Question

a) Consider first the goods market. Say, consumption, investment and taxes all are dependent on income. Government expenditure is given.
C = c0 + c1 Yd
T = t0 + t1 Y
Yd = Y – T
I = b0 + b1 Y – b2 i
a) What is the multiplier?​​​​​​​​
Next, consider the money market as well, given by the equation M/P = d1Y - d2i.
b) What is the multiplier now? ​​​​​​​​
c) Compare the multiplier derived in part (a) and part (b). Explain in words. [Note: Diagram is not mandatory for this question, but will definitely help obtain additional marks if theory goes wrong.]

Answer 1

a.

$$Y=C+I+G$$

$$Y=C_o+C_1(Y-T)+b_o+b_1Y-B_2i+G$$

$$Y=C_o+C_1(Y-t_o-t_1Y)+b_o+b_1Y-b_2i+G$$

$Y=C_o+C_1Y-C_1t_o-C_1t_1Y+b_o+b_1Y-b_2i+G$

$$Y-C_1Y+C_1t_1Y-b_1Y=C_o-C_1t_o+b_o-b_2i+G$$

$$Y(1-C_1+C_1t_1-b_1)=C_o-C_1t_o+b_o-b_2i+G$$

$Y=$ $C_o-C_1t_o+b_o-b_2i+G \over 1-C_1+C_1t_1-bi$

The multiplier is

$$1\over1-C_1+C_1t_1-b_1$$

b. $M \over P$ $= d_1Y-d_2i$

$i=$ $d_1Y- { M\over P} \over d_2$

$Y=$

$$C_o-C_1t_o+b_o-b_2$$

$($ $d_1Y- {M\over P}$ $)$

$Y=$ $1 \over 1-C_1+C_1t_1-b_1+{b_2\over d_2} d_1$

The multiplier is

$1 \over 1-C_1+C_1t_1-b_1+{b_2 \over d_2} d_1$

multiplier at (b) is greater than multiplier at (a)

The curve becomes less steep as investment becomes more responsive to change in i. in other words, as b2 increases, the curve becomes steeper as money demand becomes more responsive to change in aggregate economic activity.