# 2 Consumption: Part I

## 2.1 Household budget constraint

Household budget constraint basically equate household income flow to its expenditure flow.

1. Name all possible income flows that you can think of.

2. Name all the expenditure flows that you can think of.

## 2.2 Asset returns

In our video, there are two types of asset that can be used to accumulate wealth: machine and bond.

1. What is the return of machinery investment?

2. What is the return of bond?

3. Why do both returns equate each other in equilibrium?

4. In reality, asset returns are heterogeneous. Hence, different households have different asset returns. What affects their return values?

## 2.3 Investment demand

In macroeconomic model, investment usually refers to machinery investment.

1. Suppose future rental price is expected to increase so that $$R/P+(1-\delta)>1+i$$. What would happen to machine investment today? Can you give a scenario that future rental price is expected to increase?

2. Suppose today’s interest rate increases so that $$R/P+(1-\delta)<1+i$$. What would happen to machine investment today?

3. In reality, is it common that people borrow to invest in capital? What does it imply for the limit of our model?

## 2.4 Stock investment

A household may acquire stocks in its investment portfolio. Let S be today’s initial stock share holding and $$\Delta S$$ be the change of it so that tomorrow’s share holding will be $$S+\Delta S$$

1. Suppose at the beginning of today the stock pays a dividend of $$\d$$ per share. The household buy or sell the stock by $$\Delta S$$ units at the price of $$\q$$ after the distribution of dividends. Write down the household’s budget constraint.

2. stock price is fixed at $$\q$$ and it pays a constant dividend $$\d$$ per share. What is the income flow that can be generated from stocks? What is the investment term on stocks for household budget constraint?

3. Following (b), if the share price and the dividend is constant, what will be the implied asset return equilibrium condition between stock investment and bond investment?