1. Suppose that John, April, and Tristan have two production plants for producing orange juice. They have a total of 850 crates of oranges. The marginal product of oranges in plant 1 is MP1 = 1,000 - O1 and in plant 2 is MP2 = 1,200 - 2O2. What is the best assignment of oranges between the two plants?

2. You have an economics test in two weeks. It will cover both micro and macroeconomics. Each part will be worth 50 points. You have a total of 100 hours that you can spend studying for this exam. For the first 25 hours you spend studying microeconomics, you will get 1 point more for each hour of studying. After that, you will get 1 point more for each 3 hours you spend studying, up to the maximum possible of 50 points. Macroeconomics is different. For your first 15 hours of studying you will get 1 point for each 45 minutes you spend studying. After that, you will get 1 point for each 1.5 hours you spend up to the maximum of 50 points. How should you allocate your studying time to get the best grade? Why?

3. Jason has a boat-building firm. It uses labor L, capital K, and materials M, to build its boats. Its production function is Q = F(L, K, M) = AL^αK^βM^γ. For what values of α, β, and γ does Jason's technology have constant returns to scale? Increasing returns to scale? Decreasing returns to scale?

4. Suppose Noah and Naomi's weekly production function for garden benches is F(L) = (3/2)L, where L represents the number of hours of labor employed. The wage rate is $15 an hour. What is their cost function?

5. Suppose that the production function for Hannah and Sam's home remodeling business is Q = F(L, K) = 10L^0.2K^0.3. If the wage rate is $1,500 per week and the cost of renting a unit of capital is $1,000 per week, what is the least-cost input combination for remodeling 100 square feet each week? What is the total cost?

6. Noah and Naomi want to produce 100 garden benches per week in two production plants. The cost functions at the two plants are C1(Q1) = 600Q1 - 3Q1² and C2(Q2) = 650Q2 - 2Q2², and the corresponding marginal costs are MC1 = 600 - 6Q1 and MC2 = 650 - 4Q2. What is the best assignment of output between the two plants?

7. A price-taking firm's variable cost function is VC = Q³, where Q is its output per week. It has a sunk fixed cost of $3,000 per week. Its marginal cost is MC = 3Q². What is its profit-maximizing output when the price is P = $243? What if the fixed cost is avoidable?

8. Consider THE FOLLOWING QUESTION:Suppose Dan's cost of making pizzas is C(Q) = 4Q + (Q2/40), and his marginal cost is MC = 4 + (Q/20). Dan is a price taker. What is Dan's supply function? What if Dan has an avoidable fixed cost of $10?

If Dan's cost increases by $2 per pizza, so that his cost function becomes C(Q) = 6Q + (Q2/40) and his marginal cost becomes MC = 6 + (Q/20), how will his supply function change?

9. In each of the following cases, calculate the PDV of the specified amount under the specified circumstances.

a. $6,300 received in eight years, at an interest rate of 4 percent.

b. $115,000 received in two years, at an interest rate of 18 percent.

c. $45,000 received in 100 years, at an interest rate of 1 percent.

10. Calculate the PDV of the following bonds.

a. A 5-year bond with an annual coupon payment of $200, and a principle payment at maturity of $5,000, at an interest rate of 4 percent.

b. A 15-year bond with an annual coupon payment of $50, and a principle payment at maturity of $600, at an interest rate of 10 percent.

11. Fred and Barney are negotiating with each other to divide $4. Simultaneously, each proposes an integer between 0 and 4 (inclusive) to represent the amount that Fred gets. If they propose the same number, Fred receives the proposed amount and Barney receives the rest. If they propose different numbers, neither gets anything. Does either player have a dominant, weakly dominated, or dominated strategy? Identify all the Nash equilibria. Is there an equilibrium in which Fred and Barney don't reach an agreement (that is, in which they make different proposals)? If such an equilibrium exists, is it reasonable? Why or why not?