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

## III. Questions

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

- 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.]*

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

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

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

- 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* ].

- 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.