Eco exam

Chapter 21: Saving and Capital Formation

ECON 3 - Principles of Macroeconomics University of California San Diego

Christopher Gibson

Monday, April 20th

Saving

Let’s first get some definitions out of the way.

• saving - current income minus spending on current needs

• saving rate - saving divided by income

• assets - anything of value that one owns

• liabilities - the debts one owes

• wealth (or net worth) - the value of assets minus liabilities

• balance sheet - a list of an economic unit’s assets and liabilities on a specific date

For example:

Year-end balance sheet Assets Liabilities

Cash $ 100 Car loan $ 10,000 Checking account 500 Credit card balance 450 Savings account 2,000 Insurance bill 150 Stock 900 Car 15,000 Total $18,500 $10,600

Net worth $7,900

Capital gains and losses

• capital gains - increases in the value of existing assets

• capital losses - decreases in the value of existing assets

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For example, what if in the balance sheet above, the stock price increased in value to $1,000 and car decreased to $14,950? Then change in wealth is

∆(wealth) = savings + capital gains − capital losses

Assuming no additional savings, we have a capital gain of $100 and a capital loss of $50, so the change in wealth is an increase of $50 to $7,950.

Stocks versus flows

• flow - a measure that is defined per unit of time

• stock - a measure that is defined at a point in time

Think about stocks and flows as water filling a bathtub. The stock is the total amount of water in the tub at any given time, while the flow is the net inflow (inflows minus outflows) during any period of time.

If, for example, 2 gallons of water flow in and 1 gallon of water flows out every minute, then the net inflow would be 1 gallon of water per minute. If we start with an empty tub, this rate of flow tells us that in 10 minutes, the stock in the tub will be 10 gallons.

Why do people save?

Some of the reasons that people save include the following.

• life-cycle saving - saving to meet long-term objectives such as retirement, college at- tendance, or the purchase of a home

• precautionary saving - saving for protection against unexpected setbacks such as the loss of a job or a medical emergency

• bequest saving - saving done for the purpose of leaving an inheritance

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Savings: An example

The two families the Thrifts and the Spends are alike in all but one way. The Thrifts save 20% of their income per year while the Spends only save 5%. Both families make income of $40,000 per year as well as any interest income from saving, with an 8% rate of return.

For example, since the Thrifts save 20% of income, in the first year their income is $40,000 and their savings is $8,000. In the second year, income is $40,000 plus 8% of their total savings of $8,000, giving total income

40, 000 + 0.08 · 8, 000 = 40, 640

The Thrifts will save 20% of this income ($8,128) and consume the rest ($32,512). Total saving will be $8,000 plus the $8,128 from the current year, giving $16,128. In 1987, income will be $40, 000 + 0.08 · $16, 128 = $41, 290.24. They will save 20% of this income, adding to their existing savings of $16,128. This process continues. The table below shows the paths of income, savings, and consumption for several years.

Thrifts Spends Year Income Savings (total) Consumption Income Savings (total) Consumption 1985 $40,000 $8,000 $32,000 $40,000 $2,000 $38,000 1986 40,640 16,128 32,512 40,160 4,008 38,152 1987 41,290.24 24,386.05 33,032.19 40,320.64 6,024.03 38,304.61

... ...

... ...

... ...

... 2000 50,753.45 144,568.88 40,602.76 42,468.38 32,978.16 40,344.96

... ...

... ...

... ...

... 2010 59,484.35 255,451.19 47,587.48 44,198.02 54,685.15 41,988.12

While the Thrifts initially do not consume as much as the Spends, by 2000 their consumption catches up, as their interest income on savings more than compensates for their lower rate of consumption, 80%.

Moreover, in 2000, total savings by the Thrifts reaches $144,568.88, while the Spends have only saved $32,978.16. Then by 2000, the Spends had saved less than the Thrifts had by 1987! This difference in savings only increases as the years go on, attributable to the power of compound interest.

The figure below shows the consumption path of both the Thrifts and the Spends. What the figure does not show is the wild disparity in their total savings that the Thrifts have available for retirement over the Spends!

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Why don’t people save?

We have seen why people do save (and, arguably, why they should save), but why do people not always save as much as they should?

• self-control - people prefer consumption today to consumption tomorrow �

called present bias or discounting future consumption

• demonstration effects - effects on the behavior of individuals caused by observation of the actions of others and their consequences

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E.g., you want to keep up with neighbors so you get a summer house in the Hamptons

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Then, when you summer in the Hamptons, all of your neighbors talk about their chateaus in France! (should you then buy a French chateau?)

• capital gains grow wealth in other ways

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As the above figure shows, there seems to be a tendency for household savings to decrease as capital gains (on housing and stock market assets) increase. Households may be more concerned with achieving wealth establishment goals instead of particular savings goals.

National saving

Recall that saving is current income minus spending on current needs. On a national level, it is tricky to determine what should be included in spending on current needs and what is not. Investment should not be in spending on current needs (mostly), since most of investment involves the accumulation of long-term capital. It is more difficult to determine the role of consumption and government expenditure, since these categories can include spending on long- lived durable goods, or short-lived nondurable goods. For simplicity, we will make the following assumptions.

1. All Consumption and Government expenditures are on current needs.

2. All Investment spending is on future needs.

3. The economy is closed, so that there is no international trade: M = X = NX = 0.

If we consider a closed economy, net exports are zero and

Y = C + I + G

We will define national saving as income minus spending: S = Y − C − G. Let T = Taxes − transfers− interest, net taxes. Savings becomes

S = (Y −T −C) + (T −G)

If we define Sprivate = Y −T −C and Spublic = T −G, then savings can be rewritten as

S = Sprivate + Spublic

So national saving is the sum of private saving plus public saving.

Government saving

Public saving, Spublic = T − G, is the government’s savings, which can be positive or negative. Notice the following.

Spublic > 0 =⇒ T > G =⇒ budget surplus Spublic < 0 =⇒ T < G =⇒ budget deficit

Here is data from the federal as well as state and local governments in 2015 and 2016.

Government savings in 2015 and 2016 Federal government State and local governments

Year Receipts Expenditures Surplus Receipts Expenditures Surplus 2015 2,063.2 1,906.6 156.6 1,303.1 1,293.2 9.9 2016 3,452.1 4,149.4 -697.3 2,416.3 2,583.7 -167.4

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As the table makes clear, the federal and state/local governments ran a budget surplus in 2015, but ran a deficit in 2016.

As the figure above shows, business saving has increased over the time horizon between 1960 and 2017, while household saving has decreased. Government saving is typically negative, so the government is typically a borrower.

Investment and capital formation

Like all economic decisions, capital projects will be undertaken if the benefits exceed the costs.

Investment and capital formation: An example

Carol is considering starting a junk disposal business and anticipates she can earn $49,000 per year. She must rent hauling truck for $8,500 per year, and she can earn 10% on investment funds. Alternatively, she can earn $40,000 per year if she keeps her current job. Will she start the business?

1. If she starts her own business, Carol will make revenues of $49,000 and incur costs of $8,500, yielding profit $49, 000 − $8, 500 = $40, 500

2. If she keeps her current job, Carol will make her salary of $40,000, but she can also invest her $8,500 she would have paid to rent the hauling truck at a rate of 10%. At the beginning of the year, this will be an outflow of the $8,500 investment, and at the end of they year she will be returned her investment with 10% interest, yielding total profit

40, 000 + 8, 500 · (1 + 0.01) − 8, 500 = 40, 850

So Carol would make $40,850 by keeping her current job.

Since Carol will earn more by keeping her current job ($40,850) than starting her business ($40,500), Carol will keep her current job.

Suppose instead that investment funds yield 5%. Would Carol’s decision change?

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1. If she starts her own business, Carol will still make $40,500 since this did not depend on the interest rate.

2. If Carol keeps her current job, she will make only 5% on her investment of $8,500, yielding total profit

40, 000 + 8, 500 · (1 + 0.005) − 8, 500 = 40, 425 So Carol would make $40,425 by keeping her current job.

Now, since Carol will earn more by starting her business ($40,500) than by keeping her current job ($40,425), Carol will keep start her own business.

Factors that affect investment include

As the previous example illustrates, there are many factors that influence the decision of whether or not to invest funds.

1. A decline in the price of new capital goods

• Imagine if Carol paid less to rent the junk hauling truck.

2. A decline in the real interest rate

• We saw this change Carol’s decision of whether to invest.

3. Technological improvement that raises the marginal product of capital

• This could increase Carol’s productivity and lead to revenue greater than the pro- jected $49,000.

4. A higher relative price for the firm’s output

• Like higher productivity, a higher relative price would lead to revenue greater than the projected $49,000.

5. Lower taxes on the revenues generated by capital

• While not addressed in our example above, any additional expense discourages in- vestment spending.

The supply and demand of loanable funds

• Who supplies loanable funds?

– Households are typically the suppliers of loanable funds, as they put money into savings, retirement accounts, and the stock market.

• Who demands loanable funds?

– Firms typically demand loanable funds, borrowing in order to finance long-term capital projects.

– Governments can be net borrowers or net lenders, but since the government typically runs a budget deficit it is more likely a net borrower, so it demands funds.

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What is the price of loanable funds?

The price of loanable funds is the real interest rate. This is the reward to supplying loanable funds (lending) and the cost of demanding loanable funds (borrowing).

Notice that the market for loanable funds reaches equilibrium just like any other market of supply and demand.

• If the real interest rate is too high, the supply of savings exceeds demand so savers are willing to take lower rates.

• If the real interest is too low, there is not enough lending (saving) in the market so firms will bid real interest rate up.

Changes in any of the above factors that affect the demand for loanable funds (except changes in the real interest rate) result in shifts in the demand for loanable funds. After a shift in loanable funds, the market is forced out of equilibrium. The market regains equilibrium at a higher/lower real interest rate through the forces described above.

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