Suppose a government tried to mandate a real wage above the equilibrium real wage. Assuming that factor markets are otherwise free and competitive, explain why the higher real wage would fail to increase the share of labor income in national income

What will be an ideal response?

Given the Cobb-Douglas production function, the marginal product of labor is , and the marginal product of capital is . If each factor's price is equal to its marginal product, then its share of total income equals its exponent in the production function; 0.7 for labor, and 0.3 for capital. Firms will respond to the mandated higher real wage by reducing the quantity of labor demanded until the marginal product of labor is equal to the real wage. Workers who still have a job will have higher income, but many workers now have no job and no income. The reduced labor input lowers the marginal product of capital. Since the rental price of capital is unregulated, it will fall, so that no capital becomes idle. Since the prices of both labor and capital are equal to their respective marginal products, their shares of the reduced total output are unchanged.