# What is the marginal rate of substitution of D for F when Amelia chooses D and F to maximize her utility?

This assignment covers supply and demand as well as consumer behavior. Please answer the ques- tions below, which are related to Chapters 2 through 4 of P&R. Beyond reviewing the material from class, the problem sets are intended to develop the ability to apply the concepts from class to new situations. You are encouraged to collaborate with others, to research sources outside of class, and to ask questions during office hours. However, you must write up your responses individually.

You should explain all of your answers in detail. Your score will depend on both the correctness of your solutions and the completeness of your explanations. Please write the question number next to your answer for each question. Your answers to the assignment are due in class on Thursday, September 22. Late assignments may be penalized

This assignment covers supply and demand as well as consumer behavior. Please answer the ques- tions below, which are related to Chapters 2 through 4 of P&R. Beyond reviewing the material from class, the problem sets are intended to develop the ability to apply the concepts from class to new situations. You are encouraged to collaborate with others, to research sources outside of class, and to ask questions during office hours. However, you must write up your responses individually.
You should explain all of your answers in detail. Your score will depend on both the correctness of your solutions and the completeness of your explanations. Please write the question number next to your answer for each question. Your answers to the assignment are due in class on Thursday, September 22. Late assignments may be penalized.
1. (16 points) Suppose that the supply for potatoes is QS = 2000+200P and the demand for potatoes is QD = 4000 – 300P – 2I, where P is price and I is income. Let I = 500.
. (a) Are potatoes a normal or an inferior good based on the demand function above? Explain briefly. ?
. (b) Solve for the equilibrium price and quantity. ?
. (c) Calculate the price elasticities of demand and supply at the market equilibrium. ?
. (d) Suppose the government imposes a price support at P = 4 by paying four dollars for any potato not sold on the market. What are the quantities of potatoes sold on the market and sold to the government? ?
2. (16 points) Suppose that the equilibrium price of copper is 5 and the equilibrium quantity of copper is 20. At the market equilibrium, the price elasticity of demand for copper is -0.5, and the price elasticity of supply for copper is 1.0.
. (a) Is the demand for copper elastic or inelastic at the market equilibrium? Explain briefly. ?
. (b) Assume that the supply and demand curves are linear. Find equations for supply and demand given the information above. ?
. (c) Suppose that the quantity of copper supplied at each price falls by 50%. What is the new equilibrium price and quantity? ?
. (d) What are the price elasticities of demand and supply at the new equilibrium? ?
3. (16 points) Pierre has the utility function U(F,C) = 10FC, and Marie has the utility function ?V(F,C)=20F2C2,whereF andC representthequantitiesoffoodandclothing.
. (a) What is the set of market baskets that give Pierre a utility level of 10? Draw Pierre?s ?indifference curve for a utility level of 10. ?
. (b) What is the set of market baskets that give Marie a utility level of 20? Draw Marie?s indifference curve for a utility level of 20. ?
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(c) Do Pierre and Marie have the same or different preferences over food and clothing? Explain.
(d) Suppose that Pierre?s utility function changes to W(F,C) = 20FC2. Do Pierre and Marie now have the same or different preferences? Explain.
4. (16 points) Suppose that Amelia has the utility function U(D,F) = 10DF, where D is days of domestic travel, and F is days of foreign travel. Let the price of D be 100, the price of F be 400, and total income for travel be 4000.
. (a) What is the set of market baskets that exhaust all of Amelia?s income? Draw Amelia?s budget line. ?
. (b) What is the set of market baskets that give Amelia a utility level of 1000? Draw Amelia?s indifference curve for a utility level of 1000. ?
. (c) What is the marginal rate of substitution of D for F when Amelia chooses D and F to maximize her utility? ?
. (d) What are the choices of D and F that maximize Amelia?s utility given her budget constraint? ?
5. (16 points) Oscar?s demand for movies is given by Q = 10 – 2P .
. (a) What is the price elasticity of demand at a price of 2? Is Oscar?s demand elastic or inelastic at a price of 2? ?
. (b) Assume that the price is 3. What is Oscar?s total expenditure on movies? What is the consumer surplus? ?
. (c) What is the price that maximizes Oscar?s total expenditure on movies? What is the price elasticity of demand at this price? ?
. (d) If the price increases from 1 to 2, does Oscar?s total expenditure on movies rise or fall? If the price rises from 3 to 4, does Oscar?s total expenditure on movies rise or fall? ?v ?
6. (16points)BrianhastheutilityfunctionU(X,Y)=X+16 Y,whereXisthequantityofwater consumed, and Y is the quantity of coffee consumed. Let the price of water be PX = 1 and the price of coffee be PY = 4. Let I represent income. [Hint: there might be a corner solution in some cases.]
. (a) If I = 8, what are the quantities of water and coffee that maximize Brian?s utility subject to his budget constraint? ?
. (b) What is the marginal utility of income when I = 8? ?
. (c) If I = 32, what are the quantities of water and coffee that maximize Brian?s utility subject ?to his budget constraint? ?
. (d) What is the marginal utility of income when I = 32? ?
7. (4 points) This question is for fun. Imagine that you are in the following real life situation. You are attending a family reunion. You meet an uncle of yours. Your uncle asks what you are up to these days. You tell him that you are studying economics. He asks why you are interested in economics and what you are going to do with an economics degree. What do you tell your uncle? ?