Question

Determine the amount of capital available to society if output is $3220 and there are 1225 laborers using a Cobb-Douglas production function with an alpha of 0.5 and a level of technology that quadruples output.

Answer 1

To determine the amount of capital available to society, use the Cobb-Douglas production function with the given values of output, laborers, and the level of technology. Solve the equation to find the amount of capital.

Step-by-step explanation:

To determine the amount of capital available to society, we need to use the Cobb-Douglas production function. This function is given by the equation Y = A * K^α * L^(1-α), where Y is the output, A is the level of technology, K is the capital, L is the labor, and α is the capital's share in the production function. In this case, α is 0.5.

Given that output is $3220 and there are 1225 laborers, we can substitute these values into the production function. The equation becomes 3220 = A * K^0.5 * 1225^0.5.

Since the level of technology has quadrupled the output, we can divide both sides of the equation by 4. The equation becomes 805 = A * K^0.5 * 1225^0.5. To solve for K, we can rearrange the terms as K = (805 / (A * 1225))^2.