Intermediate Microeconomics: A Modern Approach, Seventh Edition

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Econ 301 – F07 PROBLEM SET 3 - Answers Wissink 1. For changes in Py, diagrammatically show what the price consumption curve looks like for the following utility functions: u(x,y) = y + v(x); u(x,y) = x 2 y 2 ; u(x,y) = x + y; u(x,y) = min{x,y}. [Answer] 2. For changes in I, diagrammatically show what the income consumption curve looks like for the following utility function: u(x,y) = y + v(x). [Answer] x y IC0 IC1 IC2 Price consumption curve budget lines u(x,y)=y+v(x) x y Price consumption curve u(x, y) = x 2 y 2 x y Price consumption curve IC Px/Py=1 u(x, y) = x + y x y Price consumption curve u(x, y) = min{x, y} x y IC0 IC1 IC2 Income consumption curve budget lines u(x,y) = y + v(x)
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3. For changes in Px, diagrammatically show the income and substitution effects ala’ Slutsky for the following utility functions: u(x,y) = x 2 y 2 ; u(x,y) = x + y; u(x,y) = min{x,y}. [Answer] 4. Derive the demand functions for x & y for the utility function: u(x,y) = 2X + 3Y [Answer] This is a case of perfect substitutes so: x* = I/Px when Px/Py < 2/3, and 0 if Px/Py > 2/3 y* = 0 if Px/Py < 2/3 and I/Py if Px/Py > 2/3 At Px/Py = 2/3 then it doesn’t matter how you spend between X and Y, as long as you spend it all. 5. Remember… James Bond’s favorite drink is a Vodka Martini, shaken, not stirred. His personal perfect recipe is to always use 1 part vodka to 3 parts gin. If martinis are the only thing James consumes, and we measure parts as ounces (oz) then what is the solution to James’s constrained utility maximization exercise assuming that P V = $6 per oz, P G = $8 per oz and that James’s income for drinking tonight is $70? 2 Bo Bn Bs x y Bo =Bs Bn x y Bn y Bo =Bs u=Cobb-Douglas u=x+y and assume Px < Py both before and after the price change. u=min{x, y} Notes for all graphs: 1. dotted lines are indifference curves 2. solid lines are budget lines 3. o = original, n = new, s = Slutsky substitution point 4. From Bo to Bs is the Slutsly substitution effect, from Bs to Bn is the income effect, from Bo to Bn is the total effect.
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[Answer] Suppose James Bond’s utility function is min{3V, G} where V is vodka(oz) and G is gin(oz). His budget constrain is 6V+8G=70. (1) In equilibrium, 3V=G (2) use the budget constraint, 6V+8G=70. Subbing (1) into (2) get us: 6V*+8(3V*)=70 30V*=70 Thus, the solution to James Bond’s problem is V*=7/3 and G*=3V*=7.
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