Suppose that the saving rate for an economy is 0.75, the level of per capita capital stock is 80, the rate of depreciation is 0.02 and the rate of population growth is 0.04. What is the level of per capita income if this economy is in steady state?
Question
Suppose that the saving rate for an economy is 0.75, the level of per capita capital stock is 80, the rate of depreciation is 0.02 and the rate of population growth is 0.04. What is the level of per capita income if this economy is in steady state?
Solution
To find the level of per capita income in a steady state, we can use the Solow model's steady state condition. According to this model, in the steady state, investment (savings) equals depreciation plus population growth.
The formula for the steady state condition is:
s * f(k) = (n + d) * k
where: s = saving rate f(k) = production function (in this case, we'll assume it's k because income equals capital in the per capita terms) n = rate of population growth d = rate of depreciation k = level of per capita capital stock
Given in the problem: s = 0.75 k = 80 n = 0.04 d = 0.02
Substituting these values into the formula, we get:
0.75 * 80 = (0.04 + 0.02) * 80
Solving for f(k), we find that f(k) = 60.
Therefore, the level of per capita income in this economy, if it is in a steady state, is 60.
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