Question

suppose a consumer's utility function is given....

su.instructure.com/courses/2040833/files?preview=107014298 Page < 2 1. (24 total points) Suppose a consumer's utility function is given by U(X,Y) -X12*12 Also, the consumer has 572 to spend, and the price of Good XP S4. Let Good Y be a composite rood whose price is Py$1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X a) (2 points) How much X and Y should the consumer purchase in order to maximize her utility? b) (2 points) How much total utility does the consumer receive? c) (2 points) Now suppose Py increases to $9. What is the new bundle of X and Y that the consumer will demand? d) (2 points) How much additional money would the consumer need in order to have the same utility level after the price change as before the price change? (Note: this amount of additional money is called the Compensating Variation)

please help me! I'm not sure if I'm doing it right

I'm having trouble with the substitution part where I try to figure out what y equals. if anyone could help I would appreciate it! thank you

Answer 1

tt U(X,Y) - VXF - Utility Function 4x+ y = 72 = Budget constraint. (Q Optimal Bundle which maximises the utility The point where the consumer can obtain maximum utility is: 1 MRSxx ( MUX = 7 MUY = 7 MRS : MUX, 1972-7X - Mon 1x/259 X 1.4, Y=4x substituting this value in Budget constraint 4x +4X - 72, 8X= 72, X-9, Y=36 opteinal Bundel = (9,36) ab Tatal utility from Optimal Bundle U(X,Y)= VXY = 19x36 - 3x6 = 18 Utility: 18 @ Px increases to $9 New Bundle of X and Y ax + y = 72 → New Budget constraint. ř -q [:: MRSx = for optimal Bundle 7 Y = 98 p Substituting this value in new budget constraint. 9x +9X-72 X = 4; Y = 36 New Optimal Bundel = 14,36) CamScanner Scanned with

Tag Compensating Variation New utility = √4x36 = 12 in order to get the old utility ie 18, the old bundel has to be consumed calculated as followed : JXY = 18 [since the same utility is required] -(1) Hot X: 9 [:: MRSx, y = ] —2) solving (1) & (2), we get. XY =(18), y = 9x 9x®=(18) 2 , *= 36, X = 6 , Y= 54 New Bundel = 16,54) verify:- U1X,Y) = vxy'= V6x5y = 18 Hence, verified. CS Scanned with CamScanner