Week 2 - Solo Model

Question 1

in the model set up what is the production function equal to?

Answer 1

Yt=F(Kt,Lbart)=(AbarKt^aLbar^1-a, and we assume Abar and Lbar are fixed over time

Question 2

In the model set up what is the Resource constraint equal to?

Answer 2

Yt = Ct + It, output can be used for consumption (Ct) and investment (It), This is called the resource constraint, assumes a closed economy (no imports and exports), as we’ll as no government expenditure

Question 3

In the model set up what is investment and consumption equal to?

Answer 3

• It = S bar Yt, where S bar is the fraction of output that is invested or equal to the saving rate.
• Ct= (1- S bar)Yt, as the 1-saving rate is what is consumed

Question 4

How is capital accumulated over time?

Answer 4

Investment leads to the accumulation of new capital, which can then be used in the production

Question 5

What is the capital accumulation equation and briefly describe the terms involved?

Answer 5

• Kt+1 = Kt + It - d bar Kt
• Where d is the depreciation rate, which tells us the fraction of the capital stock that is not useful in the next period, 0≤d≥1

Question 6

What is the absolute change in capital stock given by?

Answer 6

• Change in Kt+1 = Kt+1 - Kt = It - d bar Kt
• Substituting in what we know the investment and to be we get:
• Change in Kt+1 = s bar Yt - d bar Kt

Question 7

What are factor prices wt and rt equal to?

Answer 7

• Wt = MPLt = (1-a)Yt/L (Firms employ workers up until the point where wage me marginal product of labor)
• rt = MPKt = a Yt/Kt

Question 8

What are all the endogenous and exogenous variables in the Solo model?

Answer 8

• Endogenous Variables - Yt, Kt+1, Ct, It, wt, rt

- Exogenous parameters - A bar , S bar, d bar, L bar, Ko bar ( as this is what we need to start the economy) , alpha (a)

Question 9

What are the 2 ways in solving the Solo model?

Answer 9

1. Showing a graphical solution

2. Solving the model in the long run

Question 10

Under what conditions does the change in capital stock grow, decline, and stay constant?

Answer 10

• s bar Yt> d bar Kt, Kt grows the change in Kt+1 >0
• s bar Yt< d bar Kt, Kt declines the change in Kt+1<0
• s bar Yt = d bar Kt is constant, change in Kt+1=0, and the economy is in steady-state

Question 11

What are the Solow model diagram with output dynamics?

Answer 11

• When not in a steady-state, the economy exhibits a change In capital towards the steady-state.
• As Kt moves to its steady-state K, output Yt will also move to its steady-state Y
• At the steady-state, all endogenous variables are fixed

Question 12

What are the transition dynamics?

Answer 12

The process that takes the economy from its initial level of capital to the steady-state

Question 13

How do you solve analytically for the steady-state?

Answer 13

see notes

Question 14

Why does the economy reach the steady-state?

Answer 14

• As capital stock will either increase or decrease depending on whether investment > depreciation or vise versa.
• It will continue to increase or decrease until they are equal again and then reach a new steady rate.

Question 15

What are the 2 key takeaways of the solo model?

Answer 15

• Capital accumulation is not what causes growth in the long run.
• Investment is beneficial in the short run, but cannot sustain long-run growth due to diminishing returns.

Question 16

What is the effect of an increase In the investment rate s bar?

Answer 16

• The investment curve rotates upwards, while the depreciation curve remains unchanged.
• Investment temporality exceeds depreciation → capital increases towards a higher steady state.
• The new steady-state has higher capital and income per worker.

Question 17

What is the effect on the output of an increase in the investment rate s bar?

Answer 17

• Growth is constant during the steady-state.
• When the investment rate increases, the economy moves out of the steady-state and output grows quickly, but then begins to slow down and eventually level off due to diminishing returns.

Question 18

What is the effect of an increase In the depreciation rate?

Answer 18

• The depreciation curve shifts upwards, while the investment curve remains unchanged.
• Depreciation temporarily exceeds investment → capital decreases towards a lower steady-state.
• After a new steady state is reached, no growth in capital or income per worker.
• The new steady-state has lower capital and income per worker

Question 19

What is the effect on the output of an increase in the depreciation rate d?

Answer 19

• Output is Y* during the steady-state and growth is constant
• As the depreciation rate increases and the economy begins to contract output decreases very rapidly.
• After some time due to diminishing returns the fall in growth slows down and a new steady-state Y** is reached.

Question 20

Is the solo model consistent with Long-run growth rates?

Answer 20

The solo model does not explain why we observe different long-run growth rates in different economies, because of the law of diminishing returns in the LR

Question 21

Is the solo model consistent with income convergence which is the idea that poor countries are catching up?

Answer 21

The solo model predicts conditional convergence (the condition of having the same steady-state which is the same values of A bar, L bar, and d) and this is consistent shown by countries such as OECD countries.

Question 22

Is the solo model consistent in predicting long-run GDP levels?

Answer 22

The capital accumulation mechanism of the Solow model predicts cross-country gaps smaller than in the data.

Question 23

Considering 2 countries, if country 1 has a higher saving rate other than that these 2 countries are identical what does the Solo Model predict?

Answer 23

• In the long run, the GDP gap between the two countries will be positive and constant