Aggregate demand and equilibrium GDP Topic 1.1 Basic Macroeconomic relationships

Basic Macro Relationships We focus on the three basic macroeconomic relationships. Income and consumption, and income and saving. The interest rate and investment. Changes in spending and changes in output.

Learning objectives How Changes in Income Affect Consumption (and Saving) About Factors Other Than Income That Can Affect Consumption How Changes in Real Interest Rates Affect Investment About Factors Other Than the Real Interest Rate That Can Affect Investment Why Changes in Investment Increase or Decrease Real GDP by a multiple amount?

Students should be able to Describe the income-consumption and income-saving relationships. Recognize, construct, and explain the consumption and saving schedules. Identify the determinants of the location of the consumption and saving schedules. Calculate and differentiate between the average and marginal propensities to consume (and save). Describe the relationship between the interest rate, expected rate of return, and investment. Identify the determinants of investment and construct an investment demand curve. Identify the factors that may cause a shift in the investment-demand curve. Describe the reasons for the instability in investment spending. Provide an intuitive explanation of the multiplier effect. Calculate the multiplier and changes in real GDP given information about changes in spending and the marginal propensities. Discuss why the actual multiplier may differ from the theoretical examples.

Basic relationships Income, Consumption & Saving S = DI - C Income refers to disposable income which is the most important determinant of both consumer spending and saving DI = C + S Consumption is a function of income Saving is also a function of income What is not spent is called saving or unconsumed part of income is saving S = DI - C

THE GOODS MARKET NIA measures the nations output but doesn’t tell us why output increases more rapidly in some years than others. We use economic theory and models such as, the Keynesian model of income determination to determine the factors that influence economic activity. Components of the Keynesian Model: Consumption function Shows the r/ship between consumption & level of income. - Consumption varies directly with income. i.e.

Consumption fn is expressed as: 𝐶 = 𝑎 + 𝑏𝑌 Where: C - consumption a – autonomous consumption b – marginal propensity to consume Y - income Autonomous consumption is consumption that is independent of income. The MPC is the change in consumption due to a change in income. 𝑀𝑃𝐶= ∆ 𝑖𝑛 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 ∆ 𝑖𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 = ∆𝐶 ∆𝑌 e.g. if income increases by P400 resulting in an increase in consumption by P300 what will be the MPC?

Consumption and Saving The Consumption Schedule Shows the amounts that households plan to consume at various levels of disposable income Direct relationship, with households spending a larger proportion of a small DI than of a large DI. The Saving Schedule Shows the amounts that households plan to save at various levels of disposable income Direct relationship, with households saving a smaller proportion of a small DI than of a large DI. Break-Even Income The income level at which households plan to consume their entire incomes, with 0 saving.

Consumption and Saving Schedules 500 475 450 425 400 375 45° Consumption Schedule Consumption (Pula) 50 25 Income (Pula) Saving Schedule Saving (Pula) Income (Pula)

Average & marginal propensities Average Propensity to Consume (APC) the fraction or % of total income that is consumed (APC = consumption/income). Average Propensity to Save (APS) the fraction or % of total income that is saved (APS = saving/income). DI is either consumed or saved, APC and APS must exhaust the total income; (APC + APS =1)

Average & marginal propensities Marginal Propensity to Consume (MPC) the fraction or proportion of any change in income that is consumed. (MPC = change in consumption/change in income) MPC is the slope of the consumption schedule Marginal Propensity to Save (MPS) the fraction or proportion of any change in income that is saved. (MPS = change in saving/change in income) MPS is the slope of the saving schedule The sum of MPC & MPS for any change in disposable income must always be 1. (MPC + MPS = 1)

Consumption and Saving (1) Level of Output And Income (GDP=DI) (4) Average Propensity to Consume (APC) (2)/(1) (5) Average Propensity to Save (APS) (3)/(1) (6) Marginal Propensity to Consume (MPC) Δ(2)/Δ(1) (7) Marginal Propensity to Save (MPS) Δ(3)/Δ(1) (2) Consump- tion (C) (3) Saving (S) (1-2) P370 390 410 430 450 P375 390 405 420 435 P-5 5 10 15 1.01 1.00 .99 .98 .97 -.01 .00 .01 .02 .03 .75 .25

a C=a+bY Consumption ( C) Income (Y)

E. g. given the consumption function 𝐶=100+0 E.g. given the consumption function 𝐶=100+0.75𝑌 , what will be the level of consumption if Y=900million? Savings function Saving is that part of income that is not consumed. Savings fn shows us the r/ship between saving & income. Recall: 𝑌 = 𝐶+𝑆 𝑆=𝑌−𝐶 𝑏𝑢𝑡 𝐶=𝑎+𝑏𝑌 𝑡ℎ𝑒𝑛, 𝑆=𝑌− 𝑎+𝑏𝑌 =𝑌−𝑎−𝑏𝑌 =−𝑎+𝑌−𝑏𝑌 =−𝑎+𝑌(1−𝑏) S→savings, Y→ income, (1-b)→ MPS

MPS is a change in savings due to a change in income. Savings fn is a positive function of income,thus saving will increase as income increases but not proportionally meaning that 0<𝑀𝑃𝑆<1. MPS is a change in savings due to a change in income. MPS= ∆ 𝑖𝑛 𝑠𝑎𝑣𝑖𝑛𝑔 ∆ 𝑖𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 = ∆𝑆 ∆𝑌 . Note: MPC + MPS = 1. Graphically: -a S= -a+Y(1-b) Saving Income (Y)

Consumption and Saving functions 45° C=a+bY D Consumption ) B A Disposable Income Disposable Income Saving S= -a+Y(1-b)

At point B, C=Y the breakeven point. i. e At point B, C=Y the breakeven point .i.e. where hhs consume their entire income, hence S=0. Vertical distance from the 45- degree line to the horizontal axis is the income. At point A, C>Y, means that savings are negative (dissaving). At point C, C<Y, means that savings are positive. Investment function Shows the r/ship between Investment & Income. Investment is assumed to be constant i.e. I = Io (I>0). Where I is investment Io is a fixed level of investment.

Aggregate demand (AD)& aggregate supply (AS) approach to income determination. The AS-AD approach. AS represents the nation’s output of goods & services while AD is the society's demand for those goods & services. 𝐴𝑆=𝑌 𝐴𝐷=𝐶+𝐼 𝑌=𝐶+𝐼𝑜 𝑌=𝑎+𝑏𝑌+𝐼𝑜 The AS-AD approach states that for income to be at its equilibrium level, AS = AD i.e. the nations output of g/s should equal the society's demand for those g/s.

AS = Y AD = C+I (AD=AS) E C=a+bY AD/AS 45° Y* Income (Y) AS>AD

3 possible situations: If AS=AD firms will be able to sell their entire output hence there'll be no incentive to change their production. Implying that income will remain at its equilibrium level. If AS>AD- there's excess supply of g/s which leads to an increase in inventories. Firms will reduce their production causing output to fall until AS equates demand. If AS<AD – there's excess demand for the g/s produced. This causes firms to reduce their inventories & increase their production causing output to increase till AS=AD.

Equilibrium is reached at point E & corresponds to income level at Y*. Y* is the equilibrium level of income since it’s the only point where AS=AD. At income levels greater than Y* AS>AD there is inventory accumulation. At income levels less than Y* AS<AD there is inventory depletion. Examples: calculating equilibrium income & consumption. 1. Find equilibrium Income & consumption if C=100+0.75Y and I=150. 2. Find equilibrium income & consumption if C=100+0.80Y & I=50. 3. Assume a 2 sector economy where autonomous consumption expenditure is 100, the MPC is 0.80 and investment is 95. Calculate the equilibrium levels of income & consumption.

The Savings Investment Approach States that at the equilibrium level of income planned investment equals saving . Saving- leakage/ withdrawal of spending from the economy. Investment – injection of spending into the economy. Hence investment is a potential replacement for the leakage of saving. For aggregate expenditures to equal real output, the leakage of saving must be exactly offset by the injection of planned investment. - Planned investment: amount that investors are planning to invest. - Unplanned investment: changes in inventories (exess supply,excess demand)

The Savings Investment Approach cont… At low levels of levels of income savings are less than investment. The excess investment will then compensate for the leakage of saving & eventually raise income. At high levels of income savings are greater than investment. The excess saving will reduce total spending which eventually reduces income back to equilibrium.

Leakages & injections in the income stream. Recall: for the private closed economy (no govt, no foreign sector) savings are leakages & investments are injections in the income stream. For an open economy Savings (S), imports (M) & paying taxes (T) are leakages from the income-spending stream i.e uses of income that subtract from potential consumption. Exports (X), government purchases (G) & investment (I) are injections into the income-spending stream. At equilibrium the sum of injections must equal the sum of leakages.

Shifts in the S+T function Recall: I + G is an injection into the national income stream while S+T is a withdrawal from the stream, hence the economy will be in equilibrium when the two are equal. Equilibrium is at A where injections = leakages and at income Y1. An increase in the desire to save at every level of income shifts the (S+T)1 function upwards to (S+T)2 At Y1 leakages are higher than injections and the economy has to contract. The contraction will continue until point B when injections equal leakages at income Y2.

Determination of Equilibrium Incomeusing the 2 approaches Assume a closed economy where:a=120, b=0.5, I=100 The consumption function will be: 𝐶=𝑎+𝑏𝑌 𝐶=120+0.5𝑌 The saving function will be: 𝑆=𝑌−𝐶 𝑆=𝑌−(𝑎+𝑏𝑌) 𝑆=−𝑎+(1−𝑏)𝑌 𝑆=−120+(1−0.5)𝑌 𝑆=−120+0.5𝑌

Determination of Equilibrium Incomeusing the 2 approaches Using the AD-AS approach 𝑌=𝐶+𝐼 𝑌=𝑎+𝑏𝑌+𝐼 𝑌=120+0.5𝑌+100 𝑌=440 Using the Investment-Saving approach: 𝑆=𝐼 −120+0.5𝑌=100 The equivalence of the above tells us that at equilibrium 2 conditions are met: 𝐴𝐷=𝐴𝑆 𝐼=𝑆

The Multiplier effect & equilibrium GDP Multiplier: shows the change in equilibrium GDP as a result of a change in any of the components of aggregate expenditures (i.e. consumption, investment, government expenditures, net exports) Generally: Investment multiplier – measures the amount by which equilibrium GDP will increase/decrease when Investment increases/decreases by 1 unit. OR it measures change in income resulting from a change in investment. 𝐾𝑖= ∆ 𝑖𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 ∆ 𝑖𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡

Example: Introducing the government sector: Y=C+I+G Suppose C=100+0.8Y and I=75 Calculate equilibrium level of income. If Investment increases by 25, what will be the new level of equilibrium income? Calculate the size of the investment multiplier. Introducing the government sector: Y=C+I+G Government Multiplier – measures the change in income resulting from a change in government expenditure. 𝐾𝑔= ∆ 𝑖𝑛 𝑖𝑛𝑐𝑜𝑚𝑒 ∆ 𝑖𝑛 𝑔𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑠𝑝𝑒𝑛𝑑𝑖𝑛𝑔 From the above e.g calculate the government multiplier if government expenditure increases to 125 from 100.

Introducing taxes A tax increase results in a decrease in the equilibrium income. A tax increase reduces disposable income (income left after paying tax) which consequently reduces the level of consumption. Since consumption is a component of AD a reduction in C implies a decline in equilibrium income. Example: Suppose C=a+bYd where Yd = Y-T C=100+0.8Yd I=100 G=75 T=25 Calculate the equilibrium income & consumption.

Fiscal Policy Consists of deliberate changes in government spending, taxes or both to promote full employment, price-level stability & economic growth. Expansionary fiscal policy requires increases in govt spending, decreases in taxes or both to increase AD & push the economy from a recession. Contractionary fiscal policy implies decreases in govt spending, increase in taxes or both are the proper policies to deal with demand-pull inflation.

Non-income determinants of consumption & saving NIDs can cause people to spend or save more or less at various income levels, although the level of income is the basic determinant. Wealth: An increase in wealth shifts the consumption schedule up and saving schedule down. Wealth means the value of both real assets & financial assets Expectations: Changes in expected future prices or wealth can affect consumption spending today.

Non-income determinants cont…. Real interest rates: Declining interest rates increase the incentive to borrow and consume, and reduce the incentive to save. Why is this the case? Cost of borrowing lower, return to saving (interest payment) lower. Consumption will increase Household debt: when consumers as a group increase their household debt, they can increase current consumption at each level of DI. Increased borrowing shifts consumption schedule up and saving schedule down. Taxation: Higher are the taxes imposed by government, lower is consumption and saving

Other important considerations Macroeconomic models focus on real GDP more than on disposable income Changes along consumption schedules: Movement from one point to another on a given schedule due to change in income is called a change in the amount consumed. Shift in the consumption schedule is called a change in consumption schedule, and is caused by change in the non-income determinants of consumption

The Interest Rate – Investment Relationship Investment consists of spending on new plants, capital equipment, machinery, inventories, construction, etc The investment decision weighs marginal benefits and marginal costs The expected rate of return is the marginal benefit and the interest rate – the cost of borrowing funds – represents the marginal cost

The Interest Rate – Investment Relationship Expected rate of return (r) is found by comparing the expected economic profit (total revenue minus total cost) to cost of investment to get expected rate of return The real interest rate, i (nominal rate corrected for expected inflation), determines the cost of investment. The interest rate represents either the cost of borrowed funds or the opportunity cost of investing your own funds, which is income forgone If real interest rate exceeds the expected rate of return, the investment should not be made

The Interest Rate – Investment Relationship Investment demand schedule, or curve, shows an inverse relationship between the interest rate and amount of investment As long as expected rate of return (r) exceeds interest rate (i), the investment is expected to be profitable If r > i, investment should be undertaken. Why? Coz the firm expects the investment to be profitable. The firm should invest up to the point where r = i The rule applies even in cases where the firm does not borrow, but uses internal funds

Shifts in investment demand curve occur when any determinant apart from the interest rate changes. Greater expected returns create more investment demand; shift curve to right Changes in expected returns result because: Acquisition, maintenance, and operating costs of capital goods may change. Business taxes may change. Increased taxes lower the expected return Technology may change. Stock of capital goods on hand will affect new investment. Expectations about future economic and political conditions

Interest Rate and Investment Instability of Investment Capital goods are durable, so spending can be postponed or not. This is unpredictable. Innovation occurs irregularly – when they do they cause major changes in investment spending Profits vary considerably – variability of current profits feed into expectations of future profits, which in turn affect incentives to invest. Expectations can be easily changed – firms’ expectations about future business conditions can change quickly when some event suggests significant possible changes if future business conditions.

The multiplier effect Changes in spending ripple through the economy to generate event larger changes in real GDP. Multiplier effect – a change in the component of total spending leads to a larger change in GDP

The multiplier & marginal propensities The size of the MPC and the multiplier are directly related; the size of the MPS and the multiplier are inversely related. Multiplier = 1 / (1 - MPC) or 1/MPS If MPC = 0.75, MPS = 0.25 and Multiplier = 4 If MPC = 0.5, MPS = 0.50 and multiplier = 2 The significance of the multiplier is that a small change in investment plans or consumption-saving plans can trigger a much larger change in the equilibrium level of GDP

Numerical examples Multiplier determines how much larger that change will be: Multiplier = change in real GDP/initial change in consumption/investment spending. Alternatively, Change in real GDP = initial change in spending X multiplier. Consumption in an economy rises by P40 million & real GDP rises by P120 million. Calculate the multiplier. Investment falls P20 million & real GDP falls by P60 million. Calculate the multiplier. Government spending falls by P30 million & real GDP falls by P90 million. Calculate the multiplier.

Components of Aggr. Expenditure In a two sector economy aggr. Exp. consists of consumption exp (C) and investment exp (I). In a four sector modern economies, with govt. exp (G) and foreign sector (Xn), aggr. expenditure = C + I + G + Xn Aggr. Exp = Aggr. Output. This gives equilibrium GDP level

Change in Equlm. GDP- Leakages and Injections Aggregate Expenditure = C + I Part of disposable income of households is saved. Saving, therefore, is a leakage in income & exp. stream. But business sector does not sell its entire output to consumers as some part of output (capital/investment goods) will be sold with in business sector. Therefore, Investment can be thought of as injection of spending into the income-exp. stream

Equlm GDP-Government spending & Taxes Aggr. Exp = C + I + G Gov. exp. acts as injection and Increases aggr. exp and in turn influences positively GDP/ income generation process through the operation of multiplier in the economy. But taxes reduce consumption and investment spending and affect adversely GDP/income generation. Gov. exp. is injection and taxes leakage in the income generation process

Equlm GDP-Foreign Trade: Exports and Imports Aggr exp = C + I + G + Xn Equlm GDP/income generation process is influenced by foreign trade. Exports add up to the total expenditure and acts as injection in income generation process. Imports reduce total expenditure and acts as leakage in circular flow of income and expenditure. Increase in exports generate more GDP and imports reduce GDP

GDP = AGGR. EXP Higher levels of consumption, investment, govt. exp and exports (injections) increase GDP/income generation through multiplier process in the economy Higher levels of saving, taxes and imports (leakages) reduce GDP/income generation in the economy through reverse operation of multiplier.

Deriving Equilibrium level of Income & Consumption Y = C + I + G + Xn C = a+ bY; where a = autonomous consumption & b = MPC Y= C (a + bY) + I + G + Xn Assume a = 100 and b = 0.80 Then C = 100 + 0.80Y Assume I = 50; G = 75 and Xn = 20 Y = 100 + 0.80Y + 50 + 75 + 20; Y = 245 + 0.8Y Y (1-0.80) = 245/0.20; Y = 1225 C = 100+ (0.80X1225); C = 100 + 980; C = 1080