

10 160 8 14

1. Estimate the parameters (A, α and β) of a Cobb-Douglas production function using the least squares regression method.

2. Use estimated parameters to determine (a) returns to scale and (b) factor intensity

3. Determine elasticity of labour and elasticity of capital

4. Measure marginal product of labour and capital for the input combination (L=20 and k=30)

5. Construct the equation for isoquant and graph the isoquant assuming output is 100 units and L = 2,4,6,8,10,12,14.16 and 18.

Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring it's marginal rate of technical substitution is 0.15 ( in absolute value). To hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In the study of production process and markets where capital is procured, suppose that Mitsubishi determine that its marginal productivity of capital is 0.5 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study

indicates that the average selling price of Mitsubishi’s smallest car is US$ 9500. Determine the rate at which Mitsubishi can rent capital and marginal productivity of labour at its new targeted level of output. To minimize costs Mitsubishi should hire capital and labour until the marginal rate of technical substitution reaches what proportion?

The water Economist has estimated short run water responsiveness function for rice farming under major irrigation condition in the Dry Zone of Sri Lanka as follows;

Y = 21W +30.3W2 – 3W3, Where Y = Output (paddy kg /Acre) , W = irrigation Water (Cubic Meter – m3)

a) Determine three stages of this short run production process and graphically show the result.

b) Determine rational production stage and what is the maximum and minimum output level of this rational stage.

c) Determine the range of water level which is representing the low of diminishing marginal returns.