Answer to Question #169986 in Microeconomics for isaac mensah

Question

Find (a) the reduced form. (b) the numerical value of 𝑌𝑒 , and (c) the effect on the multiplier if a proportional income tax (t) is incorporated into the model. 𝑌 = 𝐶 + 𝐼, 𝐶 = 𝐶𝑂 + 𝑏𝑌 𝑑 , 𝑇 = 𝑇𝑂 + 𝑡𝑌, 𝑌 𝑑 = 𝑌 − 𝑇 where 𝐼 = 𝐼𝑂 = 30, 𝐶𝑂 = 85, 𝑏 = 0.75, 𝑡 = 0.2, and 𝑇𝑂 = 20

Answer 1

Solution:

a.). The reduced form:

Y = AD

First derive structural equation:

Y_e = C + I

Y_e = C_O + bYd + I_O

Y_e = C_O + b (Y_e – (T_O + tY_e)) + I_O

Formulate reduced form:

Y_e = C_O + b (Y_e – (T_O + t)) Ye + I_O

Y_e - b (1 – (T_O + t)) Ye = C_O + I_O

[1 – b (1 – (T_O + t)] Ye = C_O + I_O

Solve for Y_e:

Y_e =$\frac{C_{O} + I_{O}}{1 – b (1 – (T_{O} + t)) }$

 

b.). The numerical value of Y_e:

Y_e = $\frac{C_{O} + I_{O}}{1 – b (1 – (T_{O} + t)) }$

Y_e = $\frac{85 + 30}{1 – 0.75 (1 – (20 + 0.2)) }$

Y_e = $\frac{115}{15.40}$ = 7.47

Y_e = 7.47

 

d.). If a proportional income tax (t) is incorporated into the model, the multiplier effect will be low, that is the multiplier will decrease.