Y is the level of real output. The demand for real money balances, M|P = 2Y - 7i

Question

Y is the level of real output.

The demand for real money balances, M|P = 2Y - 7i.

The interest rate is set at 4% by the central bank. The price level, P, is constant at 2.

(a) Derive the IS curve and explain what it expresses. (5 marks)
(b) Find the short-run equilibrium level of output. (3 marks)
(c) Compute the goods market multiplier. (4 marks)
(d) Compute the short-run equilibrium levels of consumption and investment. (5 marks)
(e) Find the equilibrium level of real money supply. (3 marks)

In a closed economy, consumption is C=5+0.5(Y-T), investment is 1 = 3 +0.3Y-0.81; tax revenue is T-6; and government expenditure is G-3.8. Y is the level of real output. The demand for real money balances, M/P- 2Y-7i. The interest rate is set at 4% by the central bank. The price level, P, is constant at 2.

Explanation / Answer

(a) In goods market equilibrium, Y = C + I + G

Y = 5 + 0.5(Y - 6) + 3 + 0.3Y - 0.8i + 3.8

Y = 11.8 + 0.5Y - 3 + 0.3Y - 0.8i

(1 - 0.5 - 0.3Y) = 8.8 - 0.8i

0.2Y = 8.8 - 0.8i

Y = 44 - 4i.......(Equation of IS curve)

The IS curve depicts all the interest rate and output combination for which the goods market is in equilibrium.

(b) When i = 4%,

Y = 44 - (4 x 4) = 44 - 16 = 28

(c) Multiplier = 1 / (1 - MPC - MPI) = 1 / (1 - 0.5 - 0.3) = 1 / 0.2 = 5

(d) Using values of i and Y,

C = 5 + 0.5 x (28 - 6) = 5 + 0.5 x 22 = 5 + 11 = 16

I = 3 + (0.3 x 28) - (0.8 x 4) = 3 + 8.4 - 3.2 = 8.2

(e) In equilibrium, M/P = 2Y - 7i where (M/P): Real money supply

M/P = (2 x 28) - (7 x 4) = 56 - 28 = 28

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