What does the indifference curve map for the utility function in Equation 3.34 look like? Although all the indifference curve maps in Figure 3.8 exhibit homothetic preferences, this need not always be true.

Consider the quasi-linear utility function utility = U(x, y) = x + ln y. (3.34)

For this function, good y exhibits diminishing marginal utility, but good x does not. The MRS can be computed as

The MRS diminishes as the chosen quantity of y decreases, but it is independent of the quantity of x consumed.
Because x has a constant marginal utility, a person’s willingness to give up y to get one more unit of x depends only on how much y he or she has. Contrary to the homothetic case, a doubling of both x and y doubles the MRS rather than leaving it unchanged.

/ MRS = =y. aulay l/y