- HW #5 is out- The link to the course evaluations was emailed out- Office hours 5-6:30 tomorrow 6203 Social Science- Final exam: 40 multiple choice, 2.5 points eacho ~13 questions from each of the following: midterm 1 material, midterm 2 material, material from last 1/3 of the class------------------------------------------------------------------------------------------------------------------------------------Keynesian Model- Consumption functiono a = autonomous = exogenous (determined outside of the model) = the amount spent when there is no disposable incomeo Slope of the consumption function = b = ΔC/ΔDI = MPCo MPC = marginal propensity to consume, MPS = marginal propensity to saveo Δ(Y – (T – TR)) = ΔC + ΔSpo [Δ(Y – (T – TR))]/[ Δ(Y – (T – TR))] =[ ΔC + ΔSp]/[ Δ(Y – (T – TR))]o 1 = ΔC/ΔDI + Sp/ΔDIo 1 = MPC + MPSo Total amount = amount spent + amount savedo C = a + b(DI)- What about Sp?o Y = C + Sp + (T – TR)o Sp = Y – (T – TR) – C o Sp = Y – (T – TR) – [a + b(Y – (T – TR))]o Sp = (1 – b)[Y – (T – TR)] – a o Sp = -a + (1 – b)(DI)- E.g. (black = given)Y T – TR DI= Y – (T – TR) C Sp0 20 -20 200 -220100 20 80 275 -195200 20 180 350 -170300 20 280 425 -145o Y = C + Sp + (T – TR)0 = 200 + Sp +20Sp = -220o 100 = 275 + Sp +20Sp = -195o C = a + b[Y – (T – TR)]o b = ΔC/ΔDI = (275 – 200)/(80 – -20) = 0.75 = MPCo C = a + 0.75(DI)(DI, C) = (-20, 200)200 = a + 0.75(-20)a = 215C = 215 + 0.75(DI)Plug in DI = 180 & 280 to get C = 350 & 425o Sp = -a + (1-b)DISp = -215 + 0.25(DI)Plug in DI = 180 & 280 to get Sp = -170 & -145o C = 215 + 0.75(Y – 20) & Sp = -215 + 0.25(Y – 20)C = 200 + 0.75Y & Sp = -220 + 0.25Y the y-intercept changes if you only use Y (as opposed to DI) as the variable on the x-axis!- How do we use the consumption function to model the business cycle?o For simplicity assume: I = I0 autonomous/exogenous G = G0 autonomous/exogenous X – M = (X – M)0 autonomous/exogenouso Equilibrium occurs when spending = income (Y = AE)AE = C + I + G + (X – M)In equilibrium, Y = AEY = C + I + G + (X – M)45 degree reference line Y = AEAE ($)AE plannedC + I + G + (X – M)C + I + GAEeC + I(X – M)0C = a + b[Y – (T – TR)]G0I0YeY ($)o E.g. Given:- C = a + b[Y – (T – TR)] = 10 + 0.8[Y – (T – TR)]- T – TR = 20- G = 20- I = 10- (X – M) = 10 What do you know?- AE = C + I + G + (X – M)- MPC = 0.8, MPS = 0.2- Balanced budget (because G = (T – TR))- Trade surplus (because X > M)- Sp = -10 + 0.2(Y – (T – TR))Y T – TR DI C I G X – M AE Direction of Δ inventoryDirection of Δ GDP or production0 20 -20 -6 10 20 10 34 ↓ ↑ (need to produce more)10020 80 74 10 20 10 114 ↓ ↑20020 180 154 10 20 10 194 ↑ ↓(need to produceless)30020 280 234 10 20 10 274 ↑ ↓40020 380 314 10 20 10 354 ↑ ↓- DI = Y – (T – TR) plug in numbers to calculate DI- C = 10 + 0.8(DI) plug in DI to calculate C- AE = C + I + G + (X – M) Plug in #s to get AE- Compare Y and AE to see whether inventory is increasing or decreasing, and to see in which direction GDP needs to change o If Y > AE, inventory ↑, GDP ↓o If Y < AE, inventory ↓, GDP ↑ In equilibrium, Ye = AE Ye = C + I + G + (X – M) Ye = 10 + 0.8(Ye – 20) + 10 + 20 + 10 Ye = 50 + 0.8 Ye – 16 0.2 Ye = 34 Ye = 170 C = 130, Sp = 20, T – TR = 20 & C + Sp + (T – TR) =
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