investment in new capital

The story of economic growth goes on

• General framework: Y = F(L,K,T)

• Previous lecture looked at L and began an analysis of K

• Today we continue our discussion of capital (K) by using the model--developed last time--of the shares of spending in the whole economy

• We then go on to consider technology T

Spending Allocation Model(C/Y) + (I/Y) + (X/Y) + (G/Y) = 1

• In words, sum of spending shares equals 1

• Or: (C/Y) + (I/Y) + (X/Y) = 1 - (G/Y)

• LEFT HAND SIDE depends negatively on the interest rate. (Because each of C/Y, I/Y, and X/Y depends on interest rate)

• Find interest rate that satisfies the equation

• Then find (C/Y), (I/Y), (X/Y)

Recall this graph from previous lecture22_07

2.5

5.0

7.5

0.0

R

65.062.5 67.5

C

Y

(a) Consumption Share

R

2.5

5.0

7.5

0.015.012.5 17.5

I

Y

(b) Investment Share

R

2.5

5.0

7.5

0.08075 85

NG

Y

(d)

R

2.5

5.0

7.5

0.00.0 2.5

X

Y

(c) Net Exports Share

-2.5

PERCENT PERCENT PERCENT PERCENT

3. Investment andthe remainingshares are thendetermined fromthe interest rate.

First mark the shareof spending availablefor nongovernmentaluses; in this case 78because thegovernmentpurchases share isassumed to be 22percent.

1.

2.The intersection ofthese two linesdetermines theequilibrium interestrate, which can thenbe shown in all thediagrams.

NongovernmentShare

Can you draw this by hand as in an examination?

• Yes,

• Show all four graphs.

• Focus on the (d) graph

Now let’s watch what happens

Now consider the effects of an increase in G/Y

• That is, government purchases rise as a share of GDP (like 1980s Reagan defense buildup)

• “Permanent” or at least long lasting

• Look at long-run effects– About 5 years, but we are not really sure how

long the long run is

First use the rough sketch

Now look at the graphs drawn to scale to see what happens if G/Y increases by a particular amount ?

22_08

R

2.5

5.0

7.5

0.065.062.5 67.5

C

Y

(a) Consumption Share

R

2.5

5.0

7.5

0.015.012.5 17.5

I

Y

(b) Investment Share

R

2.5

5.0

7.5

0.08075 85

NG

Y

R

2.5

5.0

7.5

0.00.0 2.5

X

Y

(c) Net Exports Share

-2.5

PERCENT PERCENT PERCENT PERCENT

3.Thus, investment and theother spending shares fallby the amounts shown.

2. causing theinterest rateto rise.

1. The share availablefor nongovernmentuses falls by theamount thegovernment shareincreases...

(d) NongovernmentShare

Summary of effects of an increase in G/Y

• higher interest rate

• higher dollar exchange rate– (example: 160 yen per dollar rather than 120

yen per dollar)

• investment lower (I/Y down)

• lower net exports (X/Y down) – trade deficit rises

Key points about SAM

• Applies to the long-run– The short run effects could be different

• The interest rate is the real interest rate– real interest rate = interest rate minus

expected rate of inflation

• Can also look at other issues:– (G/Y) down, or shifts in (I/Y), (C/Y), or (X/Y)– good exam question!

Saving-investment approach

• Exploits idea that by definition national saving S = Y - C - G– or (S/Y) = 1 - (C/Y) - (G/Y) – thus S/Y is positively related to the interest rate

• Also (I/Y) + (X/Y) is negatively related to the interest rate

• Finally S = I + X– or S/Y = I/Y + X/Y

22_10 INTEREST RATE (R) (PERCENT)

2.5

5.0

7.5

0.015.012.5 17.5

SHARE OF GDP (PERCENT)

National saving rate

S

Y

22_11 INTEREST RATE (R) (PERCENT)

2.5

5.0

7.5

0.0

15.012.5 17.5

S

Y

SHARE OF GDP (PERCENT)

+I

Y

X

Y

The effects of an increase in government purchases (G/Y)

22_12

INTEREST RATE (R) (PERCENT)

2.5

5.0

7.5

0.015.012.5 17.5

S Y

SHARE OF GDP (PERCENT)

+I

Y

X

Y

A downwardshift in thenationalsaving rate...

Labor Alone: diminishing returns, subsistence, Malthusian equilibrium

23_03

LABOR INPUT

OUTPUT

Malthusian equilibrium: The output produced equals the output needed for subsistence; labor input neither increases nor decreases.

Labor input is increasing here because the output produced is greater than subsistence.

Labor input is declining here because the output produced is less than subsistence.

Subsistence line

Production function

The Malthusian dynamics23_02

20 100

1,000

5,000

In this region above the subsistence line, output per worker is greater than what is needed for subsistence. Population increases, raising labor input.

In this region below the subsistence line, output per worker is too low and people die of starvation, reducing labor input.

LABOR INPUT

OUTPUT Subsistence line

Labor and Capital Alone23_04

More output with the same labor input because there is more capital.

More capital

Less capital

A LABOR INPUT

OUTPUT

Adding capital avoids Malthusian equilibrium

23_05

More capital

Less capital

A B

If capital does not increase, output moves toward the subsistence line.

If capital increases, output can move away from the subsistence line even with the growth of labor input.

LABOR INPUT

OUTPUT Subsistence line

But capital also has diminishing returns, so growth would not continue with capital

and labor alone; need something else:

technology23_06

3 units of capital

2 units of capital

1 unit of capital

Sizes of output increases diminish.

LABOR INPUT

OUTPUT

4 units of capital

Some other evidence that technology is essential

23_07NUMBER OF PEOPLE FED PER WORKER

100

80

60

40

20

01840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

Use growth accounting formula: Y/L K/L T

Growth rate Growth rate Growth rate of real GDP per = 1/3 of capital per + of hour of work hour of work technology

where does 1/3 come from? growth rate of technology is computed as “residual” e.g.:

1955-75 = 2.0 - 1/3 (2.1) = 1.3

Now look at the productivity slowdown: productivity growth capital technology1955-75 2.0 = 0.7 + 1.31975-93 0.7 = 0.5 + 0.2

End of Lecture