Suppose an economy's output is determined by a Cobb-Douglas production function Y =AKL1-a where A=8.K-2, L=64 and a=0.2.The total amount of national income paid to labour and capital, respectively, is
Question
Suppose an economy's output is determined by a Cobb-Douglas production function Y =AKL1-a where A=8.K-2, L=64 and a=0.2.The total amount of national income paid to labour and capital, respectively, is
Solution
The Cobb-Douglas production function is a particular form of the production function, commonly used in macroeconomics, that represents output (Y) as a function of total-factor productivity (A), capital input (K), and labor input (L).
Given the Cobb-Douglas production function Y = AKL^(1-a), and the values A=8, K=2, L=64, and a=0.2, we can substitute these values into the production function to find the total output.
Step 1: Substitute the given values into the production function
Y = 8 * 2 * 64^(1-0.2)
Step 2: Simplify the equation
Y = 16 * 64^0.8
Step 3: Calculate the value
Y = 16 * 28.97 (approximately)
Y = 463.52 (approximately)
So, the total output of the economy is approximately 463.52 units.
The total amount of national income paid to labor and capital is the same as the total output in the Cobb-Douglas production function. Therefore, the total income paid to labor and capital is also approximately 463.52 units.
However, to find the individual amounts paid to labor and capital, we would need additional information such as the wage rate and the rental rate of capital.
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