Question

Assume that the production function for a country is given by and annual investment is given by the function where -0.3100, and that the yearly depreciation rate is 5.167%. Suppose that this year, the output in the country is l, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking. years

Answer 1

Answer

Y = K^1/2 and I = yY = 0.31Y

=> I = 0.31*K^1/2

Depreciation rate = 5.167% => Depreciation = 0.05167*K

dK/dt = Investment - depreciation = 0.31*K^1/2 - 0.05167*K

=> K_{t + 1} = K_t + 0.31*K_t^1/2 - 0.05167*K_t ------------------------(1)

Initially Y = 1 => Y = K^1/2 = 1

=> K = 1

We want Y = 1 + 50% of 1 = 1.5

=> K = 1.5² = 2.25

Hence we have to calculate time required to increase K from 1 to 1.5

Lets Use Excel to calculate t required to increase K from 1 to 2.25.

Initially K₀ = 1

Using (1) , We have the following result :

Y = K^1/2 and I = yY = 0.31Y = > I = 0.31 times K^1/2 Depreciation rate = 5.167% Depreciation = 0.05167 times K dK/dt = Investment - depreciation = 0.31 times K^1/2 - 0.05167 times K = > K_t + 1 = K_t + 0.31 times K_t^1/2 - 0.0516 times K_t (1) Initially Y = 1 Y = K^1/2 = 1 = > K = 1 We want Y = 1 + 50% of 1 = 1.5 = > K = 1.5^2 = 2.25 Hence we have to calculate time required to increase K from 1 to 1.5 Lets Use Excel to calculate t required to increase K from 1 to 2.25. Initially K_0 = 1 Using (1) , We have the following result: - We can see from the above table that time required to increase K from1 to 2.25 is approximately 5 years. Hence, the correct answer is 5 Years

We can see from the above table that time required to increase K from1 to 2.25 is approximately 5 years.

Hence, the correct answer is 5 Years