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The production function is given by Y=AK0.5L0.5, where Y is GDP, K is capital stock, and L is labour. The parameter A is equal to 5. if the capital is 100, labour is 400,  and both capital and labour are paid their marginal products. what is the real wage of labour?

Question

The production function is given by Y=AK0.5L0.5, where Y is GDP, K is capital stock, and L is labour. The parameter A is equal to 5. if the capital is 100, labour is 400,  and both capital and labour are paid their marginal products. what is the real wage of labour?

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Solution

The production function is given by Y = AK^0.5L^0.5.

Step 1: To find the marginal product of labor (MPL), we need to take the derivative of the production function with respect to L.

The derivative of L^0.5 is 0.5L^-0.5, so the MPL is 0.5 * AK^0.5L^-0.5.

Step 2: Substitute the given values of A, K, and L into the MPL equation.

MPL = 0.5 * 5 * 100^0.5 * 400^-0.5 = 0.5 * 5 * 10 * 0.05 = 1.25.

Step 3: The real wage of labor is equal to its marginal product, so the real wage of labor is 1.25.

This problem has been solved

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