Question

Note: this question requires careful thinking.

If output equals 30 √K , the savings rate equals 20%, and equilibrium output equals 1200, what is the depreciation rate?

Answer 1

The depreciation rate in this economy is approximately -16.14%.

Step-by-step explanation:

To find the depreciation rate, we need to use the equation for output: Output = 30 √K. We are given the equilibrium output which equals 1200, so we can plug that into the equation: 1200 = 30 √K. To solve for K, we need to isolate the variable, so divide both sides by 30: √K = 1200/30 = 40. To solve for K, square both sides: K = 40^2 = 1600.

Now that we have the value of K, we can calculate the depreciation rate. The depreciation rate is the difference between the investment and the output, divided by the investment: Depreciation rate = (investment - output) / investment. Substituting the given investment of $70 and the equilibrium output of 1200: Depreciation rate = (70 - 1200) / 70 = -1130 / 70 ≈ -16.14%. Therefore, the depreciation rate is approximately -16.14%.