Clara’s utility function is U(X, Y) = (X + 2) (Y + 1), where X is her consumption of good X and Y is her consumption of good Y.
(a) Write an equation for Clara’s indifference curve that goes through the point (X, Y) = (2, 8). Y = 26/X+2 −____. On the axes below, sketch
Clara’s indifference curve for U = 36.
(b) Suppose that the price of each good is 1 and that Clara has an income of 11. Draw in her budget line. Can Clara achieve a utility of 36 with this budget? ______
(c) At the commodity bundle, (X, Y), Clara’s marginal rate of substitution Is _____
(d) If we set the absolute value of the MRS equal to the price ratio, we have the equation
______
(e) The budget equation is _______
(f) Solving these two equations for the two unknowns, X and Y, we find X = 5 and Y = ______.