Suppose a consumer has preferences over newspapers (x) and books (y) that can be

Question

Suppose a consumer has preferences over newspapers (x) and books (y) that can be represented by the quasilinear utility function U(x, y) = x + 2 . The marginal utilities are MUx = 1 and MUy = 1 / Is the assumption that more is better satisfied for both goods? Does the marginal utililty of books (y) diminish, remain constant, or increase as the consumer buys more books? What is the expression for MRS x,y? Is the MRS x,y diminishing, constant, or increasing as the consumer substitutes more x for y along an indifference curve? On a graph with newspapers on the horizontal axis and books on the vertical axis, draw a typical indifference curve (it does not have to be exactly to scale, but It should reflect a diminishing MRS). Indicate on your graph whether the indifference curve will intersect either or both axes. Show that the slope of every indifference curve will be the same when y = 4. What is the value of that slope?

Explanation / Answer

a. no b. decrease c. MRSx,y=MUx/MUxy =sqrt(y) d. remains constant U(x,y) = x+ 2(y)^0.5 U'(y) = y^(-0.5) U'(x) = 1 Set them equal to each other 1 = y^(-0.5) The indifference curve should be a vertical line starting at y=1.

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