Which equation correctly represents the change in output per worker (ΔY), given output per worker (Y), savings rate (s), population growth rate (n), depreciation rate (δ), and technological progress rate (g)?A.ΔY = sY - (n + δ + g)YB.ΔY = sY - (n + δ)Y - gYC.ΔY = sY - (n - δ)Y + gYD.ΔY = sY + (n - δ)Y - gY
Question
Which equation correctly represents the change in output per worker (ΔY), given output per worker (Y), savings rate (s), population growth rate (n), depreciation rate (δ), and technological progress rate (g)?A.ΔY = sY - (n + δ + g)YB.ΔY = sY - (n + δ)Y - gYC.ΔY = sY - (n - δ)Y + gYD.ΔY = sY + (n - δ)Y - gY
Solution
The Solow model of economic growth suggests that the change in output per worker (ΔY) is determined by the difference between the amount of new capital per worker created through savings (sY) and the amount of existing capital per worker that is lost due to depreciation, population growth, and technological progress ((n + δ + g)Y).
Therefore, the correct equation that represents the change in output per worker (ΔY) is:
A. ΔY = sY - (n + δ + g)Y
This equation shows that the change in output per worker is equal to the savings per worker minus the sum of the rates of population growth, depreciation, and technological progress, all multiplied by the current output per worker.
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