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Purdue PSY 12000 - answerstohomework3summer2012

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Economics 101Summer 2012Answers to Homework #3Due 6/12/12Directions: The homework will be collected in a box before the lecture. Please place your name, TAname and section number on top of the homework (legibly). Make sure you write your name as it appearson your ID so that you can receive the correct grade. Late homework will not be accepted so make plansahead of time. Please show your work. Good luck!Please realize that you are essentially creating “your brand” when you submit this homework. Doyou want your homework to convey that you are competent, careful, professional? Or, do you wantto convey the image that you are careless, sloppy, and less than professional. For the rest of your lifeyou will be creating your brand: please think about what you are saying about yourself when youdo any work for someone else!1. Suppose the market for corn in a country is described by the following demand and supply equations:Demand: P = 100 – (1/2)QSupply: P = 10 + (13/10)QUse this information to answer the following set of questions. a. What is the equilibrium price and quantity in this market? For your answers you may round to the nearest whole number. b. What is the value of total revenue for farmers in this market?Suppose the government institutes a price support in this market of $80 per unit of corn. c. Given the price support, how many units of corn will consumers buy?d. Given the price support, how many units of corn will the government buy?e. Given the price support, what is the cost to the government of this program if storage costs are $10 per unit of corn stored?f. Draw a diagram illustrating this price support program. Make sure you label your diagram clearly and completely. Suppose the government cancels the price support program and, in its place, institutes a price guarantee program where the guaranteed price for corn is $80 per unit of corn.g. Given the price guarantee, how many units of corn will consumers buy?h. Given the price guarantee, what is the price per unit of corn that consumers will pay? What is the total expenditure on corn made by consumers?i. Given the price guarantee, how many units of corn will the government purchase?j. Given the price guarantee, what is the cost to the government of this program if storage costs are $10 per unit of corn stored?k. Draw a diagram illustrating this price guarantee program. Make sure you label your diagram clearly and completely. Answer:a. To find the equilibrium use the demand and supply curves: 100 – (1/2)Q = 10 + (13/10)Q or Q = 50 units of corn. When Q is equal to 50 units of corn, the price of each unit of corn is $75. b. Total revenue for farmers is equal to price times quantity. Or, total revenue is equal to ($75 per unit of corn)(50 units of corn) = $3750.1c. When the price of corn is $80 per unit of corn, consumers will purchase 40 units of corn. Use the demand curve to find this quantity: P = 100 – (1/2)(Q) or 80 = 100 – (1/2)Q or Q = 40 units of corn. d. When the price of corn is $80 per unit of corn, suppliers will supply 54 units of corn. Use the supply curve to find this quantity: P = 10 – (13/10)Q or 80 = 10 – (13/10)Q or Q = 54 units of corn (this is rounded). Since consumers consume 40 units, this means that the government will purchase the surplus of14 units. e. The cost to the government is equal to the (price per unit of corn)(units of corn purchased by the government) + (units of corn purchased by the government)(storage costs per unit of corn). Or, the cost tothe government is equal to ($80 per unit of corn)(14 units) + (14 units)($10 per unit of corn) = $1260.f. g. With a price guarantee of $80 per unit of corn consumers will purchase 54 units of corn. To see this recall that if the guaranteed price of corn is $80 per unit then suppliers will be willing to produce 54 units.With the price guarantee program the farmers will then sell all of this corn for whatever price they must inorder to sell 54 units. Thus, consumers will buy the entire 54 units of corn. h. With the price guarantee suppliers produce 54 units of corn. Consumers are only willing to pay $73 per unit of corn for this amount. To see this use the demand curve: P = 100 – (1/2)Q where Q = 54. Thus, P = 100 – (1/2)(54) = $73 per unit of corn. The total expenditure on corn made by consumers is ($73 per unit of corn)(54 units of corn) = $3942.i. With a price guarantee program the government does not buy any of the good. There are no storage costs since the government has not purchased the good. j. The cost to the government is the difference in the guaranteed price of $80 per unit of corn minus the price the corn actually sells for ($73 per unit of corn) times the number of units of corn sold. Thus, the cost to the government is ($80 per unit of corn - $73 per unit of corn)(54 units of corn) = $378. There are no storage costs. k. 22. Suppose the market for candy bars can be described as follows:- When the price of candy bars is $1.00 per candy bar, 500 candy bars are demanded. When the price of candy bars increases by 10%, the quantity of candy bars demanded falls by 20%. The demand curve for candy bars is linear. - The supply curve for candy bars is linear and contains the points (Q, P) = (300, $.60) and (200, $.50).a. What is the equation for the demand curve given the above information?b. What is the equation for the supply curve given the above information?c. What is the equilibrium price and quantity in the market for candy bars?d. Suppose the government wants to institute an effective price ceiling in the market for candy bars. What must be true for this price ceiling to be effective?e. Suppose the government wants to institute an effective price floor in the market for candy bars. What must be true for this price floor to be effective?Answer:a. We are given one point on the demand curve: (Q, P) = (500, $1.00). We are given enough information that we can easily find a second point. If the price of candy bars increases by 10% and the initial price was $1.00, then the new price would be $1.10. When the price of candy bars increasesby 10%, the quantity decreases by 20%: 20% of 500 is 100. So, we know a second point on the linear demand curve: (Q, P) = (400, $1.10). Use these two points to find the slope of the demand curve: (change in y)/(change in x) = (change in price)/(change in quantity) = -.1/100 = -.001. Plug this slope into the demand curve to get P = b - .001Q. Then, use one of the points on the demand curve to


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