Lecture 7: Keynesian Income and Expenditure Model

Lecture 7 The Keynesian Income and Expenditure Model: A Simple economy References : Hubbard and O'Brien Chapter 23 Learning outcomes of today’s lecture Understand the history and logic behind the Keynesian model. Identify and explain the components of the Keynesian model and the connection to...

Lecture 7 The Keynesian Income and Expenditure Model: A Simple economy References : Hubbard and O'Brien Chapter 23 Learning outcomes of today’s lecture Understand the history and logic behind the Keynesian model. Identify and explain the components of the Keynesian model and the connection to aggregate demand. Analyze and interpret Keynesian equilibrium both numerically and graphically. Comprehend the multiplier effect and use it to explain the impact of autonomous spending on the economy. D R. D E B O S H R E E GHOSH 2 Remember solutions to a recessionary gap? Recessionary gap solution NonDiscretionary policy Discretionary expansionary fiscal policy (can be demand side or supply side) Demand side AD = C + I + G + (X-M) D R. D E B O S H R E E GHOSH 3 History of government intervention John Maynard Keynes developed a framework to explain the high levels of unemployment experienced in the 1920s and 1930s in Great Britain. Keynes later suggested to correct the recession situation, government must intervene [KNOWN AS FISCAL POLICY]. His proposition was based on his proposed model – The Keynesian model This lecture is about the developing the Keynesian model D R. D E B O S H R E E GHOSH 4 The Keynesian model The model examines the effects of consumption, savings, and investment on equilibrium real GDP, in the short run under a fixed price assumption The effects are analysed based on the aggregate demand equation AD = C + I + G + (X-M) Remember in short run equilibrium Aggregate demand (AD) = Aggregate supply (AS) D R. D E B O S H R E E GHOSH 5 The Keynesian model Aggregate demand is the total quantity of goods and services demanded across all levels of an economy at a particular price level and in a given period. Aggregate expenditure is the total amount of spending on an economy's goods and services at a given level of income. Aggregate demand (AD) and Aggregate expenditure (AE) can be considered two sides of the same coin because they both describe the total amount of spending in an economy. However, they are viewed from slightly different perspectives. D R. D E B O S H R E E GHOSH 6 The Keynesian model Aggregate demand It is represented by the AD curve, which shows the relationship between the overall price level and the quantity of output demanded. (focus on axis labels) D R. D E B O S H R E E Aggregate expenditure The AE model focuses on the relationship between total spending and the economy's income or output. (focus on the axis labels) GHOSH 7 The Keynesian model - focus consumption AD = AE = C + I + G + (X-M) = Y Consumption in an economy is determined by the consumption function C = a + bY The intercept a in this equation measures consumption even when the income is 0. It is known as autonomous consumption The slope b of this equation measures is the fraction of a change in disposable income that is spent on consumption. It is known as as marginal propensity to consume (MPC) D R. D E B O S H R E E GHOSH 8 The Keynesian model - focus consumption- MPC Consumption function = 1.8 + 0.75Y Here 1.8 is the autonomous consumption and 0.75 is the MPC. Interpreted as With every 1 dollar increase in income, the consumption increases by 75 cents. Represented by the slope = 0.75 Consumption expenditure in trillion dollars C = a + bY Cℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 ΔC 1.5 𝑏 = 𝑀𝑃𝐶 = = = = 0.75 Change in income ΔY 2 Even if there is no income i.e Y=0, the consumption is still $1.8 trillion D R. D E B O S H R E E GHOSH C = 1.8 + 0.75Y MPC = 0.75 C = $1.5 trillion Y = $2 trillion 1.8 Real GDP in trillion dollars 9 The Keynesian model - focus savings AE = C + I + G + (X-M) = Y C=Y–S (Remember Income is either consumed or saved in a closed model) S=Y–C S = Y – (a + bY) (Remember C = a + bY) Rearranging S = –a + (1 – b)Y The intercept -a in this equation is “autonomous” savings One will have negative savings when the income is 0 The slope 1-b in this equation is the marginal propensity to save (MPS). It measures the fraction of a change in disposable income that is saved. D R. D E B O S H R E E GHOSH 10 The Keynesian model - focus savings- MPS S = –a + (1 – b)Y = -1.8 + 0.25Y Here -1.8 is the autonomous savings and 0.25 is the MPS. Interpreted as Savings trillion dollars Savings function MPS = 0.25 S = $0.5 trillion Y = $2 trillion Real GDP in trillion dollars With every 1 dollar increase in income, the saving increases by 25 cents. Represented by the slope = 0.25 S = -1.5 + 0.25Y -1.8 Cℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 Δ𝑆 0.5 𝑏 = 𝑀𝑃𝑆 = = = = 0.25 Change in income ΔY 2 Even if there is no income i.e Y=0, the saving is still -$1.8 trillion D R. D E B O S H R E E GHOSH 11 The Keynesian model – linking MPS and MPC Now we know that Y (income) = C (consumed)+ S (saved) Then, ΔY = ΔC + ΔS ΔY ΔC ΔS Then, = + ΔY ΔY ΔY 1= 𝑀𝑃𝐶+ 𝑀𝑃𝑆 D R. D E B O S H R E E GHOSH 12 Putting everything together AE = C + I + G + (X-M) Assume for now that G and (X-M) components do not exist Assume investment (I) is fixed (autonomous i.e. does not depend on other factors) Then, AE = C + I AE = (a + bY) + I (remember both a and I are autonomous) AE = A + bY where A = a + I D R. D E B O S H R E E GHOSH 13 Keynesian Equilibrium graphically speaking Aggregate expenditure in trillion dollars Equilibrium is achieved when AE = A + bY = Y (where A = a + I) The 45-degree line shows all points where aggregate expenditures and output are equal. Therefore, an intersection of the AE line with the 45degree line shows point of equilibrium A quick video on the importance of the 45-degree can be found here (link) AE0 E0 450 Y0 Real GDP in trillion dollars D R. D E B O S H R E E GHOSH 14 Keynesian Equilibrium solving numerically Then, Consumption function = a + bY = 1.5 + 0.75Y AE expenditure function = (a + bY) + I = 1.5 + 0.75Y + 0.5 = 2 + 0.75Y Equilibrium real GDP by solving for AE = Y 2 + 0.75Y = Y Y=8 D R. D E B O S H R E E Aggregate expenditure in trillion dollars Assume Investment (autonomous) (I) = $ 0.5 trillion dollars Autonomous consumption (a) = $ 1.5 trillion dollars Marginal propensity to consume = 0.75 GHOSH AE0 = 2 + 0.75Y E0 450 8 Real GDP in trillion dollars 15 Keynesian Equilibrium graphically speaking - Auto component changes D R. D E B O S H R E E AE1 = 5 + 0.75Y Aggregate expenditure in trillion dollars Suppose any component of autonomous component increases. For example, investment or autonomous consumption increases then AE line shifts up. Slope DOES NOT change since MPC has not changed but intercept on the y axis shifts up as autonomous component (i.e. the component when income is 0) has increased. Assume A = 3, if after the change the economy remains at the same real output level Y0 even when AE has increased, then at this point AE > Y leading to a fall in inventory and indicating to the firms to produce more E1 AE0 = 2 + 0.75Y E0 A 450 GHOSH Y1 Y0 Real GDP in trillion dollars 16 Keynesian Equilibrium solving numerically - MPC changes D R. D E B O S H R E E AE1 = 2 + 0.80Y Aggregate expenditure in trillion dollars Suppose instead of autonomous component, only the MPC increases from 0.75 to 0.80 and autonomous component remains at 2 ONLY the slope changes since MPC has changed but intercept on the y axis remains same as autonomous component (i.e. the component when income is 0) has not changed Intersection of the AE line with the 45-degree line shows point of equilibrium E1 AE0 = 2 + 0.75Y E0 450 GHOSH Y1 Y0 Real GDP in trillion dollars 17 Keynesian Equilibrium solving numerically - MPC changes AE1 = 2 + 0.80Y Aggregate expenditure in trillion dollars Then, Consumption function = a + bY = 1.5 + 0.80Y AE expenditure function = (a + bY) + I = 1.5 + 0.80Y + 0.5 = 2 + 0.80Y Equilibrium real GDP by solving for AE = Y 2 + 0.80Y = Y Y = 10 E1 AE0 = 2 + 0.75Y E0 450 D R. D E B O S H R E E GHOSH Y1 Y0 Real GDP in trillion dollars 18 The multiplier effect We observe that a change in autonomous component or a change in MPC leads to a change in real GDP The change in any autonomous component does not lead to the exact same change in real GDP. A ≠ Y When the autonomous component increases or decreases, it leads to a change in real GDP that can be a multiple of the initial change in magnitude. Picture credit :Investopedia / Mira Norian D R. D E B O S H R E E GHOSH 19 Example of the mechanism of the multiplier effect D R. D E B O S H R E E GHOSH 20 The multiplier In equilibrium Y = AE = A + bY (where A autonomous component and b is MPC) So, we know if A increases then Y (real GDP) would increase but by HOW MUCH? Solving for equilibrium for change ΔY = ΔA + bΔY ΔY = ΔY = ΔA 1 ΔA 1−b 1 1−b D R. D E B O S H R E E GHOSH The is the multiplier denoted by . The ratio of the increase in equilibrium real GDP to the increase in autonomous expenditure 21 The multiplier – an example AE0 = 2 + 0.75Y Calculate the multiplier 1 1 Multiplier =  = = 1−b 1−0.75 =4 Using the multiplier, calculate the change in real GDP due to a change in autonomous consumption by 10 Therefor an initial increase of 1 ΔY = Δ𝐴 10 in the autonomous 1−b expenditure leads to a change of 40 in real GDP ΔY= 10 * 4 = 40 D R. D E B O S H R E E GHOSH 22 The multiplier – an example AE0 = 2 + 0.75Y Calculate the multiplier when the MPC changes to 0.80 1 1 Multiplier =  = = =5 1−b 1−0.80 Using the multiplier, calculate the change in real GDP due to a change in autonomous consumption by 10 An increase in MPC magnifies 1 ΔY = Δ𝐴 the effect of autonomous 1−b expenditure on real GDP. ΔY= 10 * 5 = 50 D R. D E B O S H R E E GHOSH 23 Summary Keynesian model is reason and argument behind fiscal policy i.e. discretionary government policy The success of Keynesian model depends on the magnitude of the MPC since it directly effects the multiplier Higher the multiplier, higher is the effect on GDP for a change in autonomous consumption. Consumption expenditure is the biggest component of aggregate expenditure D R. D E B O S H R E E GHOSH 24 Next Week Understanding the Keynesian model using the three sector and four sector model Determining the equilibrium and change in GDP when autonomous component changes in a three and four sector model Calculate the multipliers under the three sector and four sector model and compare it with a two-sector model D R. D E B O S H R E E GHOSH 25