Consider a basic Solow–Swan model with constant labour force L and constant total factor productivity A. Suppose the saving rate is and the depreciation rate is . Suppose also that steady-state output per worker is 100. Steady state investment per worker is:

Question

Consider a basic Solow–Swan model with constant labour force L and constant total factor productivity A. Suppose the saving rate is  and the depreciation rate is  . Suppose also that steady-state output per worker is 100. Steady state investment per worker is:

BlackTom AI · Accepted Answer

Let's restate the information and then assess what we can determine from it.
- We are in a basic Solow–Swan model with constant labour L and constant total factor productivity A.
- The saving rate is given as s (value not provided in the prompt).
- The depreciation rate is given as δ (value not provided in the prompt).
- Steady-state output per worker is y* = 100.
- The question asks for steady-state investment per worker, i*.

Key relationships in the Solow model with no population growth (n = 0) are:
- In steady state, per-worker capital k* satisfies i* = δ k*, since investment per worker equals depreciation per worker at the steady state.
- Output per worker y* is a function of k*: y* = f(k*).
- Investment per worker i* equals s f(k*) = s y* in a standard model where all saving is invested.

From the data given, we know y* = f(k*) = 100. However, to determine i* = s f(k*) = s y*, we would need the saving rate s. Without s (the saving rate) and without δ (the depreciation rate) explicitly provided, we cannot compute δ k* or s y* numerically.

Therefore, even though the prompt lists a single numerical option '30' as an answer, the calculation cannot be completed correctly with the information provided. The missing values s and δ are essential to compute steady-state investment per worker i*; additionally, the specific form of the production function f (though implied to be standard per-worker production) does not by itself determine i* without s and δ.

If we were to proceed with any numerical result, we would need:
- The saving rate s to compute i* via i* = s y* = s × 100.
- Alternatively, the depreciation rate δ and the steady-state capital per worker k* (and the production function form to relate k* to y*) to compute i* = δ k*.

In summary, with the given information, the steady-state investment per worker cannot be uniquely determined, and the provided sole option '30' cannot be confirmed as correct without the missing parameters.

ECON10003_2025_SM1 Pre-Tutorial Quiz 8

Consider a basic Solow–Swan model with constant labour force L and constant total factor productivity A. Suppose the saving rate is and the depreciation rate is . Suppose also that steady-state output per worker is 100. Steady state investment per worker is:

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