3.12 The quasi-linear function Consider the function U(x,y) =x+ Iny. This is a function that is used relatively frequently in eco- nomic 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.