# Consider an economy that uses two factors of production, capital (K) and labor (L), to produce...

###### Question:

Consider an economy that uses two factors of production, capital (K) and labor (L), to produce two goods, good X and good Y. In the good X sector, the production function is X = 4KX0.5 + 6LX0.5, so that in this sector the marginal productivity of capital is MPKX = 2KX-0.5 and the marginal productivity of labor is MPLX = 3LX-0.5. In the good Y sector, the production function is Y = 2KY0.5 + 4LY0.5, so that in this sector the marginal productivity of capital is MPK = KY-0.5 and the marginal productivity of labor is MPLY = 2LY-0.5. Finally, let the total endowment of capital in this economy be K = 800, the total endowment of labor be L = 1200, the price of good X be PX = 3 and the price of good Y be PY = 6.

What is the equilibrium rental rate of capital and the equilibrium wage rate?

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