Question

We assume that the relationships in the text below describe an economy. It is a closed economy with a given (fixed) price-level and with a variable interest rate (the interest rate is given with a whole value ex. 10% is 10 and not 0,1).

C = 425 + 0,4 Y_D

T = 100

G = 140

I = 100 + 0,1 Y – 50r

M^D = L(r;Y) = Y – 100r

M^S M/P = 200

Y_D = (Y-T)

1. Find the equations for IS- and LM curves.
2. Find the equilibrium income and interest rate
3. Calculate the private and public saving surplus
4. Suppose that the government increases public spending to the value 150. Calculate equilibrium for income, interest rate, public, and private savings and explain furthermore the changes in the economy.

Answer 1

LA In a closed econonry, the goods market equilibrium is given by : Y=C+I+G. - putting the respective values of the variables in the abone equation, we get i Y = 425 +0.440 + 100+ 0.19-508 +140- Now, we know that, in Disposable Juonne: Y0 = Y-T ., .. by putting the value of To in equation , we get Y= 425+.0.4(Y-100) +0.19-508 +140+100 :>> Y- 0.47 -0.19 = 665 +0.4X C-100)) - 50r. a) 0.5= 665-40-50r = 625-50r : 2) Y = 1250 - 100r.- I Equation 6 gives us the equation for the Is wine. | Now, from the money market equilibrium, we have, Money Demand = Money supply ' => ypoor 200 => Y = 200 +100 r. - @ 9 Equation 6 gives us the equation the LM wrie.

B) from equation , we have Y = 200 + 100 r. => Y = Y-200 hutting this value of r in equation ③ we have: 13 Y = 1250 - 100 => Y = 1250 - 4 + 200 i Notons de *») 24 = 1.450 > y = 725 units = yok t w odra Y-200 725-200 ! 100 100 og 5.25% are - We have - Equilibrium Income yt 725 units : Equilibrium Interest Rate : 1 5.25%. () we have 0- 42 S + 0-4 YD - 42 S + ( 4)(1 - 1). Putting Y= y* = 725) and T = 100, we get! CE 425+014 (725.-100). ») e = 425 + 250 = 675 a> c= 675 units.

Savings, Pi, is given by : Private Pi=Y-C-T. => P, = 725- 675-100 =) Pi = -50 Private Savings is -50 units, ie, Private dissawing is taking place and it's magnitude is 50 units i Now, public savings, Pn, is given by: we will Pq = T-G 5100 -1403-40 >> P2 = -40. Public saving accounts to - 40 Units spire, the Public saving surplus is negative and there is a budget defieile (since, TKG)'and it's magnitude, is 40 units. Note: If G TYG, that would be a case of Budget Surplus]; is the only W D) New G is given by i Giwew = 150 or Change in G, AG & Gwew.- G = 150-140 = 10 Home, AG = 10 i Now, the government expenditure inmultiplier is given i-'mipa where, ay: Change in inconie 4, due to change in G, AG Protoitu to consume . HPC : могли frорелла Here, SG = 10; MPC =0:4.

AY is one th ink 46 - MPC 10 - 10 16.667 AY 1-0.4 ..=).04 = 16,667.... is change in inimnie is by 163667 units (increase in income). a Hence, the new imone devel, Yew, would be Ynew = 40 + sy = 7257160667 =791066.7 » Ywew = 741.667' = yes we z wew Equilibrium Jucome. on the new interest rate, new would be spiste Y Mew --200 41667-200 new 100. 2007 » renew = 50417% - New Equilibrium Tunterest Rates the new value of e, (New would be: Crew = 4257 0.4 l you how - T): Hbdi = 425+ 0.4 (741,667.-100). ! = 6815667 o's New Private, Spenglering, Piwew, will be note!! Piwow = y low - Cablue -I = 741.667 +688667700 » Pi New = -40. Heme, the equilibrium value of Private Dissaving is Mount Again, the new public saving, P2 New, will be i.

Penew = T- Gwew = 100-150 5 50 = PzNew = -50... - Budget The new value of public Deficit is 2.50 units. As the governmieut experditure, creases the Aggregate Demand also wréases which in turn je i increases the output (and income), as it has been shown here, as well as the overall price-level, and hence inflation will take place. In other words, the, economy wild expand in hand , (Juurearing G or reduring it are examples of expansionary