# 1. Suppose that two units of X and eight units of Y give a consume...

## Question

1. Suppose that two units of X and eight units of Y give a consumer the same utility as five units of X and two units of Y. Over this range,
a. If the consumer obtains one more unit of X, how many units of Y must be given up in order to keep utility constant?
b. If the consumer obtains one more unit of Y, how many units of X must be given up in order to keep utility constant?

2. A consumer buys only two goods, X and Y.
a. If the MRS between X and Y is 4 and the marginal utility of X is 20, what is the marginal utility of Y?
b. If the MRS between X and Y is 3 and the marginal utility of Y is 6, what is the marginal utility of X?
c. If a consumer moves downward along an indifference curve, what happens to the marginal utilities of X and Y? What happens to MRS?

3. Betty purchases only pasta and salad with her income of \$160 a month. Each month she buys 10 pasta dinners at \$6 each and 20 salads at \$5 each. The marginal utility of the last unit of each is 30. What should Betty do? Explain.

4. Suppose the demand for good X is QD = 20-4P.
a. What is total revenue when P=\$1?
b. What is total revenue when P=\$2?
c. What is total revenue when P=\$4?
d. Calculate price elasticity of demand for a change in price from \$1 to \$2 (a to b). Now, calculate price elasticity of demand for a change in price from \$2 to \$4 (b to c).

5. The general linear demand for good X is estimated to be:
QD = 250,000 – 500P – 1.50M – 240PR

Where P is the price of good X, M is average income of consumers who buy good X, and PR is the price of related good R. The values of P, M, and PR are expected to be \$200, \$60,000, and \$100, respectively. Use these values at this point on demand to make the following computations.
a. Compute the quantity of good X demanded for the given values of P, M, and PR.
b. Calculate the price elasticity of demand (ED). At this point on the demand for X, is demand elastic, inelastic, or unitary elastic?
c. Calculate the income elasticity of demand (EM). Is good X normal or inferior?
d. Calculate the cross-price elasticity (EXR). Are the goods X and R substitutes or complements?

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1. Suppose that two units of X and eight units of Y give a consumer the same utility as five units of X and two units of Y. Over this range,
a. If the consumer obtains one more unit of X, how many units of Y must be given up in order to keep utility constant?
MRS xy = dx/dy here dx= 5-2 = 3 and dy = 8-2 = 6
MRS xy= 3/6 = ½ . For keeping the utility constant, when the consumer obtains one more unit of X, 2 units of Y has to be given up....

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