Question

Let X be the quantity of hamburgers and Y be the quantity of soft drinks. Draw indifference curves that represent the following individuals' preferences for hamburgers and soft drinks. Find MRSXY in each case.

1. Joe’s preference is U(X, Y) = XY. Does Joe like hamburgers? Soft drinks?

2. Jane loves hamburgers and dislikes soft drinks. If she is served a soft drink, she

   will pour it down the drain rather than drink it. Her preference is U = 10X.

3. Molly’s preference is U(X, Y) = min {X, 2Y}. Does Molly like hamburgers? Soft

   drinks? Does she like or dislike hamburgers and soft drinks the same way as Joe?

4. Bob’s preference is U(X, Y) = 2X + Y. Does Bob like hamburgers? Soft drinks?

Answer 1

X = hamburgers

Y = soft drinks

Joe Preferences:

U = XY

Joe likes both Hamburgers and Soft drinks. His elasticity for both the goods is equal to 1.

MRS = MUx / MUy

MUx = Derivative of U wrt X

MUx = Y

MUy = Derivative of U wrt Y

MUy = X

MRS = Y/X

Indifference curves for Joe are convex

Jane Preferences:

U = 10X

MRS = 10

Soft Drink is a bad good for Jane

Molly Preferences:

U = Min(X, 2Y)

Molly likes soft drinks and hamburgers and treat them as perfect complements i.e consume them together.

Joe does not consume hamburgers and soft drinks in fixed proportions. However, Molly consume them in fixed proportions. So, the consumption nature of both the goods for Joe and Molly is different.

MRS = 0 at horizontal part of IC

MRS = infinity at vertical part of IC

MRS = undefined at kinked part of IC

at equilibrium X = 2Y

Indifference curves are L-shaped curves

Bob's preferences:

U(X, Y) = 2X + Y

Bob treats soft drinks and hamburgers as perfect substitutes of each other. He will consume either Soft Drink and no Hamburger or Only hamburger and No soft drink depending upon their relative prices.

MRS = MUx / MUy

MRS = 2 / 1 = 2

ICs are straight downward sloping lines.