Question

Suppose the economy of Ghana in 2020 was characterized by

C = ¢400m + 0.75(Y-T); I = ¢400m - 20r; G = ¢200m; T = ¢200m;

Ms = ¢250m/P; Md = 0.25Y - 10r

a. Derive the IS and LM curve equations. Give a brief explanation as to why they are

positively or negatively sloped.

b. Calculate equilibrium output and interest rates (in this case assume P=1).

 Econ313 2020/2021 PROBLEM SET 2 Page 1 of 2

c. Suppose the government of Ghana in the second half of 2020 spent an additional ¢50m to mitigate the impact of the COVID pandemic on households and businesses and government tax revenue declined by 10% as a result of the lockdown in Ghana what will be the new equilibrium output?

d. Will the policy in (c) above have an impact on interest rate? Briefly explain.

e. What is the amount of the fiscal deficit incurred as a result of the government fis

Answer 1

$$Solution$$

given that:

$C=400+0.75(Y-T)\\ I=400-20r\\ G=200\\ T=200\\ M_s=250/P\\ M_d=0.25Y-10r$

A] IS

$Y=C+I+G+(x-t)\\ Y=400+0.75(Y-200)+400-20r+200+0\\ Y=1000+0.75Y-150-20r\\ Y=850+0.75Y-20r\\ Y-0.75Y=850-20r\\ 0.25Y=850-20r\\ Y=3400-80r$

LM

$M_s=\frac{250m}{p}\\ M_s=0.25Y-10r\\ \frac{250M}{p}+10r=0.25Y\\ Y=\frac{250}{0.25p}+40r$

B]equilibrium output and rate

$IS=LM\\ 3400-80r=\frac{250}{0.25P}+40r\ if \ p=1\\ 3400-80r=\frac{250}{0.25}+40r\\ 3400-1000=120r\\ 2400=120r\\ r=20$

$Y=3400-80r\\ Y=3400-(80\times20)\\ Y=3400-1600\\ Y=1800$

C]tax at 10% decline

$Y=C+I+G\\ Y=400+0.75(Y-T)+400-20r+200\\ new\ G=250\ and\ T=180\\ Y=400+0.75y-135+400-20r+250\\ Y-0.75Y=915-20r\\ 0.25Y=915-20r\\ Y=3660-80r\\$

equate IS=LM

$3660-80r=1000r+40r\\ 2660=120r\\ r=22.17$

substitute:

$Y=3660-(80\times22.17)\\ Y=3660-1773.6\\ Y=1886.4$

The new equilibrium output is $\$1886.4$ .

D] Yes .The policy c above does impact on interest rates . it has increased from $20\%$ to $22.17\%$

E]fiscal deficit $=total\ expenditure- \ total\ receipts\ excluding\ borrowings\\$

$=250-180\\ =70m$