1) Suppose that P=100-Q, MR=100-2Q, TC= 20+Q^2 , and MC=2Q. Solve for equilibriu
ID: 1139396 • Letter: 1
Question
1) Suppose that P=100-Q, MR=100-2Q, TC= 20+Q^2 , and MC=2Q. Solve for equilibrium output, price, average cost, and profit.
a) Q=33.3, P=66.7, ATC=34, Profit= 1079
b) Q=25, P=75, ATC= 25.8, Profit=1230
c) Q=33.3, P=66.7, ATC=40, Profit= 2221
d) Q=25, P=75, ATC= 25.8, Profit=1875
2) Suppose that P=100-Q, MR=100-2Q, TC= 20+Q^2 , and MC=2Q. Suppose the government wants to eliminate the deadweight loss by imposing a price ceiling. What price could the monopoly set in order that the monopoly produces as close as possible to the efficient (welfare maximizing) output while still ensuring that the monopoly is not driven out of business? What is the associated quantity produced and profit?
a) P=75, Q=25, Profit=1092
b) P=66.7, Q=33.3, Profit=1230
c) P=75, Q=25, Profit=1230
d) P=66.7, Q=33.3, Profit=1092
3) Suppose that P=100-Q, MR=100-2Q, TC= 1125+Q^2 , and MC=2Q. Solve for output, price, average total cost, and profit.
a) Q=25, P=75, ATC=70, Profit=125
b) Q=33.3, P=66.7, ATC=67, Profit=-1
c) Q=33.3, P=66.7, ATC=67, Profit=1
d) Q=25, P=75, ATC=70, Profit=-375
4) Suppose that P=100-Q, MR=100-2Q, TC= 1125+Q^2 , and MC=2Q. Suppose the government wants to eliminate the deadweight loss by imposing a price ceiling. What price could the monopoly set in order that the monopoly produces as close as possible to the efficient (welfare maximizing) output while still ensuring that the monopoly is not driven out of business? What is the associated quantity produced and profit?
a) Price=66.7, Quantity=33.3, Profit=-33
b) Price=67.1, Quantity=32.9, Profit=0
c) Price=67.1, Quantity=32.9, Profit=-10
d) Price=66.7, Quantity=33.3, Profit=33
5) Outline the major points of the argument as asked in the homework assignment.
6) Enter the equilibrium price and quantity asked for in the homework question.
7) Is the subsidy able to obtain the efficient level of output and price? What would be some difficulties in implementing this strategy?
Explanation / Answer
Answer
1)
A firm produces that amount of quantity at which MR = MC
MR = d(TR/dQ) = d(PQ)/dQ = d(100Q - Q2/dQ = 100 - 2Q
MC = 2Q
Hence 100 - 2Q = 2Q => Q = 25
P = 100 - Q = 75
ATC = TC/Q = 20/Q + Q = 20/25 + 25 = 25.8
Profit = TR - TC = 25*75 - 20 - 25^2 = 1230
Hence The correct answer is (b) Q=25, P=75, ATC= 25.8, Profit=1230
2)
In order to minimize deadweightloss government has to set that price at price ceiling at which P = MC (like Price charged in Perfect competitive market).
So, P = MC => 100 - Q = 2Q = > Q = 33.3
P = 100 - Q = 66.7
Profit = TR - TC = 33.3*66.7 - 20 - 33.3^2 = 1092
Hence The correct answer is d) P=66.7, Q=33.3, Profit=1092
3)
A firm produces that amount of quantity at which MR = MC
MR = d(TR/dQ) = d(PQ)/dQ = d(100Q - Q2/dQ = 100 - 2Q
MC = 2Q
Hence 100 - 2Q = 2Q => Q = 25
P = 100 - Q = 75
ATC = TC/Q = 1125/Q + Q = 1125/25 + 25 = 70
Profit = TR - TC = 25*75 - 1125 - 25^2 = 125
Hence The correct answer is a) Q=25, P=75, ATC=70, Profit=125
4)
In order to minimize deadweightloss government has to set that price at price ceiling at which P = MC (like Price charged in Perfect competitive market).
So, P = MC => 100 - Q = 2Q = > Q = 33.3
P = 100 - Q = 66.7
Profit = TR - TC = 33.3*66.7 - 1125 - 33.3^2 = -12.9 As wecan see that monopoly will incurr loss hence monopoly will get out of business hence government will Average cost pricing i.e. Price where = P = AC => TR = TC. Hence 100Q - Q2 = 1125 + Q2
=> 2Q^2 - 100Q + 1025 = 0
Solving above quadratic equation we get
=> Q = 32.9
Hence P = 100 - 32.9 = 67.1
Hence Profit = 32.9*67.1 - 1125 - 32.9^2 = 0
Hence The correct answer is (b) Price=67.1, Quantity=32.9, Profit=0
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