Question

Assume that the production function for a country is given by =K‾‾√ and annual investment is given by the function =× where γ=0.320 , and that the yearly depreciation rate is 5.33 %. Suppose that this year, the output in the country is 1, 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:

Answer 1

To calculate the time required for a country's output to match its neighbor's, given that the neighbor's output is 50% higher, we use the formula relating GDP growth to time. By finding the growth rate using investment and depreciation rates, we solve for the years needed.

Step-by-step explanation:

The question asks us to calculate the time it would take for a country's output to catch up with its neighbor's, given the neighbor's output is 50% higher. Using the formula GDP at starting date x (1 + growth rate of GDP)years = GDP at end date, we can find this time by plugging in the respective growth rates, initial outputs, and the target output.

Assuming the country currently has an output of 1, and its neighbor has an output 50% higher, or 1.5, we need to find the country's growth rate and apply the formula. The investment function and depreciation rate need to be incorporated to find the net investment and hence the growth rate.

With the net investment and growth rate determined, we would solve for the number of years required for the first country to match the output of its neighbor by equating and rearranging the above formula to solve for the number of years.