Ch 4. The income-expenditure (keynesian) model and the market of goods and services

Question 1

What happens with the economy in short run?

What and who’s model aim to explain it

Answer 1

The income-expenditure model or keynesian model developed by John Maynard Keynes (1936)

Question 2

Expenditure model hypothesis

Answer 2

1. In the short run, prices and wages are rigid (unchanging). Prices vary to balance the market in response to changes in supply or demand, but many prices and wages do NOT adjust instantaneously, but slowly.
2. In the short run, the level of output in an economy is determined primarily by the level of spending that economic agents plan or wish to undertake.
3. Firms are willing to offer any quantity of output at the market price.
4. In the short run, capital and technology remain constant. It is only possible to increase output by increasing employment:
5. Production function: Y = N, where N is the number of employed persons.
6. There is (involuntary) unemployment. Since, in the short run, in order to increase output, employment must be increased, there must be unemployed people who want to work “at the market wage” but have not yet found a job.

Question 3

How does the government influence economy in the short run?

Answer 3

The economic authority of a country, through the implementation of economic policies (fiscal policies), can influence the level of production by dampening (amortiguando) periods of economic recession in order to prevent unemployment from rising too much.
As Y= C+I+G+X-M then:
* Every time production increases, employment increases, and this raises the income of the economy, which increases the disposable income (Yd) of households.
* Households: Yd = C + S
* An increase in consumption again leads to increases in demand, which generates new excess demand and new falls in stocks, so that companies increase production: secondary or induced effects.

Question 4

Consumption function (C)

Answer 4

C= C₀+ c x Y_d
where:
* C₀ : Autonomous consumption
* c: marginal propensity to consume (additional amount consumed by individuals when they recieve an additional euro of disposable income)

Question 5

About Marginal propensity to consume (MPC)…

Answer 5

It varies across people:
* Poor households with credit constraints react a lot to variation in current income, so their MPC is large
* Wealthy households, current income matters little for current consumption, so their MPC is small.

Expectations about future income are reflectes in autonomous consumption

Question 6

Factors affecting private consumption

Answer 6

Disposable income over the period (the relationship between disposable income and consumption is fairly stable over time). When talking about disposable income, we must distinguish between a one-off increase in income (sporadic, which will also modify our consumption behaviour on a one-off basis), and an increase in average or permanent income, which will affect our consumption behaviour in the long term. Yd = Y - T +TR
* Consumption increases when disposable income increases (and decreases when Yd decreases): Direct or positive relationship.
* But consumption does not increase in the same proportion as Yd. Part of the increase in disposable income goes to savings (Sp). The relationship between
the increase in consumption and the increase in disposable income is called the marginal propensity to consume (c).

Other: Expectations about the family’s future employment situation. Even if a
household has a high disposable income, if it thinks that it will not keep its job, it
will spend less.

Question 7

Savings function (S)

Answer 7

S= -C0 + s x Yd
As Y = C + S, then s = 1 - c (s: marginal propensity to save)
* At the beginning of working life and after retirement disposable income is very low. It increases until retirement
*

Question 8

Invesment function (I)

Answer 8

I = Î− 𝒃𝒊 + 𝒂𝒀
a: sensitivity of investment to a change of the economic activity (sales)
b: sensitivity of investment to a change of the interest rates (cost of financing)

• Factors affecting investment:
  
  • Companies’ current sales (+): approximated by GDP.
  • Expectations of future sales (+): through the development of indices based on business surveys (business confidence index).
  • The interest rate (-): in order to be able to buy assets (invest) companies have to take on debt and therefore the lower the cost of borrowing, the higher the investment.

Question 9

Public expenditure (G)

Answer 9

• The level of public spending is decided in the State Budget. Although governments tend to increase public spending when GDP falls, there is no stable function that can be determined in the short run.
• We therefore consider public expenditure as an EXOGEN variable (a given factor in the model, it does not depend on income).
• In addition to PSp, the public sector collects taxes (T) and pays transfers (TR):
  
  • Sg (government savings) = T - G - TR
  • If Sg > 0: public surplus (the SP is saving).
  • If Sg < 0: public deficit (the SP is dissaving)
• Taxes and transfers affect household disposable income: Yd=Y- T+TR
• There are two types of taxes to consider: proportional (income-dependent) or fixed.

Question 10

Proportional taxation scenario

Answer 10

• The amount of tax depends on the income: 𝑇 = 𝑡 x 𝑌, where t is the average tax rate in the economy (0 < t < 1).
• Therefore, given the same tax rate, lower income (GDP) implies lower tax collection and thus lower public savings.

Question 11

What is the relationship between transfers (TR) and income? + or -?

Proportional taxation scenario

Answer 11

Disposable income will be: Yd = Y – T + TR
Yd = Y – t Y + TR = (1 – t) Y + TR
And therefore, the consumption function will be:
𝐶 = 𝐶̅ + 𝑐 𝑌 − 𝑡𝑌 + 𝑇𝑅 ⇒ 𝐶 = 𝐶̅ + 𝑐 1 − 𝑡 𝑌 + 𝑐𝑇𝑅
Changes in level of income will affect public savings

Question 12

Determination of equilibrium income

Answer 12

• Only valid in the short run (rigidities in varibles and unemployed resources)
  Equilibrium condition: Agregate demand (DA) = GDP (Y)
  DA= C+I+G
  Assuming proportional taxes C= Co + c(1-t)Y+cTR
  Then DA=Y= Co + c(1-t)Y+cTR+I+G
  Y= 1/(1- c(1-t)) x (Co+cTR+I+G)
  In bold is marked the multiplier

Question 13

The multiplier effect

Answer 13

When finding income equilibrium we assume DA=Y we found that Y= multiplier x [Co +cTR +I +G]
Multiplier = 1/ [1-c(1-t)]
With this multiplier we can measure the change in output (Y) knowing the change in aggregate demand (DA).

Question 14

The multiplier process

Answer 14

Fall in investment → fall in DA → lower output(Y) and
income → further fall in demand and income → new equilibrium (Z)

Question 15

Relation between agregate demand (DA) and GDP (Y)

Answer 15

• If DA > Y (excess demand for goods): firms de-stock and decide to increase production.
• If DA < Y (excess supply of goods): firms accumulate stocks and decide to decrease production.
• DA can increase if any component of DA increases:
  
  • Private consumption increases (if ΔYd or if Δ C0)
  • Private investment increases
  • Government expenditure increases
• DA will decrease if any component of DA decreases:
  
  • Private consumption decreases (if ∇Yd or if ∇ C0)
  • Private investment decreases
  • Government expenditure decreases

Question 16

What happens if investment decreases

Answer 16

Starting from an equilibrium situation (DA=Y), the decrease in investment leads to a decrease in output: DA = f(I)
* Direct effect: ∇DA ⇒ Excess production or supply of goods ⇒ Increase or accumulation of firms’ inventories ⇒ Firms decrease their output by the same amount as DA decreases: ∇Y
* Induced effect: as ∇Y⇒ ∇Yd ⇒ ∇C y ∇Sp⇒ ∇DA since also DA = f(C) ⇒ Excess output ⇒ Increase in firms stocks ⇒ ∇Y

Question 17

What would happen in an economy if households decide to increase their savings?

Answer 17

• An increase in private saving may be caused by a reduction in autonomous consumption or by a reduction in the marginal propensity to consume.
• Given income, an increase in savings implies a reduction in consumption, which leads to a reduction in the demand for goods.
• The reduction in demand leads to an oversupply of goods and a build-up of inventories.
• Direct effect: firms decide to reduce their output by the amount by which demand has fallen. The reduction in output implies a reduction in employment and a reduction in income which generates induced effects:
  
  • The reduction in income negatively affects disposable income (and causes private consumption and savings to fall), leading to further falls in demand and reduction in output.
  • This second reduction in output leads to further declines in employment and income. The process of declining output and income will come to an end when the fall in income (output) tends to zero.
• The paradox of thrift = the aggregate attempt to increase savings leads to a fall in aggregate income.

Question 18

About expansionary fiscal policies…

Answer 18

Increase in public spending:
* ΔG ⇒ΔDA (destocking) ⇒ΔY up to Y’ = DA’
* The increase in income produces a sequence of indirect or induced effects:
* An increase in disposable income (Yd=Y(1-t)+TR) leading to an increase in private consumption and saving.
* The increase in private consumption leads to a further increase in DA.
* Excess demand for goods returns and inventories fall.
* Firms increase production again (by the same amount as demand has increased and therefore by the same amount as consumption has increased).

• The new increase in output is smaller than the first for several reasons:
  
  • Part of the increase in income goes to pay taxes.
  • Part of the increase in disposable income goes to savings.
  • If there were no taxes to pay and households did not save, this increase in output would be equal to the first one.
• The increase in income produces a new increase in Yd, in C (and Sp) and in DA, causing new excess demand and new increases in Y. The process will be repeated as many times as the first one.
• The process will be repeated so many times until the increase in Y is practically zero and therefore cannot give rise to new increases of C.

Expansionary policies are: Δ GP, Δ TR and ∇ t

Question 19

About contractionary fiscal policies…

Answer 19

Increase in taxes:
* Δ t ⇒ ∇ Yd ⇒ ∇ C ⇒ ∇ DA ⇒ Excess of production ⇒ Increase in stocks ⇒ ∇ Y
* Direct effect: as ∇ Y ⇒ ∇ Yd again⇒ ∇ C and ∇ Sp ⇒ ∇ DA
* Induced effect: ∇ DA ⇒ Excess of production ⇒ Increase in stocks ⇒ ∇ Y

Contractionary policies are ∇ GP, ∇ TR and Δ t