# 3 An Equilibrium Business-Cycle Model

For this topic, there are two videos to watch:

video 1

video 2

## 3.1 Goods Market

In our equilibrium model, we can still apply demand and supply analysis to the final output market where Y-axis is the interest rate and X-axis is the final output quantity.

Let $$Y^{s}$$ be the total output from firms, which can be affected by capital and labor. Since capital is predetermined, only labor hiring is flexible.

1. Argue that when interest rate is higher, others being equal the final output will be higher. In other words, $$Y^{s}$$ is a positive sloped line.

Let $$Y^{d}$$ be the demand of total output, which can be divided into consumption C and investment I (=$$\Delta K+\delta K$$).

1. Argue that others being equal C is a negative sloped line.

We know that under non-arbitrage condition $$i=R/P-\delta$$. Given that a firm will always hire K until $$R/P=MPK$$, the condition can be expressed as $$i=MPK-\delta$$.

1. Argue that as i increases $$\Delta K$$ will decrease so that I is a negative sloped line.

2. Draw the equilibrium graph that determines Y and i in equilibrium.

## 3.2 Ageing society

Analyze the impact of an ageing society on output, consumption, investment as well as input prices and the interest rate.

1. What would happen to labor market?

2. What would happen to capital market? And its impact on interest rate.

3. What would happen to consumption, investment and the capital stock?

## 3.3 Incentive to save

Suppose households increase their incentive to save. They decide to increase their saving and cut down their consumption. In other words, they value their current consumption more now.

1. What would happen to labor market?

2. What would happen to capital market? And its impact on interest rate.

3. What would happen to consumption, investment and the capital stock?

## 3.4 Plague

Suppose a plague hit the economy which wiped out one third of the population. Analyze its impact on output, consumption, investment as well as input prices and the interest rate.

## 3.5 Typhoon

Analyze the impact of typhoon on output, consumption, investment as well as input prices and the interest rate.

## 3.6 the Economist

“Demography, growth and inequality: Age invaders”, Apr 26th 2014.

In the article, it mentions that

Larry Summers, a Harvard professor and former treasury secretary, argued that America’s economy appeared already to be suffering this sort of “secular stagnation”.

Secular stagnation refers to an economy with a shrinking population that would bring with it diminished incentives for companies to invest—a smaller workforce needs less investment—and hence persistent stagnation.

1. The article said whether we will suffer from secular stagnation depends on three channels that demography influences the economy. What are these three channels?

2. Regarding workforce, what’s the reason that highly educated people tend to work longer than the poorly educated ones?

3. The article mentioned that, “even as more educated old folk are working, fewer less-skilled young people are.” What is the reason?

4. The workforce will shrink, but the real size of workforce may not. What does “the real size” mean?

If the money saved finds productive investment opportunities it has the potential to boost long-run growth. But where will these opportunities be?

1. What are those opportunities? How promising are they?

2. Policies may prevent the economy from the stagnation suffering. What kinds of policies do you think they are? But the article is pessimistic about them. Why?