Econ 455 Problem Set 1: Consumer and Producer Surplus Analysis - Prof. Harvey E. Lapan, Assignments of Economics

Download Econ 455 Problem Set 1: Consumer and Producer Surplus Analysis - Prof. Harvey E. Lapan and more Assignments Economics in PDF only on Docsity! Econ 455 Lapan Fall 2005 Problem Set 1 - Due September 8, 2005 (Producer and consumer surplus) 1. Consider a consumer who has the following (quasi-linear) utility function: ( ) ( )( )2, 50U x y x y y= + − 2 ) where ( ,x y denotes the goods consumed by the individual. Let I denote the individual’s income, and ( , )x yP P denote the prices the individual pays for goods x and y, respectively. a) Write the budget constraint for the individual, set up the utility maximization problem and derive the individual’s demand functions for the two goods (you may assume an interior solution so that both goods are consumed). b) Currently a consumer, with income I=3000, can buy goods at the prices . A new mall brings to town a discount store (Costco) which sells good y at the price . 1, 20x yP P= = 15yP = i. What will the consumer’s purchases be at this price and will the consumer be better or worse off as a result of the opening of this store? ii. Suppose the store charges individuals a membership fee of $F for the right to shop in the store. What is the maximum amount this individual would be willing to pay to shop in the store? Give a numerical answer. iii. Using the demand curve, show graphically how to calculate your answer from part ii. What is this area called? c) Return to the original situation with 3000, 1, 20x yI P P= = = . There is no Costco, but the individual does have the opportunity to join an online club that sells good y (CDs) at the price of . However, this club requires the individual to buy at least 45 units of good y. 15yP = i. If there were no minimum purchase requirement, how many units of good y would the person want to purchase? ii. Will the person be better off joining the club (and purchasing 40 units) or not joining? If she chooses to join, what is the maximum fee she would be willing to pay to join this club? 2. Consider a consumer who has the following utility function: ( ),U x y x y= ⋅ . Given income, I, and prices ( ),x yP P : a) Write the budget constraint for the individual, set up the utility maximization problem and derive the individual’s demand functions for the two goods. i. For these preferences, how does an increase in income affect the demand for good y? How does that differ from Problem 1. 1