Spending and Output in the Short Run

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Suppose that Y > PAE, or Y > C + I + G + NX. Then, more has been produced than people planned to buy. The extra output must go into inventory, so actual investment is greater than planned investment. The buildup of inventories is the signal to firms to produce less. In the next period, firms will respond to this signal by lowering output.

Suppose that Y PAE, or Y C + I + G + NX. Firms haven’t produced enough, so they have to run down their inventories. What will they do next period? They will produce more.

Only when Y = PAE do we have equilibrium, where there is no tendency for firms to produce more or less.

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45º[pic 7][pic 8]

[pic 9]

If the equilibrium is where Y = PAE, then we must be on the 45-degree line.

If output is less than this, then PAE is greater than Y, firms’ inventories fall, firms respond by producing more, and we move toward the equilibrium.

If output is greater than the equilibrium, then Y is greater than PAE, firms’ inventories rise, firms respond by producing less, and we move toward the equilibrium.

Algebraically, we find equilibrium output by putting our equations together.

C = 200 + 0.8 (Y – T) consumption function

IP = 100 planned investment

G = 100 government spending

T = 100 net taxes = taxes – transfers

NX = 0 net exports

PAE = C + I + G + NX planned spending

Y= PAE equilibrium

PAE = ____ + ____Y

In equilibrium, Y = PAE.

Y = 320 + 0.8Y

Y – 0.8Y = 320

(1 – 0.8)Y = 320

0.2Y = 320

Y = 320/0.2

Y = _____

The Income-Expenditure Multiplier

How does the equilibrium level of output change when something else in the economy changes?

Suppose that planned investment changes.

The final change in output will be greater than the initial change in planned investment. There is a multiple effect on output, called the multiplier.

Multiplier = ratio of the final change in equilibrium output to the initial change in spending, e.g., ΔY/ΔI.

Why is there a multiple effect on output? Remember that output = income.

Investment spending ↑

⇒ output of investment goods ↑

⇒ income ↑

⇒ consumption ↑

⇒ output of consumption goods ↑

⇒ income ↑

⇒ consumption ↑

...and so on...

Example: Suppose that Dalhousie expects more students to enroll in the future and decides to spend $10 million to build a new residence. [Planned investment ↑ by ________]

Where does that $10 million go? It goes to construction firms who supply construction services, lumber mills which supply wood, steel mills which supply steel I-beams, and so on. [Output of investment goods and services ↑ by ________]

When output goes up by $10 million, the construction workers, the lumber workers, the steel workers all have higher income than before. [Income ↑ by ________]

What do all of these households do with $10 million more in income? They consume more goods and services, and they save more. If the consumption function is C = 200 + 0.8 (Y – T), then they will consume 80% of the increase in income and save 20%. [Consumption ↑ by ________, saving ↑ by ________]

When these households consume $8 million more of goods and services, they are buying consumer goods like food, clothing, cars, or furniture. [Output of consumption goods and services ↑ by ________]

The producers of consumption goods and services now have higher income. [Income ↑ by ________]

These households consume 80% of the increase in income and save 20%. [Consumption ↑ by ________, saving ↑ by ________]

...and so on...

Notice that each round of spending in this cycle gets smaller and smaller.

First round $10 million

Second round $8 million (0.8)(10)

Third round $6.4 million (0.8)(8)

Fourth round $5.12 million (0.8)(6.4)

Fifth round $4.096 million (0.8)(5.12)

...

In each round of spending, the increase in output is getting smaller, because the increase in output in each round is equal to the increase in output in the previous round times the MPC.

Where does all of this end?

Algebraically:

ΔI = 10 so I2 = 110

PAE2 = 330 + 0.8 Y

Y = PAE in equilibrium

Y = 330 + 0.8 Y

Y – 0.8Y = 330

0.2Y = 330

Y2 = 330/0.2 = _____, so ΔY = _____.

So when planned investment increases by 10, output increases by 50.

The multiplier is therefore equal to _____ in this example.

ΔY = 50, ΔI = 10.

ΔY/ΔI