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Production Cost and Profit Maximization

Production Cost and Profit Maximization:

1. Fill in the following table from the data given below:


a. AFC for 8 units of output is 4.5.
b. AVC for 4 units of output is 15.
c. TC is increased by 14 when the 5th unit of output is added.
d. The ATC of 6 units of output is the same as the ATC of 5 units.
e. TC for 7 units of output is 168.
f. TVC is increased by 64 when the 8th unit of output is added.
g. AFC + AVC for 2 units of output is 40.
h. ATC is decreased by 10 when output is increased from 2 to 3 units.
i. It costs 26 more to produce one unit of output than to remain shut down.

2. You manage an agency that provides "Meals on Wheels" to infirm elderly residents in the county. The agency operates 3 kitchens. Each kitchen is producing one-third of the total meals per day. You learn that the marginal cost of each meal at the present output is $7 for kitchen 1, and $5 for kitchens 2 and 3. Assuming that you need to continue producing the same number of meals, how should you rearrange the production shares so as to decrease costs?

3. San Francisco Public Utilities is under pressure to upgrade its hazardous waste disposal stations. Staff has proposed two alternatives. Plan A would improve the current sites by installing new equipment with state-of-the-art technology and doing other renovations. Plan B would build new sites at nearby locations, then tear down the buildings and equipment at the current sites and sell the land. Under plan B the new sites (including cost of the land) would cost a total of $15 million. Improvements to current sites would cost $12 million. The current sites originally cost $10 million (in today's dollars) to build. It will cost $1 million to demolish the old buildings and equipment, but the land under the current sites could be sold for $5 million. Both plans produce the same quantity and quality of toxic wastes disposal. If the San Francisco Public Utilities wants to minimize costs, which plan should it choose? Why?

4. Sketch on one diagram the short run AVC, ATC, and MC curves for a firm with a fixed capital stock. (Assume a typical cost function as shown on page 194.)
a. Suppose the town where this firm is located passed a law requiring every business, no matter what its size, to purchase a $500 business permit. Which curves would be affected by the new law?
b. Repeat part (a) assuming the wage rate for labor rose instead of a new law.
c. Repeat again assuming instead that a tax on all capital equipment equal to 2% of its value is enacted.

5. The California Department of Health and Human Services is under pressure to reduce fraud in Medicaid. Although the extent of such fraud is not known, an article in the state's largest newspaper claims that 20 percent of the 2,000 weekly claims for Medicaid payments to physicians or hospitals contain some form of fraud (overcharges, billing for services not performed, etc.)
The Department Secretary is considering whether to hire more auditors. Experience in other states suggests that for each additional auditor hired, the percent of fraudulent claims can be reduced by half. That is, starting with a 20 percent rate, one more auditor will lower fraud to 10 percent, 2 more to 5 percent, and so on. This experience also shows that the state will save $100 on average for each fraudulent claim that is detected or prevented.
If the total cost to the state of hiring an auditor is $2,000 per week (includes cash wages, fringe benefits, travel costs and other support costs) and if the newspaper's estimate of the extent of fraud is correct, how many new auditors should be hired if the Secretary's main objective is to minimize the net budgetary impact of fraud? Assume auditors can only be hired on a full time basis.

6. An urban rapid-transit line runs crowded trains (200 passengers per car) at rush hours, but very empty trains (10 passengers per car) at off-hours. By law the rapid-transit line must make the same number of trips per hour at both rush and non-rush hours. A management consultant makes the following argument:
"The cost of running a car for one trip on this line is about $50 regardless of the number of passengers. So the per-passenger cost is about $.25 at rush hour but rises to $5 per passenger in off-hours. Consequently, you had better discourage off-hours business."
What do you think of the quality of this advice?

7. How would each of the following phenomena affect the long-run supply curve of apples? (assume that apple production is an increasing industry).
a. Workers in the apple industry form a union.
b. Consumers find out that apples cause cancer
c. Hard-to-control bugs that eat apples invade from Mexico.
d. The government sets a maximum legal price (price ceiling) at which apples can be sold.
e. Immigration laws change to permit more itinerant apple pickers to enter the country.
f. The government passes a minimum wage law for apple pickers.

Solution Preview

1. First, fill in the information you are given. Your chart will look like this:
0 26
2 D C 40-C
3 D-10
4 B 15
5 B+14 E
6 E
7 168 F
8 4.5 F+64

Now use the definitions of variable cost, fixed cost, and average total cost to fill in the missing lines. The chart will then look like this:

0 36 0 0 0 0 0
1 62 26 62 36 26 26
2 80 18 40 18 44 22
3 90 10 30 12 54 18
4 96 6 24 9 60 15
5 110 14 22 7.2 74 14.8
6 132 22 22 6 96 16
7 168 36 24 5.1 136 19.4
8 236 64 29.5 4.5 200 25

Remember that Total Variable Costs = Total Costs - Fixed Costs. Marginal cost is the additional cost we have when we produce one more unit of the good. Fixed costs will remain the same and we can calculate them because we are given the average fixed cost for 8 units. So 4.5 x 8 = 36 = TFC.

2. You want as much of the production as possible done in kitchens 2 and 3. It isn't clear from the problem what the capacity of each kitchen is, but if possible the best arrangement is half the meals from kitchen 2 and half from kitchen 3.

3. San Francisco Public Utilities is under pressure to upgrade its hazardous waste disposal stations. Staff has proposed two alternatives. Plan ...

Solution Summary

Production Cost and Profit Maximization, marginal benefit, and supply curve solutions.