In a small closed economy, its aggregate demand and output are given as the equations below, Y = C + I + G; national output or GDP. C = 100 + 0.5(Y-T); consumption, marginal propensity to consume MPC = 0.5. I = 150 – 10*r; investment is a negative function of real interest rate (r as %). (M/P)d = Y – 20*r; real money demand which is adjusted by price level (inflation). G = 200; as government spending. T = 200; as tax. M = 2,400; as money supply. P = 4; the price level. (1) With the equations above, try to derive the IS curve. Tip: recall IS curve represent the relation between national output (Y) and real interest rate (r) in goods market. To derive IS curve, you need to put all components of Y together and find its connection with r. (2) Use the same equations, now try to derive the LM curve. Tip: recall LM curve represent the relation between national output (Y) and real interest rate (r) in money market. So to derive LM curve, you need to consider money supply and demand. (3) How much is the equilibrium national output (Y) and the equilibrium interest rate (r)? Tip: recall the IS-LM model represent the short-run equilibrium in both goods market and money market. The intersection of the IS curve and the LM curve satisfy conditions for equilibrium in the two markets. You can get equilibrium interest rate (r) and equilibrium level of output (Y). (4) Suppose the price level (P) now increases from 4 to 6, which curve shifts, the IS curve or the LM curve? What happens to the new equilibrium interest rate (r) and equilibrium output (Y)? Tip: this question practices how to derive the aggregate demand (AD) curve, which presents a negative relationship between the price level (P) and aggregate output (Y).
In a small closed economy, its aggregate
- Y = C + I + G; national output or
GDP . - C = 100 + 0.5(Y-T); consumption, marginal propensity to consume MPC = 0.5.
- I = 150 – 10*r; investment is a negative function of real interest rate (r as %).
- (M/P)d = Y – 20*r; real money demand which is adjusted by price level (inflation).
- G = 200; as government spending.
- T = 200; as tax.
- M = 2,400; as money supply.
- P = 4; the price level.
(1) With the equations above, try to derive the IS curve.
Tip: recall IS curve represent the relation between national output (Y) and real interest rate (r) in goods market. To derive IS curve, you need to put all components of Y together and find its connection with r.
(2) Use the same equations, now try to derive the LM curve.
Tip: recall LM curve represent the relation between national output (Y) and real interest rate (r) in
(3) How much is the equilibrium national output (Y) and the equilibrium interest rate (r)?
Tip: recall the IS-LM model represent the short-run equilibrium in both goods market and money market. The intersection of the IS curve and the LM curve satisfy conditions for equilibrium in the two markets. You can get equilibrium interest rate (r) and equilibrium level of output (Y).
(4) Suppose the price level (P) now increases from 4 to 6, which curve shifts, the IS curve or the LM curve? What happens to the new equilibrium interest rate (r) and equilibrium output (Y)?
Tip: this question practices how to derive the aggregate demand (AD) curve, which presents a negative relationship between the price level (P) and
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