Exercise 2
INDIFFERENCE CURVES

I. Objectives

• To sketch indifference curves
• To interpret the slope of an indifference curve at a point
• To understand the Law of Diminishing Marginal Utility
• To illustrate the Law of Diminishing Marginal Rate of Substitution

II. Data

• The equation for an indifference curve is given by: Y = 10000/X,
  where X is the amount of Good 1 (coconuts) and Y is the amount of Good 2 (bagels). This equation represents combinations of coconuts and bagels that yield the consumer the same level of utility (10,000 units in this exercise).

• Sketch the indifference curve. Plot coconuts on the horizontal axis. Note that the curve doesn't intersect either axis.

• Using the calculator below:
  1. Select a value for X.
  2. Click on Gimme Indifference Curve! to obtain the corresponding amount of bagels, and the slope of the indifference curve at that point.
  3. Technical note for the calculus-inclined: Slope = -Y/X.

III. Questions

1. Using the given equation, sketch the indifference curve with Good 1 (coconuts) on the horizontal axis.

2. Indicate Point M on the curve such that the number of coconuts consumed is 20. The corresponding number of bagels is _____, and the slope of the curve at that point is ______. [Note: You may obtain both values from the calculator above.]

3. At Point M, the consumer is willing to give up ________ bagel(s) in order to gain _____ coconut(s).

4. Consider Point N on the curve such that X = 100. At N, the marginal rate of substitution is ________ [ coconuts per bagel / bagels per coconut ].

5. Does the given indifference curve exhibit the Law of Diminishing Marginal Rate of Substitution? Explain.

6. Suppose the indifference curve is a negatively-sloped straight line. Using a sketch (with Good 1 on the horizontal axis), one may show that as the amount of Good 1 increases, the MRS [ decreases / increases / remains constant ].

7. According to the Law of Diminishing Marginal Utility, as the consumption of coconuts increases, ceteris paribus, the consumer's utility [ rises / falls ] at [ an increasing / a decreasing ] rate.