# Profit Maximization

Please be as specific as possible and break-down answers in simple steps.

1. A monopolistically competitive firm faces a demand curve given by p=475 - 11q. It has a total cost curve given by LTC=500q - 21q2 + q3. The firm's long run average and marginal cost curves are LAC=500 - 21q + q2 and LMC=500 - 42q + 3q2. The slope of the LAC is 2q - 21.

a. Calculate the long-run equilibrium output for this firm. What price will the firm charge for this equilibrium output? Is the price equal to LAC? Prove your answer.

b. If the firm were producing at the minimum point on its LAC curve, as a perfectly competitive firm would be in the long run, what would its equilibrium price-quantity combination be?

3. Suppose the productitvity of labor and capitol are as shown below. The output of these resources sells in a perfectly competitive market for \$1 per unit. Both labor and capital are hired under perfectly competitive conditions at \$4 and \$3 each, respectively.

Units of capital MP of capital Units of labor MP of labor
1 24 1 11
2 21 2 9
3 18 3 8
4 15 4 7
5 9 5 6
6 6 6 4
7 3 7 1
8 1 8 0.5

a. What is the profit-maximizing combination of labor and capital for the firm to employ? What is the resulting level of output? What is the economic profit?

b. If the price of the output in the perfectly competitive market falls to \$0.50, what is the new profit-maximizing combination of labor and captital for the firm to employ? What is the resulting level of output? What is the economic profit?

3. Coke and Pepsi are two American soft drink companies that have been operating in Russia, which was part of the Soviet Union until 1991, for some time now. The market demand curve for soft drinks in Russia is given by Q=119 - 0.5P. Coke's short-run total and marginal cost curves are given by STC=3q2 + 48q + 572 and SMC=6q + 48. Pepsi's short-run total and marginal cost curves are given STC=6q2 + 18q + 849 and SMC=12q + 18.

a. If Coke and Pepsi for a cartel to market soft drinks in Russia, calculate the ccartel's profit-maximizing, price-quantity combination.

b. Calculate the profit-maximizing output produced by Coke and Pepsi.

c. Calculate the profits earned by the cartel and by each firm.

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#### Solution Preview

...e must have the Marginal Revenue Product (MRP) of one input equals its MC, which is MP*P = MC,
or MP = MC/P while P is 1\$
For Labor, the MCl = 4, then we should find the optimal MPl=MCl/P=4/1=4. From the table, we can easily find that 6 units of labor's MPl is 4.
In the same way, for capital, MCk=3, MPk=MCk/P=3/1=3. We can find from the table that 7 units of capital's MPk is 3
Then the profit-maximizing combination of labor and capital is 6L+7K. At this level of input,
For labor, output is 11+9+8+7+6+4=45. Then revenue=45*1=45, and cost = 4*6=24;
For capital, output is 24+21+18+15+9+6+3=96. Then revenue=96*1=96, and cost = 3*7=21.
Therefore, the total resulting level of output= 45+96= 141
The total revenue=141*1=141, the total cost =24+21=45
So the economic profit=141-45=96\$

b) Still, we have MP = MC/P while P falls to 0.5
For ...