Quiz 7. DemandFcn2Ans

Quiz 7. - x 1 0.5 =-p 1 p 2 =-p 1 since p 2 = 1 Squaring both sides we get x 2 x 1 = p 1 2 or x 2 = p 1 2 x 1 Substitute for x 2 in the budget

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Shomu Banerjee ECON 201 DEMAND FUNCTION QUIZ #2 ANSWERS Anu’s utility function over two goods x 1 and x 2 is given to be u ( x 1 , x 2 ) = 2( x 1 ) 0.5 + 2( x 2 ) 0.5 . Her marginal utility for the first good is MU 1 = 1/( x 1 ) 0.5 while her marginal utility for the second good is MU 2 = 1/( x 2 ) 0.5 . (a) Calculate Anu’s marginal rate of substitution. ( Hint : MRS = - MU 1 / MU 2 ) MRS = x 2 0.5 x 1 0.5 (b) The price of good x 2 is fixed at p 2 = $1. Find the demand for x 1 as a function of p 1 and income m . ( Hint : Set MRS = - p 1 / p 2 and use the budget equation p 1 x 1 + p 2 x 2 = m .) Set the MRS equal to the slope of the budget: –( x 2 ) 0.5 /(
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Unformatted text preview: x 1 ) 0.5 = -p 1 / p 2 = -p 1 since p 2 = 1. Squaring both sides, we get x 2 / x 1 = ( p 1 ) 2 , or x 2 = ( p 1 ) 2 x 1 . Substitute for x 2 in the budget equation: p 1 x 1 + p 2 x 2 = p 1 x 1 + 1 x ( p 1 ) 2 x 1 = m . Solve for x 1 : x 1 = m p 1 + p 1 2 . (c) The price of good x 2 is fixed at p 2 = $1. Find the demand for x 2 as a function of p 1 and income m . Substitute x 1 = m /[ p 1 + ( p 1 ) 2 ] into x 2 / x 1 = ( p 1 ) 2 and solve to get x 2 = mp 1 2 p 1 + p 1 2 ....
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This note was uploaded on 10/26/2010 for the course ECONOMICS ECON 201 taught by Professor Dr.shomubanerjee during the Summer '07 term at Emory.

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