Consider an economy described by the textbook Solow model with a production function . The economy is producing 100 units of output and the productivity parameter is equal to 1. If the depreciation rate is 6%, the investment rate is 6%, and there are 125 workers, the growth rate of the economy_____:Group of answer choicesis positive because the economy is below its steady state.cannot be determined.is equal to zero because the economy is at its steady state.is negative because the economy is above its steady state.
Question
Consider an economy described by the textbook Solow model with a production function . The economy is producing 100 units of output and the productivity parameter is equal to 1. If the depreciation rate is 6%, the investment rate is 6%, and there are 125 workers, the growth rate of the economy_____:Group of answer choicesis positive because the economy is below its steady state.cannot be determined.is equal to zero because the economy is at its steady state.is negative because the economy is above its steady state.
Solution
In the Solow model, the steady state level of capital per worker is determined by the equation sA = (n + d)k, where s is the savings rate, A is the productivity parameter, n is the population growth rate, d is the depreciation rate, and k is the capital per worker.
In this case, we are given that the economy is producing 100 units of output, the productivity parameter A is 1, the depreciation rate d is 6% or 0.06, the investment rate s (which is the same as the savings rate in this model) is 6% or 0.06, and there are 125 workers.
First, we need to calculate the current level of capital per worker. Since the production function is not given, we will assume a standard Cobb-Douglas production function of the form Y = AK^αL^(1-α), where Y is output, K is capital, L is labor, and α is the capital share of income. If we assume α = 1/3 (a common assumption), then the current level of capital per worker (k = K/L) is (100/125)^(3/2) = 0.9487.
Next, we substitute the given values into the steady state equation to find the steady state level of capital per worker: 0.06*1 = (n + 0.06)k. Since the population growth rate n is not given, we cannot solve for the steady state level of capital per worker.
Therefore, without information on the population growth rate, we cannot determine whether the economy is above, below, or at its steady state, and thus cannot determine the growth rate of the economy. The correct answer is: cannot be determined.
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