Question

2. Justin ‘s utility function for two goods, x and y, is U(x, y) = xy . The marginal utility of good x is y + 1 and the marginal utility of y is x. Initially, the price of good y is S4 per unit. Justin's income is $100. (a) If the price of good x rises to S5 per unit, what is the income effect with respect to good x and what is the substitution effect with respect to good x'? b) What is the compensating variation (CV) with respect to the increase in the price of good x? (c) Show your answers on the appropriate graph

Initial Price of X can be assumed to be $1

Answer 1

u(x, y) = xy + x, M = 100, p_y = 4, p_x = 1 at eqn MRS = p_x/p_y, MRS = Mu_x/Mu_y = y + 1/x thus y + 1/x = 1/4, 80 4y + 4 = x from BC rightarrow x p_x + y p_y = M x + 4y = 100 put x = 4 + 4y, 4 + 8y = 100, 80 8y = 96 y = 12, x* = 4 + 48 = 52 when p_x uparrow to p_x' = 5, then so at eqn rightarrow y + 1/x = 5/4, 4y + 4 = 5x from BC 5x + 4y = 100 4 + 8y = 100, y = 12 x = 48 + 4/5 = 52/5 = 10.4 thus y* = 12, x* = 10.4 Now total effect is = 52 - 10.4 = 41.6 Now for sub effect original utility u_1 = u(12, 52) = 12 times 52 + 52 = 52 times 13 =