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Simple Keynesian Model

Simple Keynesian Model. G, T and I simple model. Y = C + I + G C = a + b(Y-T) Solution Y = a + b(Y-T) + I + G Or Y - bY = a + I + G -bT Y = k(a + I + G - bT) where k = 1/(1-b). Sample Problem. a = 500, b = 0.9, I = 500, G = 500, T = 500 Y? k = 10 Y= 10(500 + 500 + 500 -450)

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Simple Keynesian Model

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  1. Simple Keynesian Model

  2. G, T and I simple model • Y = C + I + G • C = a + b(Y-T) • Solution • Y = a + b(Y-T) + I + G • Or Y - bY = a + I + G -bT • Y = k(a + I + G - bT) where k = 1/(1-b)

  3. Sample Problem • a = 500, b = 0.9, I = 500, G = 500, T = 500 • Y? k = 10 Y= 10(500 + 500 + 500 -450) • Y = 10500 • Implications: Multiplier for a, I, G and T. • Short term: it makes no difference • Long term: Need to consider increasing output.

  4. D equations • Private sector: Consumers DY = k Da • Firms or DY = k DI • Fiscal Policy: Expenditures DY = k DG • Taxes DY = -kbDT • Now Y=Y(N) is function of labor • Reelection increase Y to decrease unemployment and get reelected.

  5. Fine Tuning a = 500 b = 0.8 and k = 5. If consumers Decrease a by 100B => DY =- 500 • How can fiscal policy keep Y where it is. • I - increase G by 100B or • II - decrease T by 125B • If a up by 50 and I down by 150 what is compensating fiscal policy: Show both.

  6. Balanced Budget Multiplier • No deficit: Initially G = T • Need to increase Y: DY = kDG - kbDT • Keeping G = T. Let DG= DT = Q • Therefore DY= kQ - kbQ = k(1-b)Q = DQ • This is a mathematical oddity of model

  7. Tax Model • Y = C + I + G • C = a + b(Y-T) • T = tY marginal versus effective tax rate • Substitute up the stack C = a + b(Y - tY) • Y = a + b(1-t)Y + I + G • [1 - b(1-t)] = a + I + G • Y = k1(a + I + G) where k1 = 1/[1-b(1-t)]

  8. a = 200 I = 400 G = 400 and t = 0.2 b = 3/4 What is Y and T? k1 = 1/[1 - (3/4)(1-.2)] = 2.5 Y = 2.5[1000] = 2500 and T = .2(2500) = 500. Suppose t is cut to 1/9, what happens to T? k1 = 1/[1 - (3/4)(8/9)] = 1/[1 - 2/3] = 3 Y = 3[1000] = 3000 and T = (1/9)[3000] = 333.33 Note: If you have had calculus you will note that T = tk1 (a + I + G) dT/dt < 0 for 1 > b > t > 0

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