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Five microeconomics problems involving supply and demand

1. Consider a competitive industry consisting of 100 identical firms each with the following cost schedule:
Output Total Cost
0 300
1 400
2 450
3 510
4 590
5 700
6 840
7 1020
8 1250
9 1540
10 1900

Market demand is given by the following schedule:
Price: $360 290 230 180 140 110 80
Quantity Demanded: 400 500 600 700 800 900 1000

a. Draw the supply curve for an individual firm. On a separate graph, draw the demand and supply curves for the industry as a whole. Indicate the equilibrium price and output. Now draw the individual firm's demand curve on your first graph and show the firm's equilibrium, price and output.

b. Explain why the equilibria found in part (a) are only short-run equilibria. What will happen to the industry in the long run? Describe the long-run equilibrium in detail.

2. Turnip farmers are complaining that the price of turnips is too low. They want the government to buy turnips for the school lunch program. Senator Smith notes that several years ago they had the same complaint. In response the government started to buy turnips to produce energy, a program that continues today. That made turnip farmers happy for a while, but now they're upset again, and there seems to be more of them than ever. Explain what happened, using a diagram or two.

3. After several years of rapid technological advance, the home insulation industry has settled down. All firms now use the same production method and entry into the industry is so easy that it is considered perfectly competitive. Each firm in the industry has the following cost functions:
TC = Q2 + Q + 90
MC = 2Q

where Q is the quantity of insulation, measured in pounds.

a. What is the supply curve for a single firm? Suppose there are 1,000 firms in the industry. What is the supply curve for the industry as a whole?
b. The market demand curve for insulation is: Q = 30,000 - 1,000(P). What are the equilibrium price and quantity in the insulation market?
c. How much does each firm produce and how much profit does each firm make?
d. [Parts d and e are harder than the other problems you have been assigned.] To encourage conservation, the government offers firms a subsidy of $3 per unit of insulation produced. What happens to price, quantity, and profits in the short run? Explain the changes in the insulation industry that this subsidy will lead to in the long run. Identify the welfare loss induced by the subsidy in the long run and compute its value.
e. Suppose instead of a subsidy, the government mounts a publicity campaign to encourage conservation, and as a result, the demand curve shifts to 35,000 - 1,000(P). What will happen in the short run and the long run?

4. The Quantum Electronics Company is about to market a new combination cell phone//PDA/camera/espresso maker. Its market research team predicts the following demand schedule for this revolutionary product:
Price ($) 400 380 360 340 320 295 270 240
Quantity 1000 1200 1400 1600 1800 2000 2200 2400

The company's engineers have estimated the costs of production as follows:
1. Development costs: $100,000.
2. Planning and construction of assembly lines: $80,000.
3. Overhead: $80,000.
4. Materials: $100 per set.
5. Labor: $60 per unit (10 hours at $6 per hour).
a. Calculate TR, MR, TC, TFC, TVC, and MC for each quantity of output given in the demand schedule.
b. What quantity should Quantum produce and what price should be charged if the company wants to maximize profits? What would profits be?
c. Suppose that the engineers discover an error in cost estimates. Assembly line costs should be $100,000 rather than $80,000. What quantity should Quantum produce and what price should be charged? What would profits be?
d. Suppose instead that Quantum's workers win a new contract calling for a wage of $10 per hour. What quantity should Quantum produce and what price should be charged? What would profits be? (Assembly line costs remain at $80,000.) Assume materials cannot be substituted for labor.
e. Now suppose an excise tax of $40 per unit is imposed. What happens to quantity, price and profits? (Wages and assembly line costs are as in part b.)

5. You are in charge of deciding how to allocate food-concession spaces at a large new airport. There are many spaces available. Two proposals have been made:
a. Auction the spaces in a single block, thus granting the winning bidder a monopoly of food services at the airport.
b. Auction the spaces individually, with the requirement that no firm can buy more than one space.
Under either option, many firms will be interested and will bid. Assume that there are no economies of scale here; i.e. it costs no more for two firms to sell 500 meals each than for one to sell 1,000 meals.
Which proposal would you pick to maximize the airport's receipts from the auction? Which would you pick to maximize overall net benefits to society of this activity? Explain.

Solution Preview

1. See attached spreadsheet "1." You can see how to graph supply and demand
curves. You should be able to construct another chart with both curves. You
can also find equilibrium by equating the equations for supply and demand,
which are shown on the charts.

In the long run, all inputs are variable, and firms can enter and exit the
market place.

2. See the attached file. Government subsidies move the supply curve
outward over the long term. This causes the price to fall. Prices will fall
in the long term as long as turnip growers are free to enter and ...

Solution Summary

Spreadsheet and graphs demonstrate how the forces of supply and demand create equilibrium in different circumstances.