Question

Consider a consumer whose preference for burgers from “In-N-Out” and “The Habit” are such that she can perfectly substitute out one for another. That being said, the utility that she receives from consuming an In-N-Out burger (I) is four times that of the utility she receives from consuming a burger from The Habit (H).

(a) Write down the utility function.

(b) Find the MRS.

(c) Suppose I = $60,PI = $6,&PH = $5. Write down the budget con- straint.

(d) Draw an indifference curve and the budget constraint on the same graph using the numbers given in part (b). Make sure to label.

(e) Determine the optimal quantities of goods I and H.

(f) is I∗ homogenous? If so, to what degree?

(g) is H a normal good or an inferior good?

Answer 1

(a)Utility function:

u(I,H)= I+H

(b) MRS= constant

As the given two goods are substitutes, MRS will remain constant through out.

MRS= ∆Y/∆X or MUy/MUx.

It is the rate at which one good has to be given up for each additional unit consumed of another good.

With the help of given information, consumer gets 4 times more utility from In N out burgers than Habit burgers.

MRS=4

MRS is calculated in the picture attached.

(c) 60=6I+5H

Calculation done in picture attached.

(d) The IC and budget line will be same, negatively sloped towards X Axis. MRS will be 4 which had been calculated early.

Diagram attached in picture.