1. A good is currently produced in a perfectly competitive market. The market de
ID: 2440836 • Letter: 1
Question
1. A good is currently produced in a perfectly competitive market. The market demand for the good is P = -0.01QD + 15. There are 50 firms in this market each with a MC = 0.8qf + 2 so the market supply is . is P = 0.016QS + 2
a) Find the equilibrium price and quantity. Now place a tax of 5.2 per unit on the consumers of this good. Find the new market price and quantity, the total tax revenue, and how much of that comes from producers and how much from consumers. You will find that one of the two pays more of the tax. Explain why this makes sense. (3 points)
c) Now place the tax on the producer and show that, while the market price changes, all the other answers from above remain the same. (2 points)
2. A consumer starts with an income of $120 which she can spend on either food (measured on the x-axis), or on booze (measured on the y axis). If the price of food is $5 and the price of booze is $2, the consumer’s budget constraint is 5x + 2y = 120. We are going to compare three different policies for two different consumers. The policy options are:
A) The government subsidzes the price of food by 1 dollar for the consumer
B) Gives the consumer $15
C) Gives the consumer 3 units of food which cannot be traded for booze.
a) For the first part, assume the consumer has an MRS = y/x. Show the following: (3 points)
i) Given the consumer’s choice under policy (A), policy (A) and (B) cost the same
ii) Draw the two budgets under policy (A) and (B) together on the same graph. Specifically find where they intersect. Draw the indifference curve through the optimal in (A), then explain why the optimal point with (B) must make the consumer better off.
iii) Policy (B) and (C) are exactly the same for the consumer
b) Now assume the consumer has an MRS = y/17x . Now show that the policy in (B) and the policy in (C) are not the same for this consumer. Do this by finding the optimal food and booze under budget (B) but explain that is not possible under policy (C). (2 points)
Explanation / Answer
Consider the given problem here the market demand curve is given by, “P = 15 – 0.01*Q”. Now, there are “50 firms” each having same “MC = 2 + 0.8*q”. So, the individual supply curve is given by, “P = 2 + 0.8*q, => 0.8*q = P – 2, => q = 1.25*P – 2.5”, => the market supply curve is given by, “Q = 50*q = 50*(1.25*P – 2.5) = 62.5*P – 125”, => Q = 62.5*P – 125. So, the market supply curve can be written as, “62.5*P = 125 + Q, => P = 2 + 0.016*Q”.
So, at the equilibrium the demand must be same as supply.
=> 2+0.016*Q = 15 – 0.01*Q, => 0.026*Q = 13, => Q = 13/0.026 = 500, => Q = 500. So, the equilibrium price is given by “P = 2 + 0.016*Q = 2 + 0.016*500 = 10. So, here the equilibrium price and the quantity is given by, “P=10” and “Q=500”.
b).
Now, a tax of “5.2 per unit” on consumer is imposed, => the new demand curve is given by, “P=15-0.01*Q – 5.2, => P = 9.8 -0.01*Q”. So, at the equilibrium the demand must be equal to supply.
=> 9.8 – 0.01*Q = 2 + 0.016*Q, => 7.8 = 0.026*Q, => Q = 300. So, the equilibrium price is given by, “P = 9.8-0.01*Q = 9.8-0.01*300 = 6.8. So, as the tax is imposed on the consumer the equilibrium pri9ce will increase to “6.8+5.2=12” and the quantity demanded decreases to “300”.
Now, the total tax revenue is given by, “300*5.2 = 1560”. Now, initially the equilibrium price was “10” and it increase to “12”, => tax revenue comes from consumers is “(12-10)*300 = 2*300 = 600”. Now, after tax producer will receive “12-5.2=6.8”, => tax revenue comes from producers is given by, “(10-6.8)*300 = 3.2*300 = 960”. So, here “producers” are paying “3.2” and consumers are paying “2” of the tax. So, here producer are paying more than the consumer. Here the demand curve is more elastic compare to the supply curve, => if tax is imposed then consumer are relatively more responsive compare to the producer, => as the tax is imposed the producer will share the larger portion of the “tax”.
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