Instructions: Answer all five questions in this problem set. Each question is worth 20 points and consists of sub-parts. Partial credit is possible. For any questions involving mathematical problem solving, show your work. Wrong answers without work shown will receive 0 points. For questions that request graphing, you may create graphs on your computer, or you can draw the picture on a piece of paper and upload a .jpg to the Word doc.

You are the economic analyst for Cereal Brand A. Two attributes are important to different consumer segments buying cereal: the amount of sugar in grams, and the amount of fiber in grams. You are targeting consumers that have stated they budget \$5 for a box of cereal.
Cereal Brand Price Sugar (g) Fiber (g) Ratio Cereal per \$5 Sugar per \$5 Fiber per \$5
A \$2.69 11 4
B \$2.99 10 6
C \$3.99 11 3

``````Fill in the table above. Round to two decimal places whenever necessary.
Use the product attribute framework to graph the information above. Put sugar in grams on the y-axis and fiber in grams on the x-axis.  Construct product rays and an efficiency frontier. Label the three competitors carefully.

Is it possible to draw an indifference map to suggest there is a consumer segment that would maximize utility by purchasing A? If so draw it. Describe their marginal rate of substitution, or if not, describe why.
The CEO is concerned that consumers think of A as being a low-quality product because it is inexpensive, and wants to raise price to \$3.99 to compete with higher-quality cereals. Explain why you agree/disagree with this idea; if you agree, show this graphically and explain the impact on consumers in this market. If you disagree, what would be a more productive next step? Explain.
You sell good X. There are only two goods that people in your world can consume, good X and good Y. The average income of people in your world is \$1000. Good Y costs \$40. Good X costs \$40. You decide to offer a buy two, get one promotion, limit one per customer.
Draw budget constraint (B1) defined by this scenario with Good Y on the y-axis and Good X on the x-axis prior to the promotion. Draw budget constraint (B2) defined by the promotion. Label all axes and intercepts clearly.

Imagine that both X and Y are normal goods. Draw an indifference map that shows a plausible equilibrium condition for the consumer prior to, and following, the promotion. Explain.

What is the consumer’s marginal rate of substitution at the optimal consumption point?

Would a buy two, get one promotion be better than offering 33% off for you as the seller? Explain. (You are not required to draw this change on your diagram, though it may be helpful.)``````

In the graph below, a firm produces gizmos using capital and labor. The firm’s budget is \$3000. The wage rate of labor is \$50 per hour.

``````What is the price of capital?  Round to 2 decimal places if necessary.

How many units of output should the firm produce? Explain.

You would like to use additional capital and realize that you can maintain your output level at point A. Explain whether this would be a profit-maximizing choice, and why; if not, and you can afford point A, what should be done to fix it? ``````

Consider part d completely separately from a-c above.
A perfectly competitive firm sells 15 units of output at the going market price of \$10. Suppose its average fixed cost is \$15 and its average variable cost is \$8. Explain whether the firm should continue to produce or shut down.

Suppose the production function of automobiles is given by Q=K^(1⁄2) L^(1⁄2). Given a fixed amount of capital, the marginal product of labor is 0.5K1/2L-1/2.
What will happen to the marginal product of labor as the amount of labor rises, according to the production function? Why?
Suppose automakers in Country A and Country B produce on identical isoquants with this Cobb-Douglas production function and that labor costs are higher in Country A. Explain whether this means that workers in Country A are more productive than workers in Country B.
Now suppose automakers in both countries produce on identical isoquants, but the price of cars produced in country B is higher. Would autoworkers from Country A or Country B have a higher marginal product? Why?

Consider part d separately from parts a-c above:
A firm produces 4,000 units of output using 500 workers. Marginal cost is \$10, the wage rate is \$160, and total fixed cost is \$100,000. What is average variable cost?

A monopolist has demand and cost functions given by:

``````    P = 300 - 5Q
TC = 700 + 40Q
MC = 40``````

a. Find the monopolist’s profit maximizing/loss minimizing quantity and price.
b. Find the monopolist’s profit or loss based on part (a).
c. Based on the information in part (a), what is the elasticity of demand?
d. Given all of the information, explain whether this could be a long run outcome for a monopolist.

Sample Solution