[PDF] Note b a - SSCC



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Note b a - SSCC

Output : Y = C + I + G = 20 + 0 75Y + 100 = 120 + 0 75Y => 0 25Y = 120 => Y = 480 b) Progressive Taxes: Taxes are a function of income (i e T = c + dY) Y T Y-T C S 0 -20 20 110 -90 100 0 100 150 -50 200 20 180 190 -10 500 80 420 310 110 700 120 580 390 190 Tax Function : T = -20 + 0 2Y



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Econ 102: Fall 2007 Discussion Section Handout #9 Answer Key

1. Consumption Functions

We are given the following equations from the Keynesian Model, find the autonomous consumption level, marginal propensity to consume (MPC) and marginal propensity to save (MPS). Find the savings

function with respect to disposable income, and then use the given information about net taxes to find the

consumption and savings function with respect to real output. If the consumption function with respect to

disposable income is not given, find that first! Note: Remember when we have the consumption function in the form C = a + b(Y - T) that autonomous consumption is a and the marginal propensity to consume is b.

To solve for the consumption and savings functions with respect to real output rather than disposable

income we need to enter the value of net taxes. The savings function with respect to disposable income is S = -a + (1 - b) (Y - T) (a) C = 125 + 0.75(Y-T) Net Taxes = 100

Autonomous Consumption Level : a = 125

MPC : b = 0.75

MPS : MPS = 1-MPC = 0.25

Savings Function w/ respect to DI : S = - a + MPS(Y - T) = -125 + 0.25(Y - T) Consumption Function w/ respect to Y : C = 125 + 0.75(Y - 100) = 50 + 0.75Y Savings Function w/ respect to Y : S = -125 + 0.25(Y - 100) = -150 + 0.25Y (b) C = 0.80(300-T+Y) Net Taxes = 50 = 240 - 0.8(T - Y) = 240 + 0.8(Y - T)

Autonomous Consumption Level : a = 240

MPC : b = 0.8

MPS : MPS = 1-MPC = 0.2

Savings Function w/ respect to DI : S = - a + MPS(Y - T) = -240+ 0.2(Y - T) Consumption Function w/ respect to Y : C = 240+ 0.8 (Y - 50) = 200 + 0.8Y Savings Function w/ respect to Y : S = -240+ 0.2(Y - 50) = -250 + 0.2Y (c) 2T = 2Y - 3C + 300 Net Taxes = 90 => 3C = 300 + 2(Y - T) => C = 100 +2/3(Y - T)

Autonomous Consumption Level : a = 100

MPC : b = 2/3

MPS : MPS = 1-MPC = 1/3

Savings Function w/ respect to DI : S = - a + MPS(Y - T) = -100+ 1/3(Y - T) Consumption Function w/ respect to Y : C = 100+ 2/3 (Y - 90) = 40+ 2/3 Y Savings Function w/ respect to Y : S = -100+ 1/3(Y - 90) = -130+ 1/3 Y (d) 600 = 35(T - Y) + 50C Net Taxes = 0.2Y => 50C = 600 + 35(Y - T) => C =12 +0.7(Y - T)

Autonomous Consumption Level : a = 12

MPC : b = 0.7

MPS : MPS = 1-MPC = 0.3

Savings Function w/ respect to DI : S = - a + MPS(Y - T) = -12+ 0.3(Y - T) Consumption Function w/ respect to Y : C = 12+ 0.7 (Y - 0.2Y) = 12+ 0.56 Y Savings Function w/ respect to Y : S = -12+ 0.3 (Y - 0.2Y) = -12+ 0.24 Y Econ 102: Fall 2007 Discussion Section Handout #9 Answer Key

2. Equilibrium

Solve for the short run equilibrium output using the Keynesian Model. Use the fact that

Output = Y = C + I + G + X - M in equilibrium.

(a) C = Consumption function = 125 + 0.75(Y-T)

T = Net Taxes = 100

G = Government Spending = 100

I = Investment Spending = 120

Closed economy

Y = C + I + G + X - M in equilibrium

Y = 125 + 0.75(Y-100) + 120 + 100 = 345 + 0.75Y - 75

Y = 270 + 0.75Y

0.25Y = 270

Y = 1080

(b) C = Consumption function = 20 + 0.75(Y - T)

T = 0.2Y

G = Government Spending = 50

I = Investment Spending = 20

X = M + 10

Y = C + I + G + X - M in equilibrium

Y = 20 + 0.75(Y - 0.2Y) + 20 + 50 + 10 = 100 + 0.75(0.8Y)

Y = 100 + 0.6Y

0.4Y = 100

Y = 250

(c) S = Savings function w/ respect to output = -100 + 0.2Y

T = Net Taxes = 50

G = Government Spending = 100

I = Investment Spending = 175

M - X = 125

Solve for Y first, we know S = -100 + 0.2Y = -90 + 0.2(Y - 50) = -90 + 0.2(Y - T) Using the relationship that MPS = 1 - MPC, we know MPC = 0.8 and autonomous consumption is 90.

C = 90 + 0.8(Y - T)

Y = C + I + G + X - M in equilibrium

Y = 90 + 0.8(Y - 50) + 175 + 100 - 125 = 240 + 0.8Y - 40

Y = 200 + 0.8Y

0.2Y = 200

Y = 1000

Econ 102: Fall 2007 Discussion Section Handout #9 Answer Key

3. Tables, Functions, & Equilibrium (Challenging Problems)

Given the information in the following tables, fill the blanks (assuming that the consumption function is

linear with respect to disposable income). Find the consumption function with respect to disposable

income, the consumption function with respect to output, the savings function with respect to disposable

income, and the savings function with respect to output. Then find the equilibrium output level in the closed

economy if G + I = 100. a) Flat Taxes: Taxes are a constant number

Y T Y-T C S

0 40 -40 20 -60

100 40 60 95 -35

400 40 360 320

40

800 40

760 620 140

1000

40 960 770 190

To solve the table:

ཛ From the first line we know T = 40 for all levels of Y

ཛྷ From the first and second line, we know MPC = ǻC/ǻ(Y-T) = (95 - 20)/(60 - -40) = 75/100 =

0.75 ཝ From the second line, knowing MPC, we have that 95 = a + 0.75(60) = a + 45 which implies that a = 50. ཞ We have the consumption function now, so use MPC and autonomous consumption to find the savings function with respect to disposable income. ཟ Use this function to find the income level in the third line. འ Use the consumption and savings functions to find the level of consumption and savings in the forth and fifth lines. Consumption Function w/ respect to DI : C = 50 + 0.75(Y - T) Consumption Function w/ respect to Y : C = 20 + 0.75Y Savings Function w/ respect to DI : S = -50 + 0.25(Y - T) Savings Function w/ respect to Y : S = -60 + 0.25Y Output : Y = C + I + G = 20 + 0.75Y + 100 = 120 + 0.75Y => 0.25Y = 120 => Y = 480 b) Progressive Taxes: Taxes are a function of income (i.e. T = c + dY)

Y T Y-T C S

0 -20 20 110 -90

100 0 100 150 -50

200

20 180 190 -10

500

80 420 310 110

700 120 580

390 190

Tax Function : T = -20 + 0.2Y

Consumption Function w/ respect to DI : C = 100 + 0.5(Y - T) Consumption Function w/ respect to Y : C = 110 + 0.4Y Savings Function w/ respect to DI : S = -100 + 0.5(Y - T) Savings Function w/ respect to Y : S = -90 + 0.4Y Output : Y = C + I + G = 110 + 0.4Y + 100 = 210 + 0.4Y => 0.6Y = 210 => Y = 350quotesdbs_dbs15.pdfusesText_21