Answer :
The lowest cost necessary to produce y 40,000 outputs is $24,003,000.
Given the production function y = 10²k, where k is the capital input, the cost necessary to produce y should be derived under given constraints.
a) Production Function: y = 10²k
To produce y = 40,000, we solve for k:
40,000 = 10²k
k = 40,000 / 10²
Since 10² = 100, we get:
k = 40,000 / 100 = 400 units of capital.
Cost Calculation:
The given cost of the job is $3,000 and the interest rate is $60,000. We need to calculate the total cost using these values.
Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
Given FC = 3000 and if VC includes interest rate:
When k = 400 and interest rate (i) = 60,000:
VC = k x interest rate
VC = 400 x 60,000
VC = 24,000,000
Total Cost:
TC = FC + VC
TC = 3,000 + 24,000,000
TC = 24,003,000
Based on the available information, the correct answer is the lowest cost necessary to produce y = 40,000 is 4,000.
To find the lowest cost necessary to produce y = 40,000, substitute y = 40,000 into the production function and solve for k.
Given:
y = 10²k
40,000 = 10²k
Dividing both sides by 10², we get:
k = 40,000 / 10²
k = 4,000
Therefore, the lowest cost necessary to produce y = 40,000 is 4,000.
