Question

d. Assume that G increases by 200. By how much will Y increase in short-run equilibrium? What is the government-purchases multiplier (the change in Y divided by the change in G)? e. Assume that G is back at its original level of 1,000, but M (the money supply) increases by 200. By how much will Y increase in short-run equilibrium? What is the multiplier for money supply (the change in Y divided by the change in M)? - - -

My question is d and e

Please details thank you

Answer 1

Answer (d)

We solve 2 equations as follows:

(i) Y = C + I + G

(ii) M_s  = M^{​​​​​​}_d

_{(i) ​​​​​​Y = C + I + G}

Substituting given values in the above equation gives,

Y = 0.8(Y - T) + 800 - 20r + 1000

Y = 0.8Y - 800 + 800 - 20r + 1000

0.2Y = 1000 - 20r

Y = 5000 - 100r .....eq(1)

(ii) M_s = M_d

  _{1200 = 0.4Y - 40r}

_{Y = 3000 + 100r .....eq(2)}

_{Equating eq(1) and eq(2) gives,}

3000 + 100r = 5000 - 100r

200r = 2000

r = 10

Y = 5000 - 100(10) => 4000  

Now, increase G by 200

Re-writing eq(1) gives,

0.2Y = 1200 - 20r

Y = 6000 - 100r .....eq(3)

Equating eq(2) and eq(3)

6000 - 100r = 3000 + 100r

3000 = 200r

r = 15

Y = 6000 - 100(15) = 4500  

With the increase in government spending by 200 units, the income increases by 500 units (4000 to 4500).

Government purchase multiplier = (500)/(200) = 2.5

Answer (e)

  Now, we increase the money supply by 200 units

​​​​M_s = 1400

Put, M_s = M_d

  1400 = 0.4Y - 40r

Y = 3500 + 100r .....eq(4)

Equating eq(1) and eq(4) gives,

3500 + 100r = 5000 - 100r

200r = 1500

r = 7.5

Y = 5000 - 100(7.5) = 4250

  

With the increase in money supply by 200 units, total income rises by 250 (4000 to 4250) units.

Money supply multiplier = (250)/(200) = 1.25

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