Question

4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?

Answer 1

A) MRS = MUx/MUy

MUx = dU/dx = 1

MUy = dU/dY = 1/y

So MRS = y,

MRS is independent of good X,

so MRS is Constant along any line, for which Y is Constant .

Thus, with rise in Consumption of X, the rate at which one is willing to exchange X for Y, ( or rate at which X is substituted for Y) remains constant .

B) eqn of IC :

ln(y) = k - x

( For some Constant k)

C) MUx = 1, MUy = 1/y

So if Consumption of X rises by 1 unit, then Utility rises by 1 unit .

If Y Consumption rise by 1 unit, then Utility rise by 1/y units

Since good 1 is a necessity, so it's consumption is independent of income,

So when income rises, consumption of Y remains unchanged, so only consumption of X rises, & so utility also rises linearly with X.