Clara\'s utility function is U(X, Y) = (X + 2)(Y +1). Write an equation for Clar

Question

Clara's utility function is U(X, Y) = (X + 2)(Y +1). Write an equation for Clara's indifference curve that goes through the point (X, Y) - (2, 8). Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. Find an equation the describes Clara's MRS for any given commodity bundle (X, Y). Use the equations in parts b) and c) to solve for Clara's optimal bundle. Linus has a utility function U(x, y,) = x + 3y draw an indifference curve passing through the point (x, y) = (3, 3), then draw an indifference curve connecting ever bundle such that U = 6. What is an equation the describes Linus's budget if p_x= 1, p_y= 2, and income is 8. Add this line to your graph in part a). What bundle would Linus choose if prices change to if p_x= 1, p_y= 4, and income is 8.

Explanation / Answer

a) At (2,8) U(x,y) = (2+2)(8+1) = 36 Now 36 = (X+2)(Y+1) So Y = 36/(X+2) - 1

b) Equation from budget constraint is X+Y=11

c) MRS = dUx/dUy

dUx = dU/dX = Y+1

dUy = dU/dY = X + 2

so absolute value of MRS with price ratio is (Y+1)/(X+2) = 1

d) From X+Y = 11 & (Y+1)/(X+2) = 1 we get Y = 6 & X = 5

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