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# Problem sets answers ECON 340

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This 2 page Bundle was uploaded by Wenhan Yan on Monday November 9, 2015. The Bundle belongs to ECON 340 at Purdue University taught by Andres J Vargas in Fall 2015. Since its upload, it has received 91 views. For similar materials see Intermediate Microeconomic Theory in Economcs at Purdue University.

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Date Created: 11/09/15

Intermediate Microeconomics ECO 340004 Problem Set 2 Due on Monday September 21 at the beginning of class You must show how you arrived at every single answer on the problem set Even if you did it in your head write down what your head did You will receive ZERO credit for any answer where you don t show your work ECON 340 30 pts Julie s preferences for food F and clothing C can be represented by the following utility function U F C F C 5 pts Does this utility function have the property that MRSEC is diminishing Explain Assume that you would graph F on the horizontal axis and C 0n the vertical axis 5 pts Suppose that food costs 1 a unit and that clothing costs 2 a unit Julie has 12 to spend on food and clothing Find the optimal utilitymaximizing choice of food and clothing and the corresponding level of utility 5 pts Show this result graphically let the amount of food be on the horizontal axis and the amount of clothing be on the vertical axis labeling as many points as you can Spts What is the marginal rate of substitution of food for clothing at her optimal basket Show this graphically and algebraically 5 pts Write Julie s dual problem of the optimization problem you solved in part b Solve this problem and show that the solution is the same you found in part b 5 pts Suppose Julie decides to buy 4 units of food and 4 units of clothing with her 12 budget instead of the optimal basket Would her marginal utility per dollar spent on food be greater than or less than her marginal utility per dollar spent on clothing What does this tell you about how she should substitute food for clothing if she wanted to increase her utility without spending any more money Explain 10 pts Helen s preferences over Clothing C and shoes 5 are given by U C 55 10C The price of a piece of clothing is 90 and the price of a pair of shoes is 30 and Helen can spend a combined total of 300 on these goods Find Helen s optimal consumption basket 20 pts David has a quasilinear utility function of the form Ux y x12 y a 10 pts Derive David s demand curve forx as a function of the prices PX and Py Verify that the demand forx is independent of the level of income at an interior optimum b 10 pts Derive David s demand curve for y s y a normal good How are X and Y related Explain Fall 2015 Andres J Vargas 4 25 pts Lou s preferences over pizza x and other goods y are given by Ux y xy His income is 120 a 5 pts Calculate his optimal basket when PX 4 and Py 1 Call this basket A What is Lou s utility at basket A b 5 pts Calculate his optimal basket when PX 3 and Py 1 Call this basket C What is Lou s utility at basket C c 10 pts Decompose the total chance From A to C into income and substitution effects d 5 pts show the decomposition graphically 5 15 pts There are two consumers on the market Jim and Donna Jim s utility function is Ux y xy Donna s utility function is Uxy xzy Income ofJim is I 100 and income of Donna is ID 150 a 10 pts Derive Jim s and Donna s demand curve for x as a function of PX Assuming Py1 b 5 pts Compute the aggregate demand when Jim and Donna are the only consumers ECON 340 Fall 2015 Andres J Vargas

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