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