Question

A country has a production function of 100 √K a savings rate of 10%, a depreciation rate of 10%, and current capital stock, K, of 10,000. Assuming no change in technology, what will be the growth rate for this country?

Answer 1

Given the country's production function, savings rate of 10%, and an equal depreciation rate, the net investment is zero, leading to a growth rate of 0%. This simplification assumes no technology change or human capital improvement.

Step-by-step explanation:

The question is asking to calculate the growth rate of a country's economy given its production function, savings rate, and depreciation rate. Since we have a production function of 100 √K, a savings rate of 10%, and a depreciation rate of also 10%, with the current capital K being 10,000, we can begin our calculation for growth rate.

The output from the production function is 100 √(10,000) = 100 * 100 = 10,000. With a savings rate of 10%, the country reinvests 1,000 (10% of 10,000) in capital. Since the depreciation rate is also 10%, this means the entire amount saved just replaces the capital that depreciates; that is 1,000 (10% of 10,000). Hence, the net investment is zero and the growth rate of the economy in terms of capital is 0%.

It is important to note that while capital accumulation is a key factor in economic growth, other variables such as technological improvements and human capital investments also play a significant role in determining the actual growth of an economy.