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Marginal Output and Productivity

Imagine there are 100 firms in a perfectly competitive industry. Each produces an output, q, using labour L and capital K according to the following short-run production function:
q = 5 + 4L - .25L2 + K
Each firm currently has five units of K. The price of each worker is $50 per day. The price of capital, K, is $100 per day. Suppose the industry is in long and short-run equilibrium.
a. How much output does each individual firm produce?
b. How much output does the entire industry produce?
c. What is the price of output in this industry?

Solution Preview

Each firm will produce an output where its marginal cost or total cost is minimized. This will happen where marginal product of labor per dollar of labor equals marginal product of capital per dollar of capital.
MPL/Labor wage = ...

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The solution goes into a great amount of detail regarding the question being asked. Step by step explanation is provided for each part of the question which makes it very easy to follow along for anyone with just a basic understanding of the concepts. Overall, an excellent response to the question being asked.