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Homework answers / question archive / Suppose a Neu is the only gas supplier in town
Suppose a Neu is the only gas supplier in town. She is facing a market demand for gas of Q = 2,000 - 0.2P. She has a cost function of C = 5,000,000 + 100Q. a. b. Find the profit-maximizing output level, price level and the profit of Neu. Show these results in a well-labelled diagram. (12 marks) In order to achieve an efficient output level, a legislator suggests a price control on Neu. Explain the price the government should set in achieving so. Explain the disadvantage of doing so. (5 marks) Instead of a price control, another legislator suggests charging a lump-sum tax on Neu. Explain why this does not improve the efficiency of Neu.
Demand : Q = 2000 - 0.2P
Inverse demand : 0.2P = 2000 - Q
or, P = 10000 - 5Q
Revenue : R = PQ = 10000Q - 5Q2
Marginal revenue : MR = 10000 - 10Q
Total cost : TC = 5000000 + 100Q
Marginal cost : MC = 100
a) Since New is the single gas supplier, thus it holds monopoly in gas supply.
Hence Neu will maximize profit where it can equate its MR with its MC.
Hence at MR = MC,
10000 - 10Q = 100
or, 10Q = 9900
or, Q = 9900/10 = 990
Price : P = 10000 - 5Q
= 10000 - 5 * 990 = 10000 - 4950 = 5050
Profit = Revenue - Cost
Revenue = 10000*990 - 5*9902 = 9900000 - 4,900,500 = 4,999,500
TC = 5000000 + 100 * 990 = 5000000 + 99000 = 5,099,000
Profit = 4,999,500 - 5,099,000 = -99,500
Hence Neu faces loss of amount -99500.
This can be shown as follows:
b) Efficient level of output can be obtained P = MC. This equality shows the socially optimum level of output.
P = 10000 - 5Q
MC = 100
By P = MC,
10000 - 5Q = 100
or, 5Q = 9900
or, Q = 9900/5 = 1980
P = 10000 - 5*1980 = 100
Hence efficient level of output is 1980
Price at that level is 100.
Hence to achieve efficinent level, government should set price = 100 and quantity = 1980.
Due to this, price will reduce from equilibrium level (MR = MC). and as a result, producer surplus will reduce. But since price reduces, consumer surplus increases. But due to price reduction supply may decrease. As a result there may arise shortage of supply in next phases.
c)Instead of price control, if government imposes lump sum tax then that would be increase firm's fixed cost. But there will be no change in total cost and marginal cost. However due to lump sum tax, total cost will increase and average cost will increase.
Thus to be specific, if MC is unchanged, thus equilibrium price and quantities will be same (follow part a). but since TC has increased, AC will also increase and AC curve will shift further upwards. As a result firm's loss will increase. And firm will deviate more from efficiency.
please see the attached file for the complete solution.
