Determining Rental Price of Capital and Real Wage in Equilibrium Factor Markets

Calculating Marginal Product of Capital and Labor

The production function provided is Y = 1.5 * (K^0.3)(L^0.7), where K = 343 and L = 512. To find the marginal product of capital (MPK) and labor (MPL), we need to take the partial derivatives of the production function with respect to K and L.

Calculating MPK:

dY/dK = 1.5 * 0.3 * (K^(-0.7))(L^0.7) = 0.45 * (343^(-0.7))(512^0.7)

Calculating MPL:

dY/dL = 1.5 * (K^0.3) * 0.7 * (L^(-0.3)) = 1.05 * (343^0.3)(512^(-0.3))

Determining Rental Price of Capital and Real Wage

When factor markets are in equilibrium, the rental price of capital equals MPK and the real wage equals MPL. By equating the calculated values of MPK and MPL to the respective factor prices, we can determine the rental price of capital and real wage in the given economy.

Once you have obtained the values of MPK and MPL using calculus, you can substitute these values back into the equations to find out the approximate rental price of capital and real wage in the equilibrium factor markets.

It's important to remember that these calculations are based on the assumptions of the production function and equilibrium in factor markets. Factors such as technological advancements and changes in market conditions can also impact the rental price of capital and real wage in an economy.

For further reference and understanding of Production Function, you can explore more resources on the topic here.