ECON 3710 – Assignment 3: Due Tuesday 4/28106 pts.
Please answer all of the questions and show all of your work. Partial credit will be given.
This is your last assignment so enjoy the questions!!
1. (22) Suppose you run a business that produces high end dog food. Your business produces 3,000 dog food cans per day, and can sell all cans at $2.00/can regardless of how much is produced. Your firm currently employs twenty workers, each of whom earns $12/hour and work 8 hours per day. Inputs, like the meat for the food and the metal for the can, cost $1.00/can. Your overhead expenses, including rent, property taxes, insurance, etc., which doesnotvary with the number of cans produced, equals $250 per day.
- (5) Calculate your company’s current daily profit.
You must decide whether or not to produce additional cans. To produce more you would need to hire additional workers, all of whom will be paid $12/hour. Material costs remain constant at $1.00/can and you could sell all additional cans at $2.00/can. You determine that if you hire a 21st employee, your firm would produce an additional 200 cans per day, and that the number of additional cans from each additional worker would be decreasing by 30 (so a 22nd employee could produce an additional 170 cans per day, a 23rd employee could produce an additional 140 cans per day, etc.).
- (5) Calculate the marginal costs associated with producing additional cans for employees
21 to 25.
c. (8) How many employees should your firm hire, how many cans should you produce, and what is your company’s daily profit?
d. (4) Suppose your fixed costs were $350 per day instead of $250 per day. What is the profit maximizing number of employees and what is your company’s daily profit?
2. (10) A bottling company uses two input to produce bottles of the soft drink Sludge: bottling machines, K, and workers, L. The isoquants have the usual convex shape. The machine costs $1,000 per day to run; the workers earn $200 per day. At the current level of production, the marginal product of the machine is 200 bottles per day, and the marginal product of labor is 50 bottles per day.
a. Is this firm producing at minimum cost? Briefly explain how you know.
b. If it is not minimizing costs, explain how the firm should change the ratio of inputs it uses to lower its cost.
3. (20) A U.S. apparel manufacturer is considering moving its production abroad. Its production function is Q=L0.7K0.3. In the U.S., w=$8 and r=$3. In Asia, the firm would pay w=$4 and r=$4. The firm plans to produce 1,000 units in each plant.
a. What are the optimal amounts of L and K in each country?
b. What are their total costs in each country?
c. What are the marginal costs associated with producing the last unit in each country?
d. What would the cost of production be in Asia if the firm had to use the same factor quantities as in the U.S.?
e. Suppose the firm sells all of the clothes it manufactures in the U.S. Will this firm move production to Asia or keep production in the U.S. (what else does it depend on)?
4. (15) Many large pharmaceutical companies spend billions of dollars every year on the research and development of new drugs.
a)(10) Suppose a pharmaceutical company estimates that if they spend $1 billion on the development of a new drug, they can expect to earn $100 million in accounting profit as a result (so their stream of future revenue would be $100 million higher than all of their explicit costs, including the R&D costs). Just based on this information, does it necessarily mean that this company should develop this drug? What does the decision of whether to invest in this new drug (or another) depend on?
b)(5) Some people have criticized pharmaceutical companies for not investing heavily in drugs that could treat debilitating illnesses like Tourette syndrome or muscular dystrophy. Why would pharmaceutical companies be willing to invest more heavily in drugs that treat say, erectile dysfunction or hair loss, than these highly debilitating illnesses? What could the government do to address this issue?
5. (15) Suppose all firms in a perfectly competitive industry have a cost function given by:
TC = 10Q2 + 100Q + 100.
a.) What is the profit maximizing quantity of each firm if the current market price equals $500?
b.) What are the profits of each firm?
c.) Calculate the firm’s marginal cost and average cost at the profit maximizing quantity
6. (24) A competitive constant cost industry consists of 100 firms. The total cost function for each firm is given by TC = 200Q + 15Q2 + 375. The market supply curve is given by P = 200 + 0.3Q.
The demand curve faced by the industry is given as P = 400 - 0.1Q.
a.) What is the equilibrium price and quantity produced by the industry as a whole?
b.) What is the profit maximizing quantity for each firm?
c.) How much profit is each firm making?
d.) What is the producer and consumer surplus in the entire market?
e.) What is the producer surplus for each firm?
f.) Suppose demand increases to P = 500 – 0.1Q. Explain what will happen to the market price, quantity of production, and each firm’s profit in the short-run and the long run (no math required, just explain).