. Assume that an economy is characterized by the following equations: C = 100 +

Question

. Assume that an economy is characterized by the following equations:

    C = 100 + (2/3)(Y – T)

    T = 600

   G = 500

    I = 800 – (50/3)r

    Ms/P = Md/P = 0.5Y – 50r

a. Write the numerical IS curve for the economy, expressing Y as a function of r. Does the government of this economy have a balanced budget, surplus or deficit?

b.Write the numerical LM curve for this economy, expressing r as a function of Y. Assume P=1 and M=1,200.

c.Solve for the equilibrium values of Y and r.

d.What are the new equilibrium values of Y and r when P = 2.0?

e. Plot a graph of the aggregate demand function.

Explanation / Answer

(a)

(1) IS Curve equation:

Y = C + I + G

= 100 + (2/3) (Y - T) + 800 - (50/3)r + 500

= 100 + (2/3) (Y - 600) + 800 - (50/3)r + 500

= 100 + (2/3)Y - 400 + 800 - (50/3)r + 500

[1 - (2/3)]Y = 1,000 - (50/3)r

(1/3)Y = 1,000 - (50/3)r

Multiplying both sides by 3,

Y = 3,000 - 50r ...... (1) [IS Curve equation]

(2)

Government budget balance = T - G = 600 - 500 = 100 > 0

A positive budget balance indicates a budget surplus.

(b) LM Curve equation:

(Ms / P) = (Md / P)

(1,200 / 1) = 0.5Y - 50r

1,200 + 50r = 0.5Y

Dividing both sides by 0.5,

Y = 2,400 + 100r ....... (2) [LM Curve equation]

(c)

Equilibrium is obtained when IS = LM. From (1) & (2),

3,000 - 50r = 2,400 + 100r

150r = 600

r = 600 / 150 = 4

Y = 2,400 + 100r = 2,400 + (100 x 4) = 2,400 + 400 = 2,800

(d)

When P = 0, only LM will be affected:

(1,200 / 2) = 0.5Y - 50r

600 + 50r = 0.5Y

Y = 1,200 + 100r

Equating with unchanged IS:

3,000 - 50r = 1,200 + 100r

150r = 1,800

r = 12

Y = 1,200 + (100 x 12) = 1,200 + 1,200 = 2,400

NOTE: First 4 sub-questions are answered.

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