In the short run, the change in the trajectory above features
[ Select ]
a negative
no
a positive
level effect and
[ Select ]
a negative
no
a positive
growth effect.

Note: The growth effect is determined by the growth rate of GDP per capita between
𝑡
∗
(the date of the parameter change) and
𝑡
∗
+
1
.

Question

In the short run, the change in the trajectory above features 
[ Select ]
a negative
no
a positive
 level effect and 
[ Select ]
a negative
no
a positive
 growth effect.

Note: The growth effect is determined by the growth rate of GDP per capita between 
𝑡
∗
 (the date of the parameter change) and 
𝑡
∗
+
1
.

BlackTom AI · Accepted Answer

A positive level effect and a positive growth effect: increasing a parameter that raises productivity or the effective output-per-worker (for example, a permanent rise in A in a Cobb–Douglas production function) immediately shifts the output path upward and also raises the growth rate during the transition to the new steady state.

1) Relevant knowledge points
- Level effect: the immediate vertical shift in the time path of GDP per capita at the date t* when a parameter changes.
- Growth effect (short-run/transitional): the change in the growth rate of GDP per capita measured between t* and t*+1. In Solow-style models, a permanent positive shock (higher A or higher saving rate) raises current output per capita and induces extra capital accumulation, generating above-normal growth until the new steady state is reached.

2) Step-by-step reasoning
- At t* a parameter (e.g., productivity A) increases. With capital unchanged at that instant, output per capita y = A·f(k) rises proportionally with A: this is an immediate positive level effect.
- Because output is now higher, savings (s·y) and hence investment are higher, so next period’s capital stock k_{t*+1} increases relative to the no-shock case. That extra investment produces additional output growth between t* and t*+1 above the previous growth rate: a positive short-run growth effect.

3) Numerical illustration (intermediate steps)
- Assume y = A·k^{0.5}, k_{t*}=4, initially A=1: y_{t*}=1·√4=2.
- Suppose A jumps to 1.1 at t*: y_{t*}=1.1·√4=2.2 → immediate level increase of 0.2 (10%).
- With s=0.2 and n+δ=0.1: k_{t*+1}=4 + 0.2·2.2 − 0.1·4 = 4 + 0.44 − 0.4 = 4.04.
- y_{t*+1}=1.1·√4.04 ≈ 1.1·2.01 ≈ 2.211. Growth from t* to t*+1 = (2.211−2.2)/2.2 ≈ 0.5% > 0. So growth effect is positive.

4) Why the correct answer is correct
- The immediate upward movement in output at t* is the positive level effect. The higher output raises investment and capital accumulation so the growth rate in the next period is higher than before — the positive growth effect.

5) Why other options are incorrect
- “Negative level” or “no level” contradict the fact that output rises immediately when productivity or a parameter that directly multiplies output increases.
- “Negative growth” would require the shock to reduce incentives, productivity, or effective demand; here the parameter change is assumed positive, so growth cannot be negative in the short-run transitional period.

Conclusion: Both the level effect and the short-run growth effect are positive, matching the provided answer: a positive level effect and a positive growth effect.

类似问题

24. In countries with well-developed economies, economic growth tends to:

24. In countries with well-developed economies, economic growth tends to:

24. In countries with well-developed economies, economic growth tends to:

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.

In the long run, the change in the trajectory above features [ Select ] level effect and [ Select ] growth effect.

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