Consider a consumer who each week purchases two goods, X and Y. The following table shows three different combinations of the two goods that lie on three of her indifference curves-A,B, and C.
Indifference Curve
Quantities of goods X and Y, respectively
Quantitities of goods X and Y, respectively
Quantities of goods X and Y, respectively
A
1 unit of X and 4 of Y
2 units of X and 2 of Y
3 units of X and 1 of Y
B
1 unit of X and 7 of Y
3 units of X and 2 of Y
5 units of X and 1 of Y
C
2 units of X and 5 of Y
4 units of X and 3 of Y
7 units of X and 2 of Y
- With good X on the horizontal axis and good Y on the vertical axis, draw the implied indifference curves. Be sure to label all curves and axes completely.
- On Curve A, what is the marginal rate of substitution (MRS) between the first two combinations of goods X and Y?
- Suppose this consumer has $500 available to spend on goods X and Y and that each costs $100. Add her budget line to the graph you drew in part (a). What is the slope of the budget line?
- What is the utility-maximizing combination of goods X and Y for this consumer? (Assume in this exercise that the utility-maximizing combination always occurs at one of the combinations shown in the table.)
- What is the MRS at the utility-maximizing combination?
- Now suppose the price of good X falls to $50. Draw the new budget line onto your graph and identify the utility-maximizing combination. What is the MRS at the utility-maximizing combination? How much of each good does she consume?
- Draw the demand curve for good X between prices of $50 and $100, assuming it is linear in this range.