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Q1. A firm faces the following AR (demand) curve:

P=120-0.02Q

Where Q is the weekly production and P is the price measured in rupees per unit.

The firms cost function is given by C=60Q+ 25000.Assume that the firm maximizes profits.

What is the level of production, price and profit per week? (5)

Answer:

P=120-0.02Q

PQ = 120Q- 0.02Q^2 =TR

MR=120-0.04Q

TC= 60Q+25000

MC= 60

Profit maximized at MR=MC

120-0.04Q=60

Q= 60/0.04 = 1500

Therefore, P= 90.

Profit = TR-TC

= 60Q-0.02Q^2-25000

= 20000

Q2. A monopolist faces a demand curve P=11-Q, where P is measured in Rs. per unit and Q in thousands

of units. The monopolist has a constant AC of Rs. 6 per unit.

a) What are the monopolists profit maximizing price and quantity?

Answer:

TR= 11Q-Q^2

P= 11-Q

MR= 11-2Q

AC= 6

TC= 6Q

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MC=6

Profits maximized at MR=MC

11-2Q=6

2Q=5

Q=2.5

P= 8.5

Maximum quantity =2500, Maximum Price = Rs.8.5/unit

b)

What is the resulting profit?

Answer:

Profit = 5Q-Q^2

= 5*2.5-2.5^2

=6.25

Profit per unit is Rs.6.25

c) Calculate the firms degree of monopoly power using the Lerner Index. What can you say about

the degree of monopoly power

Answer:

Lerner index = -1/Ed

Ed = (Dq/Dp)*p/q

= -1 * 8.5/2.5

L = -2.5/-8.5 = 5/17

= 0.294811

Since the learners index is closer to 0 the degree of monopoly power is much lesser.

Q3. The table shows the demand curve facing a monopolist who produces at a constant MC of Rs. 10.

Price Quantity

18 0

16 4

14 8

12 12

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10 16

8 20

6 24

4 28

2 32

0 36

a) Calculate the firms MR curve

Answer:

Equation for demand curve:

(P-18)/(Q-0) = (18-16)/(0-4)

-4P+72=2Q

Q+2P=36

P=18-0.5Q

Revenue=P*Q

(18-0.5Q)*Q

18Q

0.5Q2

Marginal Revenue(MR) = dR/dQ

18-Q

b) What is the firms profit-maximizing output and price? What is its profit?

-20

-10

0

10

20

30

40

0 5 10 15 20

Price

Quantity

MC

MR

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Answer:

To maximize profit, MR=MC

Given MC=10; 18-Q=10, or , Q=8

P=18-0.5*8 = 14

Q=8 and P=14

c) What would the equilibrium price and quantity be in a competitive industry?

Answer:

For a competitive industry, equilibrium price and quantity would be at the point where

Demand =Supply

Hence, 18-0.5Q = P = 10 (Since, MC curve above the price line is the Supply curve)

Q=16 and P=10

Q4. What is the relationship between P, MC and Ed? (Relate it to the Rule of Thumb for Pricing). (1)

Answer:

P= MC or, P-MC = -1

1+1/Ed P Ed