Answer to Question #191424 in Macroeconomics for Emmanuel

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

(a) We know that-

$Y=C+I+G\\ Y=400+0.75(Y-T)+400-20r+200\\ Y= 400+0.75(Y-200)+600-20r\\ Y-0.75Y=850-20r$

$0.25Y=850-2r$

$Y=\dfrac{850}{0.25}-\dfrac{20r}{0.25} ---\text{ IS equation }$

Also, $\dfrac{250}{P}=0.25Y-10r$

   $\dfrac{250}{P}+10r=0.25Y \\[9pt] \Rightarrow Y= \dfrac{250}{0.25p}+40r -- LM equation$

(b) Solving LM and IS equation simultaneously-

   $3400-80r=\dfrac{25}{0.25P}+40r~~~~~~~~~~ if P=1 \\ 120r=3400-1000 \\[9pt] r=\dfrac{2400}{120}=20$

Substitute value of r in IS equation and we get-

   $Y=3400-80\times 20=3400-1600=1800$

The equilibrium level of interest rate and income are 20 and 1800.

(c)Tax at 10% declined 

   $Y=C+I+G\\ Y=400+0.75(Y-T)+400-20r+200$

Now, G=250 and T will be $=200-\dfrac{10}{100}\times 200=180$

So,

$Y=400+0.75Y-135+400-20r+250 \\ Y-0.75Y=915-20r \\ 0.25Y=915-20r$

  $Y=\dfrac{915}{0.25}-\dfrac{20r}{0.25}.........\text{IS Equation}$

LM equation is Y=1000+40r

  Equation both LM and IS equation-

   $3660-80r=1000+40r \\ 2660=120r \\[9pt] r=\dfrac{2660}{120}=22.16$

Substitute r in IS equation-

    $Y=3660-80\times 22.16 \\Y =3660-1772.8 \\ Y=1887.2$

  The new equilibrium output is 1887.2

(d) Yes The policy in part c does not impact interest rate. It has increased from 20% to 22.16%.

(e) Fiscal deficit = Total expenditure- Total receipts excluding borrowings

           $=250-180=70$