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An electricity-generating firm estimates its production function to be: Q = 10K(0.5) F(0.5) Where: Q =...

An electricity-generating firm estimates its production function to be: Q = 10K(0.5) F(0.5)

Where: Q = monthly electricity production measured in kilowatt-hours

K = machine hours (capital) per month

F = fuel in gallons per month

The rental cost of capital is $8 per machine hour and the cost of fuel is $4 per gallon.

A.) State and illustrate the conditions that determine the firm’s cost-minimizing use of fuel and capital. Determine the firm’s optimal ratio of fuel to capital.

B.) Suppose that this electricity firm is required by law to both operate within a fixed budget of $1200 per month as well as to produce enough that, at current prices, all demand is satisfied. It is estimated that the current demand is 5,000-kilowatt hours. Will the firm be able to satisfy both its budgetary and its demand requirements if it uses its inputs optimally?

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