3.13 The quasi-linear function Consider the function U(x, y) x ln y. This is a function that is used relatively frequently in economic

3.13 The quasi-linear function Consider the function U(x, y) ¼ x þ ln y. This is a function that is used relatively frequently in economic modeling as it has some useful properties.

a. Find the MRS of the function. Now, interpret the result.

b. Confirm that the function is quasi-concave.

c. Find the equation for an indifference curve for this function.

d. Compare the marginal utility of x and y. How do you interpret these functions? How might consumers choose between x and y as they try to increase their utility by, for example, consuming more when their income increases? (We will look at this ‘‘income effect’’ in detail in the Chapter 5 problems.)

e. Considering how the utility changes as the quantities of the two goods increase, describe some situations where this function might be useful.