Question8 Consider an economy with a Cobb-Douglas production function. Assume that the labour income share parameter is 1/3. The economy is producing 100 units of output and the productivity parameter is equal to 1. If the depreciation rate for capital is 6%, investment rate is 6%, and there are 125 workers in the economy. The growth rate in the economy: is equal to zero because the economy is at its steady state. is positive because the economy is below its steady state. cannot be determined. is negative because the economy is above its steady state. ResetMaximum marks: 1 Flag question undefined单项选择题
A
is equal to zero because the economy is at its steady state.
B
is positive because the economy is below its steady state.
C
cannot be determined.
D
is negative because the economy is above its steady state.

Question

Question8 Consider an economy with a Cobb-Douglas production function. Assume that the labour income share parameter is 1/3. The economy is producing 100 units of output and the productivity parameter is equal to 1. If the depreciation rate for capital is 6%, investment rate is 6%, and there are 125 workers in the economy. The growth rate in the economy: is equal to zero because the economy is at its steady state. is positive because the economy is below its steady state. cannot be determined. is negative because the economy is above its steady state. ResetMaximum marks: 1 Flag question undefined单项选择题

A

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

B

is positive because the economy is below its steady state.

C

cannot be determined.

D

is negative because the economy is above its steady state.

BlackTom AI · Accepted Answer

To assess the growth rate in this Solow-type setting with a Cobb-Douglas production function, we need to connect investment, depreciation, and population (labor force) growth.
Option 1: 'is equal to zero because the economy is at its steady state.' This would only hold if the economy is truly in a steady state with no exogenous technological progress and with population growth accounted for. However, whether we are at steady state cannot be concluded from the data given, because steady state requires balancing investment with effective depreciation plus population growth, which depends on the growth rate of the labor force n. We are not told n, so we cannot assert g = 0.
Option 2: 'is positive because the economy is below its steady state.' If the economy were below its steady state, we would expect positive per-capita or aggregate growth as capital accumulates to reach the steady state. Yet, again, determining whether we are below the steady state hinges on n and the current k level, neither of which is specified with enough precision here. Without n, we cannot confirm this scenario.
Option 3: 'cannot be determined.' This option acknowledges the missing information—the population growth rate (n) or the exogenous rate of technological progress (if any) needed to pin down the steady-state condition and the dynamic growth path. Since the Solow steady-state condition s f(k) = (δ + n) k involves n, and we only know s = 0.06, δ = 0.06, α = 1/3, Y = 100, A = 1, and no n, the growth rate g cannot be uniquely determined from the given data.
Option 4: 'is negative because the economy is above its steady state.' Being above the steady state would drive a negative growth phase (due to disinvestment or capital decumulation) only if we could confirm we are above that level, which again relies on n and the current k. Without those details, this claim cannot be established.
In summary, each of the first, second, and fourth statements relies on information (notably the population growth rate n or the presence of technology growth) that is not provided. Therefore, the only defensible stance given the data is that the growth rate cannot be determined from the information available at hand.