Question

Given: U(x,,x,)-3x 6x2 P 4, P5,1 20 a) Write the function for the indifference curve and graph it. b) Write the function for the budget constraint and graph it c) What are the utility maximizing amounts of xand x2 given the budget constraint:? d) Do the utility maximizing amounts of x and x2 change if P increases to 5 while P stays constant at 5? Why or why not? e) Do the utility maximizing amounts of x and x2 change if P2 increases to 9 while P stays constant at 4? Why or why not?

PLEASE WRITE NEATLY SO I CAN UNDERSTAND AND DIFFERENTIATE THE VARIOUS SYMBOLS AND VARIABLES.

Answer 1

2 XL hirm u (2jK2) = 3x + 6*2 1. Ane Marginal utility of x, i.e. MUI = 20 (X1) Xa) - 3 x =0 and Marginal utility of Xz ie MU2 = 20 (X1, Xz) = 6 Here slope of the inditforence Cave = M = 3 = 1 / 1 As the slope of the in difference care ina staight line, i constant, the indifference cure will be a straight line or we will get in distuence enue for pufact substitutes x2 U (R1, K2) = 3x1 + 6X2 -> b2 Now, P,=4, P2 = 5 and I = 20 . Hunce equation of the budget constraint I = Pixit P2 X2 => 20=4x1+ 5 X2 Now, it the consmen spuds his into entire income on the horizontal inducept of the budget line will be found by substituting X2=0 in the budget constraint. 20=421+ 5 (0) =) 21 = 5 Scanned with CamScanner

If the consman spmds his entire income on K2, then the untical in tncept of the budget line will be bound by substituting X2=0 in the budg it constrant. 20= 400) + 5X2 T =) H2=4 Now by Joining horizontal and unitical in Incept, we will get the budget line AB . I - Ki y now, mul = 2 2 = 0,75 P, 2 and MUR = e = 1.2 Now as, MU2 > Mul hence the consues will spad 1. his entire in come on Xa and the optimal consumption bundle will be bound by substituting Xi =0 in the budget constraint. Hence substituting x150 in the budget constraint we get! - 20=4(0) +5X2 cs Scanned with => X2=4 CamScanner

consmption budle is Hunce utility manimizing (x1, 62) - (04) . d Ib Po increases to 5 while P₂ stays at 5 Hace now, mul = 3/8 = 0.6 and MURL = = 1.2 - Hace here as muz) Mui, consmes will still spend all Pē of his income on X2 and utility manimizing amount of a and ter will not change in this casc. hence here (21, Ke) = (0,4) Р. = 0.67 P2 es et P2 increases to a while po stays constant at 4. Hace mus - 0.75 and MU2 = As muiy mue, hence now consumes will spend his entire in come on xi and utility manimizing consumption bundle will be found by substituting K2=0 in the budget constraint Hace 20=401+ 510) => x1 = 5 Hunce here utility manimizing amount of x, and Kz will Change to (21, H2) = (50) Scanned with CamScanner