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7/21/2019 Microeconomics Sample
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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
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