Introduction To Economics

ECO 100Y

Introduction to Economics Topic 13: The Simple Model Of Income and Output Determination Source: LR12, LR11 Chapters 21 and 22 (including appendix); LR10, Chapters 22 and 23 (including appendix)

 

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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From Accounting to Modelling 

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The RHS of the National Accounts is GDE  GDE = C + I + G + X – M  This is an “accounting identity” But what explains the level of GDE = GDP?  Answering this requires “economic models”  Models work on the basis of explaining the drivers for each of C, I, G, X, M  Various models/explanations  We focus on the famous one by John Maynard Keynes  Simple version first (w/o money); then more complex version (with money)

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

The Simple Model: Assumptions 

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Simplifying assumptions:  No indirect taxes or subsidies; No depreciation  Implies that Total Incomes = Total Expenditures = Y = GDP Assume no inflation until Full Employment (i.e., fixed prices)  Real values = Nominal values  Aggregate Supply (AS) is horizontal til YF (AS curve discussed later)

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Y

Topic 13: The Simple Model

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The Consumption Function: Key Assumptions 

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Keynes’ Observation #1: (Real) Consumption (C) is a function of (real) Disposable Income (Yd)  C = C(Yd)  Yd = Y – T where T = Personal Taxes Keynes’ Observation #2: As disposable income rises, households consume more, but not all of the additional income  ∆C / ∆Yd < 1 Aside: C is also a function of Wealth, Price Expectations, Life Cycle, Interest Rates  These are all assumed to be held constant in the simplest model (“ceteris paribus” assumption)

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

The Consumption Function: Equation and Graph 

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Consider first model, with no government, so T=0  Then Yd = Y Here is a typical Consumption Function that adheres to Keynes’ observations:  C = 10 + 0.8Y ∆C / ∆Y = Marginal Propensity to Consume (MPC)  MPC = 0.8 C / Y = Average Propensity to Consume (APC)  APC falls as Y rises

ECO 100 W.G. Wolfson

C C

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Y C = 10 + 0.8Y Slope = 0.8 = MPC

Topic 13: The Simple Model

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The Savings Function: Equation and Graph 

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In the simplest model, households can use income either to spend (consume) or to not spend (save)  Y=C+S Implies that the Savings Function is S = Y – C  S = Y – (10 +0.8Y)  S = - 10 + 0.2Y There is a Marginal Propensity to Save (MPS) and Average Propensity to Save (APS)  MPS = ∆S / ∆Y = 0.2  MPC + MPS = 1

ECO 100 W.G. Wolfson

S

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Topic 13: The Simple Model

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S = - 10 + 0.2Y Slope = 0.2 = MPS

Shifts of the Consumption Function 

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An increase in wealth, a fall in interest rates, greater optimism about the future will lead to an upward shift in the Consumption Function A decrease in wealth, an increase in interest rates, and pessimism about the future will lead to an downward shift in the Consumption Function Shifts of the Consumption Function imply shifts of the Saving Function in the opposite direction Note that a change in disposable income does not shift the Consumption Function

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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The Investment Function: Equation and Graph 

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In the simple model, we assume initially that investment spending is constant  There is “autonomous” spending by firms  Based on “expectations” that are fixed at a point in time  More realistically, Investment is influenced by the rate of interest (done later), and other factors For now, here is a constant Investment Function  I = 10

ECO 100 W.G. Wolfson

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Topic 13: The Simple Model

Y I = 10

Shifts of the Investment Function 

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Investment depends on several variables: Interest rates Changes in the level of sales Expectations about the future / business confidence In our simple model, we assume all these variables to be constant (“ceteris paribus”) The Investment Function is a constant Note that changes in any of the determining variables (interest rates, level of sales, and business confidence) will cause the investment curve to shift

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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Aggregate Expenditure: The Concept 

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Aggregate Expenditure (AE) is the total desired expenditure on goods and services in the economy Sum of demands for output by households, firms, government, foreign sector AE = C + I + G + X – M With no government or foreign sector, in the simplest model: AE = C + I

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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Aggregate Expenditure: Equation and Graph  

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AE = C + I Solving below: C = 10 + 0.8Y I = 10 AE = C + I = 10 + 0.8Y + 10 AE = 20 + 0.8Y AE has an autonomous (constant) component  Value in this case = 20

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AE has a component that is driven by income  In this case, component is 0.8Y = MPC*Y

ECO 100 W.G. Wolfson

Y AE = 20 + 0.8Y Slope = 0.8 = MPC (in this case)

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The Simple Model: Deriving the Equilibrium 

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We have the Demand for output, namely AE  AE = 20 + 0.8Y Equilibrium will occur where the Supply of output equals the Demand for output  Supply = GDP = Y  Hence Equilibrium Equation is Y = AE Solving below: Y = AE = 20 + 0.8Y .2Y = 20 Y* = [1/.2] * 20 = 100

ECO 100 W.G. Wolfson

Y=AE

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Topic 13: The Simple Model

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The Simple Model: The Equilibriating Process 

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What if current output (production, supply = Y) does not equal AE?  Y < AE (Supply less than Demand)  Y > AE (Supply exceeds Demand) Economy will adjust until Y = AE  Signal is not through prices (which are constant)  Signal is through (unexpected, involuntary) inventory change

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ECO 100 W.G. Wolfson

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Topic 13: The Simple Model

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The Simple Model: The Equilibriating Process (Diagram) 

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Consider point Y1 to the left of the equilibrium (Y*)  Then AE1 > Y1  Inventories fall  Production rises  Y and AE move towards equilibrium Vice-versa for point Y2 to the right of the equilibrium (Y*)

ECO 100 W.G. Wolfson

Y=AE

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Topic 13: The Simple Model

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The Simple Model: Alternate Version of Equilibrium 

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Put these two equations together: 1. Y = AE = C + I (The “Equilibrium Equation”) 2. Y = C + S (The Choices of Households) Some simple math: 1. Y - C = I 2. Y – C = S Hence I = S (Alternate equilibrium equation, in this case) This is the “Injections – Withdrawals” Approach to Equilibrium

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Alternate Version of Equilibrium: Equations and Graph 

The Math: S = -10 + 0.2Y I = 10 S=I -10 +.2Y = 10 -.2Y = 10 Y* = 100

ECO 100 W.G. Wolfson

S, I S 10 - 10

Topic 13: The Simple Model

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Alternate Version of Equilibrium: Equilibriating Process 

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Equilibriating Process:  If I > S  Y grows  If I < S  Y contracts Equilibrium Point:  (Desired) I = S In general, Equlib’m Point:  Injections=Withdrawals

S,I S I Y*

Topic 13: The Simple Model

ECO 100 W.G. Wolfson

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Alternate Version of Equilibrium: Equilibriating Process (Numerics) 

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If Desired I does not equal S, the economy is not in equilibrium  There will be an (unintended) change in inventories A change in inventories affects Actual Investment  E.g., a rise in inventories counts in Actual I Equilibrium only when Desired I = Actual I = S

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Desired ∆Invent Actual I . I 10 -2 10 0 Topic 13: 10The Simple Model +2

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The Simple Model: The Multiplier 

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Suppose business expectations become more optimistic  This increases Desired Investment  I increases to I = 11  AE = C + I = 21 + 0.8Y Solve for the new equilibrium  Y2 = 105 ∆I = 1 has led to larger ∆Y =5  This is the Investment Spending Multiplier (KI ) 

KI = ∆Y / ∆I = 5 (in this case)

ECO 100 W.G. Wolfson

Y = AE AE2

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A shift up in AE by $1 has caused eq’m Y to increase by $5

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The Simple Model: The Multiplier In The I-S Diagram 

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An increase in Desired I shifts up the I schedule  I = 11 No change in the Savings Function  S = - 10 + 0.2Y Solve I = S for the new equilibrium  Y2 = 105 As before, we see the multiplier effect  KI = ∆Y / ∆I = 5

ECO 100 W.G. Wolfson

S,I S I2 I1

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105 Y Y2

A shift up in I by $1 has caused eq’m Y to increase by $5

Topic 13: The Simple Model

The Simple Model: Use of the Multiplier (Example 1) 1.

Business expectations take a turn down; Desired Investment falls from I = 10 to I = 8. 

By how much will GDP change?

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What is equilibrium GDP now?

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“Swings” in an exogenous variable will cause GDP to change

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Sometimes called “external shocks”

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Can lead to the “business cycle”

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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The Simple Model: Use of the Multiplier (Example 2) 2.

The Full Employment level of GDP is YF = 120. 

By how much would Investment need to change to reach Full Employment (i.e., to eliminate the GDP Gap)?

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Note that this situation (Y* < YF) was a prime motivator for Keynes to develop his model

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Model implies that “demand management” can produce Full Employment

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

The Simple Model: General Formula for the Multiplier 

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Formula for KI in this simplest model:  KI = 1 / [1 – MPC] With MPC = 0.8, the value of KI is 5:  KI = 1 / [1 – MPC] = 1 / [1 – 0.8] = 1/0.2 = 5 Generalize the formula, for a shift in AE of 1 unit:  K = 1 / [1 – slope of AE] In this case, slope of AE = MPC  But this equality will not always be so (as models become more complex) Conclusion: Use the general formula!  The steeper the AE line (i.e. the bigger its slope), the larger the multiplier

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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The Simple Model: Adding the Government Sector 

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In our simple macro model , “the government” has 3 impacts:  It taxes households (T) – “lump sum” and / or % of income  It spends on goods and services (G)  It provides transfer payments to households (TR) Disposable income (Yd) changes:  Households pay (Personal) Taxes (T)  Households receive Transfer Payments (TR)  Yd = Y – T + TR AE changes to include Government Spending on Goods and Services (G):  AE = C + I + G

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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Simple Model with a Gov’t Sector: A Typical Problem Consumption Function: C = 102 + .8Yd Investment: I = 100 Government Spending: G = 200 (Lump Sum) Personal Taxes: T = 240 (TR = 0) Disposable Income: Yd = Y – T 1. 2. 3. 4. 5. 6. 7.

Full Employment GDP: YF = 1,250 What is the level of equilibrium GDP? What is the value of the GDP Gap? What is the value of the Government Spending Multiplier? By how much must G change to get to Full Employment? What is the value of the Deflationary Gap (the am’t AE must shift) ? What is the value of the (Lump Sum) Tax Multiplier? By how much must Lump Sum Taxes change to get to Full Employment?

ECO 100 W.G. Wolfson

Topic 13: The Simple Model

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Simple Model with a Gov’t Sector: Typical Problem Re Gov’t Budget Consumption Function: C = 10 + .8Yd Investment: I = 8 Government Spending: G = 10 Disposable Income: Yd = Y – T Government Budget Balance = 0 Full Employment GDP: YF = 120 1. What is the level of equilibrium GDP and the GDP Gap? 2. What is the value of the KG and required change in G to get to YF? 3. What is the value of the Deflationary Gap? 4. What is the value of the KT and required change in T to get to YF? 5. What is the value of the Balanced Budget Multiplier (KBBM)? [∆G = ∆T required] 6. By how much must G (and T) change to get to YF with the Government’s Budget remaining in balance? Topic 13: The Simple Model 26 ECO 100 W.G. Wolfson

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The Simple Model: Adding the Foreign Sector 

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In our simple macro model , the “foreign sector” has 2 components:  Exports (X)  Imports (M) The Balance of Trade = X – M  A Surplus in the B of T if X > M  A Deficit in the B of T if X < M Equation for AE changes to include the Balance of Trade  AE = C + I + G + X – M Behaviour equations in the simple model:  Exports are autonomous: X = constant value  Imports are driven by national income: M = M(Y)

ECO 100 W.G. Wolfson

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Simple Model with Foreign Sector: A Typical Problem Consumption Function: C = 15 + .9Yd Investment: I = 10 Exports: X = 5 Import Function: M = 4 + 0.4Y Full Employment GDP: YF = 60 (Ok, it’s a bizarre case: G = T = TR = 0 … i.e., no Gov’t!) 1. 2. 3. 4. 5.

What is the level of equilibrium GDP and the GDP Gap? What is the value of the KI? What is the equation for KI using symbols (MPC, MPM)? What change in I is required to get to YF? If we were to introduce a Government Sector, what would be the value of KBBM?

ECO 100 W.G. Wolfson

Topic 13: The Simple Model