1. A firm operates with the production function Q=K2L. Q represents the daily output when the...

1. A firm operates with the production function Q=K²L. Q represents the daily output when the firm rents K units of capital and employs L workers. The manager has been given a production target: Produce 8,000 units per day. She knows the daily rental price of capital is $400 per unit. The wage rate paid to each worker is $200 per day.

a. Currently the firm employs 80 workers per day. What is the firm’s total daily cost of producing if it rents just enough capital to produce at its target?

b. Given the combination of capital and labor employed in part (a), is the firm minimizing the cost of producing 8,000 units of output? Explain by comparing the MRTS_LK and the input price ratio (or the additional output per dollar spent on each input) and a carefully sketched isocost/isoquant diagram.

c. In the long run, how much K and L should the firm employ in order to minimize the cost to produce 8,000 units of output per day? What will the total daily cost of production be?

Expert Solution

MRTS(L,K)= MPL/MPK. In equilibrium this equals to the input price ratio,i.e. with (w/r).

Rahul Sunny answered 2 years ago

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