Suppose that the production function for the economy is: Y = AK¹/⁴ᴸ³/⁴.Assume that real GDP is $8000 billion,capital stock is $32 000 billion,and the labour supply is 120 million (or 0.120 billion)workers.An increase in the capital stock of $1 billion will increase real GDP by

Question

Quizplus · Accepted Answer

To find the impact of an increase of $1 billion in capital stock on real GDP, we need to take the partial derivative of Y with respect to K and multiply it by $1 billion.
Taking the partial derivative of Y with respect to K, we get:
∂Y/∂K = (1/4)AK^(-3/4)L^(3/4)
Substituting the given values, we get:
∂Y/∂K = (1/4)(8000/32000)^(1/4)(0.120)^(3/4)
∂Y/∂K = 0.0625
Therefore, an increase of $1 billion in capital stock will increase real GDP by $0.0625 billion (or $62.5 million). 
Hence, the correct answer is option (B).

Suppose That the Production Function for the Economy Is: Y