Question

# 3. Suppose that a consumer has a utility function given by U(X,Y) = X^.5Y^.5 . Consider...

3. Suppose that a consumer has a utility function given by U(X,Y) = X^.5Y^.5 . Consider the following bundles of goods: A = (9, 4), B = (16, 16), C = (1, 36).

a. Calculate the consumer’s utility level for each bundle of goods.

b. Specify the preference ordering for the bundles using the “strictly preferred to” symbol and the “indifferent to” symbol.

c. Now, take the natural log of the utility function. Calculate the new utility level provided by each bundle.

d. Specify the new preference ordering for the bundles using the “strictly preferred to” symbol and the “indifferent to” symbol.

4. Suppose that you are consuming at a specific bundle of goods, and your marginal rate of substitution at the current bundle is 4. Suppose that the price ratio is currently 3.

a. How should you change the bundle of goods you are consuming to maximize your utility if your preferences are Cobb-Douglas?

b. Suppose now that you are consuming a different bundle of goods, and that your marginal rate of substitution at the new bundle is 3. Suppose that the price ratio has not changed. How should you change the bundle of goods you are consuming to maximize your utility if your preferences are Cobb-Douglas?

5. (5 points) Suppose that a consumer has the utility function U(X,Y) = XY^3 . The price of X is 12, the price of Y is 8, and the consumer has an income of 96. Solve for the consumer’s optimal consumption bundle. How much utility does the consumer receive from this bundle?

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