Consider a consumer who each week purchases two goods, X and Y…

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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

1. 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.

2. On Curve A, what is the marginal rate of substitution (MRS) between the first two combinations of goods X and Y?

3. 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?

4. 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.)

5. What is the MRS at the utility-maximizing combination?

6. 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?

7. Draw the demand curve for good X between prices of $50 and $100, assuming it is linear in this range.

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