1. Alice has preferences over bundles (x1,r2) of goods 1 and 2 that can be repre

Question

1. Alice has preferences over bundles (x1,r2) of goods 1 and 2 that can be represented by the following utility function: (a) (1 point) Write another utility function that can represent Alice's preferences. (b) (1 point) Draw the indifference curve associated with a utility of 6. This indif ference curve contains the points 4), -, 3), (2,-), (12-) (fill in the blanks) 12 12 (c) (1 point) Suppose pl = 2, p2 = 3 and m = 10, what bundle does Alice choose? (d) (1 point) Suppose p1-1, p,-3 and m = 10, what bundle does Alice choose? (e) (1 point) Alice's demand function for good 1 is (fill in the blanks) -for > P2 *1(P1, P2, m for > a

Explanation / Answer

a). [U (x,y) = min(x,y)] and corresponds to perfect substitutes [U(x,y) = 0.5(X+Y)]

u(x,y) = 0.5x + y if x >= y and x + 0.5y if y >= x

b). for U =6, (4,4), (4.5,3) (2,8), (12,0)

c) if p1 = 2 and p2 = 3 and m = 10

MRS (x1,x2) = -MUx1/MUx2 = -0.5/1 = -0.5

absolute value = 0.5

BC = 2x1 + 3x2 = 10

Slope of the BC = -2/3

absolute value = 2/3 = 0.6

Since MRSxy< slope of the BC, consumer will only use x2

optimal bundle (x1*, x2*) = (0,10/3)

d) if p1 =1 and p2 = 3 and m =10

BC = x1 + 3x2 = 10

slope of the BC = -1/3 = -0.33

absolue value = 0.33

MRXxy>slope of the BC, Alice will choose only x1 and zero X2

optimal bundle (x1*,x2*) = (10,0)

when x2 = 0, x1 = 10

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