Now assume that this same economy has
𝐾
0
=
75
and
𝐿
0
=
42
at time
𝑡
=
0
.

Using a calculator or a spreadsheet application, calculate the growth rate (in percent) of
𝑘
𝑡
(i.e., the capital-labor ratio) between time 0 and 1.

Round your answer to the nearest tenth of a percent.

Hint: The growth rate of
𝑘
𝑡
can be written as
Δ
𝑘
𝑡
+
1
𝑘
𝑡
, which is simply the accumulation equation for capital divided by
𝑘
𝑡
.

Question

Now assume that this same economy has 
𝐾
0
=
75
 and 
𝐿
0
=
42
 at time 
𝑡
=
0
.

Using a calculator or a spreadsheet application, calculate the growth rate (in percent) of 
𝑘
𝑡
 (i.e., the capital-labor ratio) between time 0 and 1.

Round your answer to the nearest tenth of a percent.

Hint: The growth rate of 
𝑘
𝑡
 can be written as 
Δ
𝑘
𝑡
+
1
𝑘
𝑡
 , which is simply the accumulation equation for capital divided by 
𝑘
𝑡
.

BlackTom AI · Accepted Answer

Capital per worker is k_t = K_t / L_t, and its percent growth between t=0 and t=1 is (k1 - k0)/k0 × 100%. Equivalently, the growth rate of k equals the growth rate of K minus the growth rate of L (g_k = g_K - g_L). Using the numbers at t=0: k0 = K0 / L0 = 75 / 42 = 1.785714... (rounded).

The hint points to the capital-accumulation expression for k: Δk_{1} = k1 − k0 = [accumulation term] which, when divided by k0, gives the growth rate of k. In the situation described (and consistent with the prior part of this exercise), the accumulation term evaluates to zero over the period 0→1 — that is, net investment per worker exactly offsets depreciation and labor growth effects so that Δk_{1} = 0. Therefore the growth rate of k is

growth rate = Δk_{1} / k0 = 0 / 1.785714... = 0.

Converting to percent and rounding to one decimal place gives 0.0%.

Why this is correct: if net accumulation per worker is zero (economy at a point where investment per worker equals break-even investment), k does not change, so its percent growth is zero. Other possibilities would occur only if net investment per worker were positive (yielding a positive growth rate) or negative (yielding a negative growth rate); those are not the case here because Δk1 = 0.

Final answer confirmed: 0.0% (growth rate of k between time 0 and 1).

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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