Final answer:
To find the capital stock for the next period, calculate the investment (0.25 × (1,000¹/₂) = 250) and depreciation (0.05 × 1,000 = 50), then add the investment to the current capital and subtract the depreciation (1,000 + 250 - 50 = 1,200). The capital stock next period will be 1,200, which is not among the provided options.
The corret opction is:d
Step-by-step explanation:
The question is about finding the capital stock next period in a given economy with specific parameters.
The production function is Y = K¹/₂, investment rate is 0.25, and depreciation rate is 0.05. With a current capital (K) of 1,000, we need to calculate the capital stock for the next period.
The investment made is 0.25 of the production output, and depreciation is 0.05 of the existing capital stock.
First, calculate the amount of investment:
- Investment = Investment Rate × Production
- Investment = 0.25 × (1,000¹/₂)
- Investment = 250
Next, calculate the depreciation:
- Depreciation = Depreciation Rate × Current Capital
- Depreciation = 0.05 × 1,000
- Depreciation = 50
To find the capital stock next period:
- Next Period Capital = Current Capital + Investment - Depreciation
- Next Period Capital = 1,000 + 250 - 50
- Next Period Capital = 1,200
Therefore, the correct answer is not listed among the options provided
The complete question is:Consider an economy with production function Y = K¹/2, an investment rate equal to 0.25, and a depreciation rate of 0.05. If K = 1,000 this period, the capital stock next period will be:
A) 2,000
B) 450
C) 1,250
D) 500