Question

1. a. Nickels and dimes are perfect substitutes. Draw the indifference curves that represent your preferences for them, with dimes on the vertical axis, and nickels on the horizontal axis. (12 pts)

b. Are the slopes of the indifference curves positive or negative? (2 pts)

c. The slope of an indifference curve measures the consumer’s marginal rate of substitution (MRS) between two goods. Is MRS constant in the graph you draw? (correctly answering this question, 1 pt) What is the economic meaning behind the MRS, or the slope of the indifference curve, for two perfect substitutes? (explain the economic meaning of MRS, in a way that is reasonable, 3 pts)

2. A consumer allocates her income on two products, X and Y. Consider the price of good Y rises. Draw a graph to show how the satisfaction-maximizing choice changes.

Answer 1

1.

(a) Nickels and dimes are perfect substitutes. If we denote Nickels as N and Dimes as D, then the perfect substitute utility function is of the following form:

U(N, D) = N + D

The indifference curves are drawn in the following diagram.

The indifference curves are IC1, IC2, IC3.

(b) We can see that, the indifference curves are straight line and the lines are negatively sloped. Hence, the slope of the indifference curves are negative.

The slope of the indifference curves are negative.

(c) The slope of an indifference curve measures the consumer’s marginal rate of substitution (MRS) between two goods.

Also, from the above diagram, we can see that the indifference curves are straight lines. We know that the slope of a straight line is always constant. Hence, the slope of the indifference curves are always constant. Hence, MRS is also constant.

The MRS is constant in the graph above.

✓ The economic meaning of MRS or slope of indifference curve is

The rate at which a consumer can give up one good in exchange of another good in order to maintain the same utility level. The rate may be constant or diminishing.

The economic meaning of MRS or slope of indifference curve for two perfect substitutes is:

The consumer can give up Nickels in exchange of Dimes at a constant rate to remain on the same indifference curve.

2. A consumer allocates her income on two products, X and Y. The budget constraint for X and Y is drawn in the following diagram. The indifference curves are convex (Cobb-Douglus type).

If price of Y rises, then the budget line tilts. The initial budget line is the green line AB and the budget line, after price of Y rises, is the blue line A*B.

Now, satisfaction is maximized where the IC is tangent to the budget line.

Initially the satisfaction maximization point was E1 where the consumer was consuming X1 units of X and Y1 units of Y.

After the price change, the satisfaction maximization point ia E2 where the consumer is consuming X2 units of X and Y2 units of Y.

Hence, consumption of X decreases from X1 to X2. Also consumption of Y decreases from Y1 to Y2.

Hope the explanations are clear to you my friend.