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1 - Economics 101 Spring 2011 Answers to Homework#3 Due...

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Economics 101 Spring 2011 Answers to Homework #3 Due Tuesday, March 1 Directions: The homework will be collected in a box before the lecture. Staple your homework before handing it in. Please place your name , TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section you are registered, because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck! 1. AGRICULTURAL INTERVENTION Use the following to answer parts (a) through (e). Consider the market for pineapples in a small island nation. The domestic demand curve (in Island Dollars) is P = 60 – 3Q D and the domestic supply curve is P = 10 + 2Q S . a. What is the market equilibrium price and quantity? Solution: Set prices equal and solve to get P = $30 and Q = 10 PRICE CEILINGS AND FLOORS: b. If the government, hoping to help the poor, imposes a price ceiling of $15, what will be the shortage of pineapples in the market? Graph your response. Solution: Plug P=15 into the supply and demand curves to find that quantity demand at this price is 15 and the quantity supplied is 2.5. The shortage is therefore 15-2.5 =12.5 pineapples. c. What price floor would yield a surplus of 15 pineapples? Solution: Solve both equations for quantity to get: QD=20-P/3 and QS = P/2-5 With the price floor, we know that QS=QD+15 Plug in our equations to get: P/2-5=20-P/3+15 Solving this gives P = 48. PRICE SUPPORT PROGRAMS d. Suppose the government price target is $42, which they plan to accomplish by use of a price support program. How many pineapples will the government have 1
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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. Solution: By plugging P = 42 into the supply and demand curves, we see that quantity demanded is 6 and quantity supplied is 16. The surplus is thus 10 pineapples, which will cost them $420 to buy at the price of $42 a pineapple. Your graph should show the surplus as a horizontal line between the points (Q=6, P=42) and (Q=16, P=42). The total government cost is the rectangle whose top side is the surplus line and bottom is the Q axis. PRICE SUBSIDY PROGRAMS e. Suppose the government offers the pineapple producers a $10 subsidy on every unit they sell. Graph the new market supply curve. What will the new market equilibrium quantity and price be with this program? How much does this program cost the government? At any given quantity, the supplier can afford to sell at $10 less per pineapple than before, since they are now getting the extra money from the government. Thus the new supply curve is shifted down by $10, or P subsidized =(original supply price)-$10=2Q s To find the new equilibrium price and quantity, set 60-3Q=2Q which gives Q=12.
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