CHAPTER 11 • Wages fell, but there was no increase in employment The Neo-Keynesian Model • Interest rates fell, but there was no new investment • Supply did not create its own demand (Say’s Law) Sasan Fayazmanesh Summary This chapter deals with the Keynesian (neo-Keynesian) model of the equilibrium output. It covers: 1) the consumption function, including marginal propensity to consume; 2) saving function, including marginal propensity to save; 3) investment function; 4) government expenditure function; 4) aggregate expenditure function; and 5) equilibrium level of output. It also covers the concept of Keynesian or “expenditure multiplier.” Introduction to neo-Keynesian Economics “Work is what I want, not charity. Neoclassicals’ laissez faire theories of the labor market Who will help me get a and loanable funds market made no sense during the job? Great Depression of 1929-1939. 7 years in Detroit, no money, sent away. The theories and pictures did not match! Furnish best of references, phone . .” 1 Dorothea Lange's Migrant Mother Nipomo, California, March 1936. See more images of the Great Depression In The General Theory of Employment, Interest and Money (1936), Keynes challenged some aspects of these theories, as well as the Say’s Law. See: General Theory Keynes went on to develop new theories of: 1) How outpu t and employment are determined. 2) How interest rate is determined. 3) What is the role of money in the economy. Soon after, however, Keynes’s ideas were simplified and incorporated into the neoclassical models. This was the beginning of the “ neoclassical synthesis ” or “ neo-Keynesian ” model. 2 These assumption also make output (GNP) and The Basic Neo-Keynesian Model disposable personal income equal : We start with the GNP (Y) identity: NNI = Y – Depreciation – IBTs Y = C + Ig + G + (X−M) PI = NNI + Transfer payments DPI = PI – Direct taxes Y = DPI Simplifying assumptions Since 1) Economy is “closed”: No X − M Y= DPI = Consumption + Savings Y = C + Ig + G Then : 1) Y = C+S (income side) 2) Economy is “private”: No G 2) Y = C+ I (output side) Y = C + I g 1 and 2 imply: 3) There is no depreciation: 3) S = I Gross investment = Net investment Since C+S = C+ I Y= C + I These assumption also make output (GNP) and Note: S = I is just an accounting identity. income (disposable personal income) equal : As we will see, S = I does not imply economic NNI = Y – Depreciation – IBTs stability, since I is actual investment (I a) as opposed to planned investment (I p): PI = NNI + Transfer payments Ia = Ip + ∆ Inventories DPI = PI – Direct taxes Stable economy implies: ∆ Inventories = 0 and S = Ip 3 Consumption Function Consumption function C Keynes hypothesized that consumption spending is a function of disposable personal income: C=f(Y) C= f(Y). This idea became known as the consumption function: a Def. Consumption function (C): a relationship between consumption spending and income Y (Income) (disposable personal income). -a Shifts or Changes in Consumption After Keynes, it was argued that consumption depends on various other factors: If C = f (Y, W, i, E), C = f (Y, W, i, E) then any change in W, i, or E will shift the consumption function. Where, Example, W: is wealth or assets, i: is interest rate, What happens if interest rates fall ? E: is expectation of future income. Interest rates falls Keynes assumed : C 1) There is a minimum amount of consumption ; i.e., C1 = f (Y 0, W 0, i1, E 0 ) even when national income is zero, there is still some consumption. This is called autonomous consumption. C0 = f (Y 0, W 0, i0, E 0 ) a1 Q: Where could this consumption come from? a0 A: Past savings. 2) Consumption rises as national income rises , but it Y does not rise as fast. 4 Linear consumption function: MPC = ∆C/∆Y We assume that consumption function is given by : MPC = (C2 – C1) / (Y2 – Y1) C = a + bY MPC = ($1000 – $850) / ($1200 – $1000) Where “ a” is the C intercept and “ b” is the slope of the MPC = $150/ $200 consumption function. MPC = 3/4 = .75 It must be that: 0 < b < 1 Marginal Propensity to Consume Average Propensity to Consume Def. Marginal Propensity to Consume (MPC) : The Def. Average Propensity to Consume (APC) : increase in consumption which results from an increase in income: The level of consumption divided by the level of income: MPC = ∆C/ ∆Y APC = C / Y This is obviously the same as the slope of the APC obviously changes as income changes. consumption function or “ b”: MPC = b Example Example C C C= a + by C= a + bY C2=$1000 C2=$1000 C1=$850 C1=$850 Y Y Y1 = $1000 Y 2= $1200 Y1 = $1000 Y 2= $1200 5 Marginal Propensity to Save APC 1 = C 1/Y 1 Def. Marginal Propensity to Save (MPS) : The increase in saving which results from an increase in income: APC 1 = $850/$1000 MPS = ∆S/ ∆Y APC 1 = .85 This is the same as the slope of the savings function or “1− b” APC 2 = C 2/Y 2 MPS = 1 − b APC 2 = $1000/ $1200 APC 2 = .83333 Saving Function Example C Y = S +C, Therefore, S = Y− C C= a + bY C2=$1000 If C = a + bY, then C =$850 1 S = − a + (1 − b) Y S = Y − ( a + bY) S2=$200 S = Y − a − bY S1 =$150 Y S = − a + (1 − b) Y Y1 = $1000 Y 2= $1200 Saving function MPS = ∆S/∆Y C, S MPS = (S2 – S1) / (Y2 – Y1) C = a +bY MPS = ($200 – $150) / ($1200 – $1000) MPS = $50/ $200 a S = − a + (1 − b) Y MPS = 1/4 = .25 Y -a 6 Q: What do we get when we add MPC and MPS? Q: What do we get when we add APC and APS? A: One! A: One, again! Our example: Our example: MPC =.75 APC =.85 MPS =.25 APS =.15 MPC +MPS =.75 +.25 = 1 APC +APS =.85 +.15 = 1 MPC + MPS = 1 is true by definition: APC +APS = 1 is also true by definition: MPC = b Y = C +S MPS = 1-b MPC +MPS =b + 1- b = 1 Divide both sides by Y: Y/Y = C/Y + S/Y 1 = APC +APS Similarly Investment Function Y= C +S Remember that actual investment (I) has 3 components: ∆ Y= ∆ C + ∆ S 1) Structures and equipment 2) Residential structures Divide both sides by ∆ Y 3) Changes in inventories ∆ Y/ ∆ Y = ∆ C/ ∆ Y + ∆ S / ∆ Y 1 = MPC + MPS 7 Also remember the relation between actual investment Equilibrium Level of GNP (Y) (I a ) and planned investment (I p): Q: At what level of consumption, saving and investment Ia = I p + ∆ Inventories will the GNP be in equilibrium, i.e., it is neither expanding nor contracting? Def. Planned investment (Ip ) is what firms wish or plan to invest. A: We can answer this question in 2 ways: 1) By looking at the relationship between savings and investment, or 2) By looking at the relation between expenditures (C and I) and national income. Keynes assumed that planned investment : Savings and Investment: Equilibrium level of GNP 1) Is independent of the level of national S, I S ≡ I income. a 2) Depends on interest rate , as we shall see later. IP Y Ye ∆ Inventories= 0 Planned investment function Savings and Investment: Equilibrium level of GNP Investment (I) S, I S ≡ I a ∆ I> 0 IP IP Y Y Ye Y1 ∆ I= 0 ∆ I> 0 8 Savings and Investment: Equilibrium level of GDP Aggregate Expenditure S, I AE (C, I) S ≡ I a AE = C+ I p Ip C Ip IP ∆ I< 0 Ip Y Y Y2 Ye ∆ I< 0 The 45 0 line Aggregate Expenditure AE (C, I) We can also look at the level of equilibrium GDP by AE = Y looking at where aggregate expenditure is equal to income. AE 2 AE 1 Def. Aggregate Expenditure (AE ): Is the sum of the spending. So far we have: AE = C+I 45 0 Y Y1 Y2 Aggregate Expenditure Equilibrium level of GDP AE (C, I) AE (C, I) AE = Y AE = C + I p AE e C Ip 45 0 Y Y Ye “Keynesian Cross” 9 Note: At equilibrium level of output, Ye, all Government expenditure income is spent. Suppose the equilibrium level of output is achieved Economy is neither expanding not contacting. at a low level of employment. It is stable and ∆I = 0 . Keynesian economics then advocates government spending money on goods and services. We assume that government expenditure, G, is independent of national income: Equilibrium level of GDP Government expenditure function AE (C, I) AE = Y Government expenditure (G) ∆ I> 0 AE = C + I p AE e ∆ I< 0 G 45 0 Y Y Y2 Ye Y1 Equilibrium level of GNP: Everything together Aggregate Expenditure Again AE = Y S, I, C AE (C, I) AE = C+ I p S C + I IP G 45 0 Y Y Ye ∆ I= 0 10 Aggregate Expenditure The Multiplier Effect Def. Multiplier Effect : Any change in spending AE (C, I, G) will bring about greater change in income or output: AE = C+ I + G ∆Y > ∆AE G C + I G G Y Equilibrium level of GNP again A Numerical Example AE = Y Suppose MPC=1/2 and investment increases by AE (C, I, G) $1000 , i.e., ∆I = $1000 . AE 1 = C+ I+ G What happens to he national income? AE 0 = C+ I ∆AE = G 45 0 Y Y0 Y1 Note: ∆Y > ∆AE Period 1: ∆∆∆I=$1000 ∆Y=$1000 AE = Y AE (C, I, G) Period 2 ∆C=$500 ∆S=$500 AE 1 = C+ I+ G AE 0 = C+ I ∆AE = G 45 0 ∆Y Y Y0 Y1 11 Period 1: ∆∆∆I=$1000 ∆Y=$1000 Remember the geometric series: Period 2 ∆C=$500 $500 ∆S=$500 S= a+ ar +ar 2+ ar 3 +ar 4+ .