Consider the Solow model. Which of the following are appropriate explanations of the situation represented in the above graph? (Select all that apply)

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BlackTom AI · Accepted Answer

Let’s carefully examine what the Solow model graph typically represents and what each statement implies.

Option 1: 'At point k0, the economy accumulates capital (per worker) because savings exceed the depreciation of capital and population growth rate.' This interpretation aligns with the intuition of the Solow model: if the investment (savings) per worker is greater than the required investment to cover depreciation plus the amount needed for accommodating population growth (i.e., to keep k constant), the capital stock per worker will rise from k0. On a standard s f(k) curve with depreciation δ and population growth n, the condition for an increasing k is s f(k) > (δ + n) k. The graph shows a point k0 to the left of the steady state k*, where the investment line (or the marginal product) and depreciation/popu lation dynamics would allow capital per worker to accumulate until the steady state is reached. In short, the statement captures the idea that at k0, net investment is positive, leading to capital accumulation. This makes sense conceptually for the Solow model.

Option 2: 'The economy reaches the steady state at point k*, which is stable.' In the Solow model, k* represents the steady-state level of capital per worker where the investment per worker equals depreciation plus population growth; beyond this point, if k is above k*, net investment is not enough to sustain higher capital per worker, causing k to decrease toward k*. Conversely, if k is below k*, net investment is sufficient to push k upward toward k*. This describes a stable (or globally attracting) steady state where deviations tend to revert back to k*. The graph typically demonstrates that k* is a stable equilibrium because the dynamics pull the economy toward k* from both sides. Therefore, this statement correctly describes the steadystate concept present in the Solow framework.

Option 1 vs Option 2 together cover two core aspects: (a) the early accumulation phase when s f(k) exceeds the required depreciation plus population growth, causing k to rise from k0, and (b) the existence of a stable steady-state at k*.

Option 3: 'At point k0, the economy accumulates capital (per worker) because it needs more capital to compensate for the additional workers and the depreciation of capital.' This is essentially a restatement of the positive net investment condition, but it may be interpreted as focusing solely on depreciation without explicitly mentioning population growth. In the common Solow presentation, the correct condition for k to rise is s f(k) > (δ + n) k, which combines depreciation and population growth. If the graph shows a rising path from k0 toward k*, this option could be considered partially accurate, but it is less precise because it does not explicitly acknowledge the role of savings relative to both depreciation and population growth in the per-worker context. It might be seen as an acceptable but less precise explanation depending on wording; however, the standard direct condition emphasizes both factors, not just depreciation.

Option 4: 'The economy reaches the steady state at point k*, but if we move to the right of this equilibrium point, we will find a higher steady state.' This statement conflicts with the typical Solow dynamics: there is a single steady-state per the model (in the basic version with constant n and δ and savings rate s). Moving to the right of k* would typically lead to a decline back to k*, not a higher steady state, because the net investment becomes negative above k*. Hence, this option describes an unstable or multiple steady states scenario, which is not correct for the standard Solow model represented by this graph. The graph’s slope around k* indicates convergence back to k*, not to a higher one, making this option incorrect.

In summary, the statements that correctly reflect the Solow model’s explanation of the graph are those that identify: (a) positive net investment at k0 leading to capital accumulation toward the steady state, and (b) the presence of a single stable steady state at k*. The remaining options either repeat a similar idea with less precision or contradict the standard steady-state dynamics of the Solow model.

ECON 13210 94 Introduction to Macroeconomic Models Midterm Exam

Consider the Solow model. Which of the following are appropriate explanations of the situation represented in the above graph? (Select all that apply)

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