Solve this problem on paper, as usual, but you will also submit the numerical answer from part (a) in the space at the bottom of the question. Suppose Cody has utility function U (x, y) = avi + By over goods x and y, where a = 1 and B = 2. a) If prices are Px=4 and Py=6 and income is 5000, how many units of good x will Cody purchase? Enter this number in the space below (You can round to the nearest integer if needed.) b) Suppose that the price of x doubles, but Cody receives compensation so that he remains exactly as well off as before. How many units will he buy in this scenario? Show your derivation clearly.1 . Cody utility function U ( x , y ) = & J X + BJy over good * * 4, where x = 1 & B = 2 a. If prices are P. = 4 and P= 6 and income is 5000. How many units of x will he buy? MU, = LEX, Mug + FET ;IMRS E 2 5X E 6 = x- BC. : ala T ary = 1 + CH = I ala + 7 ( 4) KI P , 5000 - 34091 (4) = 340 91 6 = bob.ob b. Suppose price is x doubles but Cody receives a compensation so that he remains as well as before. How many units will he buy? from port a ) y = Caps ((ag) = 67 70 replace it into utility constraint : 67. 70 1+2(8) /2(6) + X 18 46 = 340. 91Given d= 1 and B = 2. Utility function v (x y) = d Fax + Bly Price of * (P. ) = 4 Price of y ( Py ) = G Income ( I) = 5000 Solution. Step, Budget Constraint Income = Px X + Py. Y 5000 = 40+ 64 Utep 2 . Mux = ist ader derivative of utility funchon wat of Muy = ist order derivative of utility function wit y HIVY = 244 = step 3 At optimal Combination MUX PX MUY 4 + = 64"= 16 9 SC 36 13 9 Jubblute 4= 1620 in ( 1) from step , 5000 = 43 + 6 (1650) 9 solving for ac OC = 241.94 4 = 16x 24194 9 4 = 430-10part b If Price of X Doubles PR= 4 x2: 8 Utility function U ( hy) = fac + 214 Price of + ( PN) = 8 Price ofy ( Py ) = 6 crolution From part a we have oc = 241.94 and 4 = 430.10 Utility U = 1x Jac+ 2 5y U = 124149 + 21430.10 = 57.017 To by equally well off the Consumer must have the craime utility as it was before the price change we 57.017 = F0+254 From part , a] Step 2 we know = MUY At optimal Condition ty = 2 Fac = 64 6 19 4 = 64 x DC subbitite 4= S40c in utility function. 9 57. 017 = 40+ 2 840 9 57. 017 = Joc+ 2x 64 x JC 9 57.017 = FC+ 16 50 9 57. 017 = 62 5c DC = 21 and y = 16 x 81 = 144 9