Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their long-run capital labor decisions.
Q = 500L0.6K0.8,
Where Q = annual output measured in pounds,
L = labor measured in person hours,
K = capital measured in machine hours.
Davy's employees are relatively highly skilled and earn $15 per hour. The firm estimates a rental charge of $50 per hour on capital. Davy forecasts annual costs of $500,000 per year, measured in real dollars.
a. Write the equation for the isocost line.
b. Determine the MRTS for the firm.
c. Determine the firm's optimal capital-labor ratio (expansion path).
d. How much capital and labor should the firm employ given a $500,000 budget?
e. Determine the firm's output.f. Is this an increasing, decreasing, or constant returns to scale production function? Explain