Based on the information you have so far, you know that the economy is
[ Select ]
at
above
below
its steady state and GDP per capita is growing at
[ Select ]
a positive rate
a negative rate
a rate of zero
at time t.

Question

Based on the information you have so far, you know that the economy is 
[ Select ]
at
above
below
 its steady state and GDP per capita is growing at 
[ Select ]
a positive rate
a negative rate
a rate of zero
 at time t.

BlackTom AI · Accepted Answer

At the steady state capital per worker (k*) does not change over time, so output per worker (GDP per capita) is constant and its growth rate is zero. Relevant knowledge points: - In the Solow model, k = capital per worker and y = f(k) = output per worker. Investment per worker is sf(k) and break-even investment is (n + δ)k (population growth n and depreciation δ). - The steady state k* satisfies sf(k*) = (n + δ)k*, which implies Δk = 0. If capital per worker is constant, output per worker is constant (y = f(k*)). - If there is no exogenous technological progress, a steady state implies zero growth of GDP per capita. (With technological progress, GDP per capita grows at the exogenous tech rate — but that case is not indicated here.) Step-by-step reasoning: 1. Let k be current capital per worker. At steady state k = k* and by definition Δk = sf(k) − (n + δ)k = 0. 2. Because y = f(k), when k is constant at k* then y is constant at y* = f(k*). 3. A constant level of GDP per capita means the instantaneous growth rate of GDP per capita equals zero: (Δy/y) = 0. 4. If instead k > k*, then sf(k) < (n + δ)k so Δk < 0 and y would fall (negative growth). If k < k*, then sf(k) > (n + δ)k so Δk > 0 and y would rise (positive growth). Why the correct answer is correct: - “At” the steady state directly matches k = k*; under that condition net investment is zero, so capital per worker and output per worker do not change. Therefore GDP per capita grows at a rate of zero. Why other options are incorrect: - “Above” steady state implies GDP per capita is declining (negative growth). - “Below” steady state implies GDP per capita is increasing (positive growth). - Positive or negative growth rates contradict the steady-state condition of no change. Conclusion: The economy is at its steady state and GDP per capita is growing at a rate of zero, which matches the provided answer.

Based on the information you have so far, you know that the economy is [ Select ] at above below its steady state and GDP per capita is growing at [ Select ] a positive rate a negative rate a rate of zero at time t.Multiple dropdown selections

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