3. Consider an economy with the following equations and relationships: Yd =Y-T T

Question

3. Consider an economy with the following equations and relationships: Yd =Y-T T = t0+ t1Y Note: There are two cornponents i-i' this is an interest rate target Co=200 g=0.6 bo -300 b 0.1 k, = 30 k1= 0.5 k2=5 o - 100 t -0.2 4 G500 P-1.0 a) What are the endogenous variables when the FED (Central Bank) Targets the interest rate? b) What are the consumption function and the MPC? c) What is the expenditure multiplier? Explain the components and their impact on the multiplier d) What is the equilibrium level of output/income, disposable income, consumption, savings, and the budget deficit or surplus! e) What is the level nominal Money supply needed to meet the interest rate target'?

Explanation / Answer

(a) Endogenous variables are: Z, CD, Yd, ID and T (since these values depend on other variables)

(b) MPC = c1 = 0.6

Consumption function (CD) = 200 + 0.6 x (Y - T) = 200 + 0.6 x [Y - (100 + 0.2Y)]

CD = 200 + 0.6 x (Y - 100 - 0.2Y)

CD = 200 + 0.6 x (0.8Y - 100)

CD = 200 + 0.48Y - 60

CD = 140 + 0.48Y

(c) Expenditure multiplier = 1 / [1 - c1(1 - t1) - b1]

= 1 / [1 - 0.6 x (1 - 0.2) - 0.1]

= 1 / [1 - (0.6 x 0.8) - 0.1]

= 1 / (0.9 - 0.48)

= 1 / 0.42

= 2.38

From the multiplier,w e observe that

(i) Multiplier increases (decreases) with increase (decrease) in c1 and b1

Here, c1 is the MPC which is the ratio of change in consumption to change in disposable income. When c1 rises (falls), higher (lower) proporiton is consumed out of additional $1 income, thus increasing Y by higher (lower) amount. In addition, b1 is the marginal propensity to invest, which is the ratio of change in investment to change in disposable income. When b1 rises (falls), higher (lower) proporiton is invested out of additional $1 income, thus increasing Y by higher (lower) amount.

(ii) Multiplier increases (decreases) with increase (decrease) in t1.

Here, t1 is the tax rate. As tax rate rises (falls), disposable income falls (rises) and Y decreases (increases).

(c) In equilibrium, Y = C + I + G. Plugging in given values,

Y = 140 + 0.48Y + 300 + 0.1Y - (3 x 4) + 500

Y = 940 + 0.58Y - 12

(1 - 0.58)Y = 928

0.42Y = 928

Y = 2,209.52

T = 100 + (0.2 x 2,209.52) = 100 + 441.9 = 541.9

Yd = Y - T = 2,209.52 - 541.9 = 1,667.62

C = 140 + (0.48 x 2,209.52) = 140 + 1,060.57 = 1,200.57

Savings = Y - C = 2,209.52 - 1,200.57 = 1,008.95

Budget balance (BB) = T - G = 541.9 - 500 = 41.9 (Since BB > 0. there is a budget surplus).

NOTE: As per Answering Policy, 1st 4 parts have been answered.

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