Consider the fllowing economy: C = C a + 0.80 ( Y – T ) C a = 400 – 10 R T = 750

Question

Consider the fllowing economy:

C = Ca + 0.80 ( Y – T )        Ca = 400 – 10 R          T = 750 + 0.2 Y                (M/P)^d= 0.25 Y – 25 R

(M^s/P)=2000/P This means that Ms = 2000.       Ip = 1800 – 30 R         G = 2000            NX = 700 – 0.04 Y     

a.) Find the equilibrium interest rate equation for YIS = YLM. This should be a function of P.

b.) Derive the equation of the aggregate demand curve AD. [Hint: Replace the equilibrium interest rate in either the IS or LM function. This should give you the AD curve in the form:

YAD= Constant + Constant/P

Explanation / Answer

a) We know, Y=C+I+G+NX

or, Y=Ca+0.80(Y-T)+1800-30R+2000+700-0.04Y

or, Y=400-10R+0.80(Y-750-0.2Y)+1800-30R+2000+700-0.04Y

or, Y(1-0.80+0.16+0.04)=400-600+1800+2000+700-40R

or, 0.40Y=4300-40R

or, Y=10750-100R .................(1)

In case of money market real money demand is equal to real money supply.

Thus, 0.25Y-25R=2000/P

Puttinh the value of equation1 we get;

or, 0.25(10750-100R)-25R=2000/P

or, 2687.5-25R-25R=2000/P

or, 50R=2687.5-2000/P

or, R= 53.75-40/P

Thus, equilibrium rate of interest is (53.75-40/P)

b) From the LM curve we get;

0.25Y-25R=2000/P

Putting the value of R we can write,

or, 0.25Y-25(53.75-40/P)=2000/P

or, 0.25Y=1343.75+3000/P

or, Y=5375+12000/P

Thus, aggregate demand equation is (5375+12000/P)

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