1. Leslie's current consumption bundle of 15 hot dogs and 10 sodas each week is on his budget constraint. At Leslie's current level of consumption, his marginal utility from hot dogs is equal to 7, and his marginal utility from soda is equal to 5. (Assume a Cobb-Douglas Utility Function.) The price of a hot dog is $3, and the price of a soda is $1.50.

A. Has Leslie maximized utility? Explain; and if she has not, tell if she should increase or decrease her consumption of each good.

B. Graphically depict this situation -illustrate his bundle, the budget constraint and indifference curve. Also, include where the optimal bundle would possibly fall if the current bundle is not optimal.

2. Jim's preferences over good (x) and good (y) are given by U(x, y) = 2xy. His income is $1000.

A. Calculate his optimal basket when Px = $50 and Py = $20. Show your work.

B. Calculate his income and substitution effects (to two decimal places) if Px falls to $40. Show your work.

C. Is good (x) normal or inferior? Support/Explain your answer.

D. Solve for the Compensating Variation. Explain what the value represents. Illustrate this in a graph. (In the graph - label all curves, baskets, and values of goods X and Y when appropriate - i.e., bundle levels and axis-intercept values.)

3. Suppose that Jack's indifference curves are graphed with good Y on the vertical axis and good X on the horizontal axis. At Jack's current consumption bundle the slope of his indifference curve is equal to -5. The price of good X is $10, and the price of good Y is $2.

A. How many units of good X would Jack be willing to give up to obtain one more unit of Y?

B. How many units of good Y would Jack be willing to give up to obtain one more unit of X?

C. Has Jack made an optimal choice? If not should he consume more X and less Y, or should he consume more Y and less X?

4. A cost-minimizing firm has the following production function: Q=K^1/3 L^1/3 . The price of labor, w, and the price of capital, r, are both $20.

A. (i) What is the solution to the firm's long run cost minimization problem (i.e.: solve for K and L) given that the firm wants to produce 400 units of output. (ii) What is the total cost of this level of output?

B. (i) What is the solution to the firm's short-run cost minimization problem (i.e.: solve for K and L) when the firm wants to produce 400 units of output, but capital is fixed at k-bar = 200 in the short-run. (ii) What is the total cost of this level of output when capital is fixed?

C. Fully explain the difference between your answers in (A) and (B).

5. You are given the following production function for a cost-minimizing firm: Q = 500K^0.5 L^0.5 The price of capital is $1,600 and the wage is $100.

A. The firm wants to produce 20,000 units of output. (i) Using the lagrangian approach compute the optimal levels of the capital and labor inputs. (ii) What is the total cost of production? Show all of your work.

B. Graph (A) - include the Isoquant (label Q=20,000 units), the Isocost line (label TC=______fill in the cost you solved for in (A)), the optimal input bundle (label A), the intercept values of the isocost line (provide values - not formulas), and the optimal levels of capital and labor (circle these on their proper axes). Don't forget to label your axes.

C. Now consider that the firm faces a financial (i.e. budget) constraint of $20,000. If the firm seeks to maximize output, using the lagrangian approach compute the optimal capital and labor inputs (assume long run adjustments). Also compute the resulting quantity of output with this financial constraint.

6. A firm finds that at its current level of output the marginal product of capital is equal to 5,000 units, and the marginal product of labor is equal to 250 units. The price of capital is equal to $10,000, and the wage is $400.

A. Does this firm currently have an optimal capital-labor ratio?

B. If the current capital-labor ratio is not optimal, should the firm employ more capital and less labor, or should the firm employ less capital and more labor?

C. Depict this scenario graphically (include the properly labeled input axes, the isocost line, the isoquant curve the firm is currently operating on (assume Cobb-Douglas), a potential point (X) that depicts the current input-bundle; and a potential optimal bundle (Z) with the corresponding isoquant curve).