# Economics 101 Fall 2011 Homework #3 Due 10/11/11

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3 (b) Graph the market supply curve for peanut butter. 3

4 Horizontally sum the two graphs from part (a). There should be a kink in the line at P = 10. (c) What is the equation for the market supply curve for peanut butter? We want to add the two quantities supplied together: Qs Total = Qs Jif + Qs Skippy Qs Total = 2P + 4P 40 = 6P 40 P = 1/6 Qs Total + 20/3 Note that this is equation for when P > or equal to 10. For P < or equal to 10, the market supply curve is equal to Jif s supply curve, because Skippy will not enter the market. 3. Quota and Deadweight Loss Consider the market for haircuts in the small town of Harrison, Wisconsin, during a typical day. In this market, hair stylists are producers and any resident of Harrison with hair is a consumer. There is only one type of haircut in Harrison. The demand curve and supply curves for the market for haircuts are given by Demand: Qd = 25 ½P 4

5 Supply: Qs = 2P (a) Find the equilibrium price and quantity in this market for haircuts. Set supply and demand equal: 25 1/2P = 2P P = \$10 Plug this price into supply or demand: Q = 2P = 2*10 = 20 (b) Calculate the consumer's surplus and producer's surplus in the market for haircuts. Sum consumer and producer surplus to get the total surplus in the market for haircuts. For consumer surplus, find the area beneath the demand curve and above the price line. In this case, this is a triangle with height 40 and base 20. The area equals ½ b*h = ½ * 40 * 20 = \$400. For producer surplus, find the area above the supply curve and below the price line. In this case, it s a triangle with height 10 and base 20. ½ b*h = ½ * 10 * 20 = \$100. Total surplus = \$400 + \$100 = \$500. Assume now that the government of Harrison imposes a quota of 10 haircuts per day. That is, the government of Harrison is going to limit the number of haircuts per day to a total of 10 haircuts irrespective of the demand for haircuts. To implement this quota, the government requires that hair stylists purchase an operating license that allows them to cut hair. (c) For parts (c), (d) and (e) of this question you will find it helpful to draw a graph and then use that graph as a roadmap for the calculations you will be making. At what price will consumers demand exactly 10 haircuts? Plug in 10 for Qd and solve for P. This gives P = \$30. 5

6 (d) What price must producers receive in order to be willing to sell exactly 10 haircuts? Plug in 10 for Qs and solve for P. This give P = \$5. (e) The hair stylists will be forced to pass on the cost of the operating license to their customers in order to stay in business. Based on (c) and (d), how much should the government charge hair stylists (per haircut) for the operating license in order to impose the quota of 10 haircuts per day? If the government licenses at \$25 per haircut, the stylists can get \$5 per haircut (and therefore produce 10) and the customers will pay \$30 per haircut and therefore demand 10. Any more than \$25 per haircut, and fewer than 10 haircuts would be sold. Any less than \$25 per haircut, and more than 10 haircuts would be sold. (f) Calculate the consumer surplus, producer surplus, and the total amount of money collected by the town from selling licenses. Add these three numbers to find the total surplus with the quota. You will find it helpful in making these calculations to draw a graph where you label these areas. Now CS is a triangle with height 20 and base 10. Area = ½ * 20 * 10 = \$100. Now PS is a triangle with height 5 and base 10. Area = ½ * 5 * 10 = \$25. 6

7 If the government is charging \$25 per haircut for licenses and there are 10 haircuts sold, the government must earn \$25 * 10 = \$250. Total surplus = \$100 + \$25 + \$250 = \$325. (g) Subtract the new total surplus from the total surplus of the market you obtained in (b) to find the deadweight loss. DWL = \$500 - \$325 = \$125. This is also the area of the triangle to the right of the quota quantity (10) which has base = 10 and height \$30 \$5 = \$25. ½ * 10 * \$25 = \$125. (h) Based on your calculations, do think the quota policy is a good idea? Why or why not? Based on the calculations above, the policy seems to be negative since it causes the total surplus in the market for haircuts to drop by \$ Agricultural Intervention Use the following information to answer parts (a) through (d). Consider the market for coconuts in a small island nation. The domestic demand curve (in Dollars) is P = 140 4QD and the domestic supply curve is P = QS. (a) What is the market equilibrium price and quantity? Set prices equal: 140 4Q = Q Q = 20 Then plug in to solve for P: P = (20) = \$60 PRICE CEILINGS AND FLOORS (b) If the government, hoping to help poor consumers, imposes a price ceiling of \$40, what will be the shortage of coconuts in the market? Graph your response. 7

8 Draw your graph with the supply and demand curves, and mark where on each curve the line P = 40 intercepts. If you plug the value P = 40 into each curve, you will get Qs = 10, Qd = 25. Shortage = Qd Qs = 15. (c) What price floor would yield a surplus of 9 coconuts? We want to calculate the price at which Qs Qd = 9. If we solve for our demand and supply curves in terms of P: Qd = -1/4P + 35 Qs = 1/2P 10 Then plug these into Qs Qd = 9: 1/2P /4P 35 = 9 P = \$72 PRICE SUPPORT PROGRAMS (d) Suppose the government price target is \$80, which they plan to accomplish by use of a price support program. How many coconuts will the government have to buy with this program, and how much will the program cost the government? Graph your results, and shade the region corresponding to total government cost. 8

9 Draw your graph with the supply and demand curves, and mark where a price of \$80 intersects each of these two curves. We can plug the value P = 80 into each curve, and get Qs = 30, Qd = 15. So in order to support a price of 80, suppliers must be able to sell 30 coconuts. But consumers only want to buy 15 at that price, meaning that the government must buy an additional 15. The government s cost is 15 x \$80 = \$1200. This is the rectangle on the graph from Q = 15 to Q = 30, and P = 0 to P = International Trade Let s say the U.S. has the following supply and demand curves for oil where quantity is measured in millions of barrels of oil and price is measured as price per barrel of oil: Supply: Qs = (1/5)P Demand: Qd = 30 (1/10)P In your answers please make sure you provide accurate units of measurement!! (a) Assuming the U.S. does not export or import any oil, find the equilibrium price and quantity for U.S. oil. We want to set supply and demand equal: (1/5)P = 30 (1/10)P. Now solve for P: P=\$100 per barrel of oil. And we can plug that into either supply or demand to find Q = 20 million barrels. 9

10 (b) Calculate consumer surplus, producer surplus, and total surplus. Consumer surplus is a triangle with height \$200/barrel of oil and base 20 million barrels of oil. So CS = ½ * 200 * 20 = \$2 billion. Producer surplus is a triangle with height \$100/barrel and base 20 million barrels of oil. So PS = ½ *100*20 = \$1 billion. Total surplus = CS + PS = \$2 billion + \$1 billion = \$3 billion. (c) Now suppose the U.S. allows oil to be imported and exported. If the world price is \$200 per barrel of oil, what are the new consumer surplus, producer surplus, and total surplus when this market opens to trade? Is the U.S. importing or exporting oil? At a price of \$200 per barrel of oil, the U.S. will demand 10 million barrels of oil and produce 40 million barrels of oil. Therefore the U.S. will export oil. Consumer surplus is now a triangle with height \$100 per barrel of oil and base 10 million barrels of oil. CS = ½ * 100 * 10 = \$500 million. Producer surplus is now a triangle with height \$200 per barrel of oil and base 40 million barrels of oil. PS = ½ * 200 * 40 = \$4 billion. Total surplus = PS + CS = \$500 million + \$4 billion = \$4.5 billion. 10

11 (d) Recalculate the consumer surplus, producer surplus, and total surplus if the world price is \$50 per barrel of oil. Is the U.S. importing or exporting oil? At a price of \$50 per barrel of oil, the U.S. will demand 25 million barrels of oil and produce 10 million barrels of oil. Therefore, the U.S. will import oil. Consumer surplus is now a triangle with height \$250 per barrel of oil and base 25 million barrels of oil. CS = ½ * 250 * 25 = \$3.125 billion. Producer surplus is now a triangle with height \$50 per barrel of oil and base 10 million barrels of oil. PS = ½ * 50 * 10 = \$250 million. Total surplus = CS + PS = \$3.125 billion + \$250 million = \$3.375 billion. 11

12 (e) With the world price at \$50, the U.S. decides it wants to reduce its dependence on foreign oil so it places a tariff on imported oil of \$10 per barrel of oil. Find consumer surplus, producer surplus, government revenue (from the tariff), and deadweight loss. The U.S. can now purchase oil from the rest of the world at \$50 + \$10 = \$60 per barrel of oil. At that price, the U.S. will demand 24 million barrels of oil and produce 12 million barrels of oil. So the U.S. will import = 12 million barrels of oil. (No U.S. producers will want to sell to the world at \$50 per barrel of oil when they could sell for \$60 per barrel of oil domestically.) Consumer surplus is now a triangle with height \$240 per barrel of oil and base 24 million barrels of oil. CS = ½ * 240 * 24 = \$2.88 billion. Producer surplus is now the triangle with height \$60 per barrel of oil and base 10 million barrels of oil. PS = ½ * 60 * 12 = \$360 million. Since the U.S. must import 12 million barrels of oil and the government is charging 10 per barrel of oil, government earn revenue of 12 * 10 = \$120 million. Total surplus = CS + PS + Government Revenue = \$2.88 billion + \$360 million + \$120 million = \$3.36 billion. DWL = \$3.375 billion \$3.36 billion = \$15 million. 12

13 (f) If the world price is still \$50 per barrel of oil and the U.S. instead institutes a quota (a limit on the quantity imported) of barrels of 9 million barrels, what are the new consumer surplus, producer surplus, license holder revenue and deadweight loss? From part (d), we found that at a price of \$50 per barrel of oil, the U.S. will demand 25 million barrels of oil and produce 10 million barrels of oil. Therefore, the U.S. will want to import 15 million barrels but will only be allowed to import 9 million. The price must rise so that U.S. producers supply more oil. We know the difference between the quantity demanded and quantity supplied should 9 million barrels (since that s how much is allowed to be imported). This occurs at a price of \$70. At that price, the U.S. will demand 23 million barrels of oil and produce 14 million barrels of oil. Consumer surplus is now a triangle with height \$230 per barrel of oil and base 23 million barrels of oil. CS = ½ * 230 * 23 = \$2.645 billion. Producer surplus is now a triangle with height \$70 per barrel of oil and base 14 million barrels of oil. PS = ½ * 70 * 14 = \$490 million. License holder revenue = \$20 per barrel of oil * 9 million barrels of oil = \$180 million. Total surplus = CS + PS + License Holder Revenue = \$2.645 billion + \$490 million million = \$3.315 billion. DWL = 1/2*20*4 + ½*20*2 = \$60 million. Note that the sum of CS + PS + License Holder Revenue + DWL should equal the value of total surplus when this market is open to trade and there is no government intervention in the market. Let s check that this is true: CS + PS + License Holder Revenue + DWL = \$2.645 billion + \$.49 billion + \$.18 billion + \$.06 billion = \$3.375 billion. 13

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