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A firm’s production is represented by the following Cobb-Douglas function: ? = ?^2/3?^1/3. The rental rate,...

A firm’s production is represented by the following Cobb-Douglas function: ? = ?^2/3?^1/3. The rental rate, r, of capital is given by $200 and the price of labor is $100.

a) For a given level of output, what should be the ratio of capital to labor in order to minimize costs?

b) How much capital and labor should be used to produce those 300 units?

c) What is the minimum cost of producing 300 units?

d) What is the short run and long run cost of increasing output to 500 units?

e) Does this production function exhibit increasing, decreasing, or constant returns to scale? Answer based on the cost calculations in parts c and d.

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