The production function for a country is: Y= √(KL)
1. What will the real wage and the real rental price of capital be in equilibrium (a situation where firms maximize profits under perfect competition, and markets clear, that is the demand for capital is equal to 10 and the demand for labor is equal to 10)? Hint: MPK = 1/2√(L/K) and MPL = 1/2√(K/L).
2. What are the firm’s costs in equilibrium (expressed in dollars)? What are the firm’s profits?
3. Suppose now that technological progress changes the production function to Y=6 √(KL)
Does this new production function have constant returns to scale? (f) If the price of output is still $5, what are now the real wage and the real rental price of capital in equilibrium?
4. What are now the firm’s revenues and costs in equilibrium (expressed in dollars)?
5. How does technological progress affect the firm’s demand for capital and the firm’s demand for labor? You can draw graphs that include the demand for each factor before and after technological progress takes place.