Consider an economy described by the textbook Solow model with a Cobb-Douglas production function with constant returns to scale with respect to K and L. Moreover, you know that the economy is producing 80 units of total output and the productivity parameter is equal to 1. If the depreciation rate is 10%, the investment rate is 10%, and there are 75 workers, the growth rate of GDP per person ____________.Single choice
A
is equal to zero because the economy is at its steady state
B
is negative because the economy is above its steady state
C
is positive because the economy is below its steady state
D
cannot be determined

Question

Consider an economy described by the textbook Solow model with a Cobb-Douglas production function with constant returns to scale with respect to K and L. Moreover, you know that the economy is producing 80 units of total output and the productivity parameter is equal to 1. If the depreciation rate is 10%, the investment rate is 10%, and there are 75 workers, the growth rate of GDP per person ____________.Single choice

A

is equal to zero because the economy is at its steady state

B

is negative because the economy is above its steady state

C

is positive because the economy is below its steady state

D

cannot be determined

BlackTom AI · Accepted Answer

Because s = δ = 0.10, the Solow steady-state condition s f(k*) = δ k* simplifies so that f(k*)/k* = 1. For a Cobb–Douglas per‑worker production function y = f(k) = k^α (A = 1), this yields k*^α / k* = k*^(α−1) = 1, and therefore k* = 1 (the nonzero solution). Consequently y* = f(k*) = 1^α = 1. Step-by-step reasoning and calculations: 1. Express output per worker: y = Y/L = 80/75 = 1.0666667. 2. Steady-state condition (no population or tech growth): s f(k*) = δ k*. With f(k) = k^α and s = δ, s k*^α = δ k* ⇒ (s/δ) k*^(α−1) = 1 ⇒ since s/δ = 1, k*^(α−1) = 1 ⇒ k* = 1. 3. Hence steady-state output per worker y* = f(k*) = 1. 4. Compare current y to steady-state: 1.0667 > 1, so current output per worker is above its steady-state level. Why this implies negative growth of GDP per person: Net accumulation of capital per worker is k̇ = s f(k) − δ k. If k > k* (equivalently y > y*), then s f(k) < δ k and k̇ < 0, so capital per worker falls over time; with a falling k, output per worker falls as well. Therefore GDP per person will decrease (negative growth) until the economy returns to the steady state. Why other outcomes are incorrect: - Zero growth would require y = y* = 1 (so s f(k) = δ k), but current y = 1.0667 > 1, so growth is not zero. - Positive growth would require y < y* (so investment exceeds depreciation), which is not the case here. Conclusion: The growth rate of GDP per person is negative because the economy is above its steady state, matching the provided answer.

Similar Questions

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