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Profit Maximization and Total Revenue

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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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The solution explains the concept of marginal revenue/marginal costs and profit maximization really well. Overall, it is an excellent response with detailed answers to all the questions being asked by the student. The response clearly explains all the math involved in a step by step way which makes it easy for any student to understand these concepts.

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1.a) The firm's total revenue is: TR=p*q=(475 - 11q)q=475q - 11q^2
Then MR=dTR/dQ=475 - 22q
To maximize its profit, the firm will produce at the quantity where MR=MC, which is:
475 - 22q=500-42q + 3q^2 or 3q^2-20q+25=0 or (3q-5)(q-5)=0
Then q = 5 or 5/3.
If q=5, p=475 - 11*5=420 and LAC=500 - 21*5 +5^2=420, so P=LAC
If q=5/3, p=475 - 11*5/3=456+2/3 and LAC=500 - 21*5/3 +(5/3)^2=462+2/9 and P<>LAC
However, q=5/3 is at the beginning period of the scale of production.
b) As a perfectly competitive, the firm will produce at the quantity where p=LAC, which is:
475-11q=500-21q+q^2 or q^2-10q+25=0 or (q-5)^2=0 then q*=5
And p*=475 - 11*5=420. Since p = LAC, profit is zero.

2.a) Because as soon for each additional unit of input, it can produce more revenue than its cost, the firm can therefore make profit. Thus, to maximize its profit, ...

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