300i = 0.5Y – 2000.
i = Y - [4].
Equation [4] represents the LM curve and it flat with a slope of . It describes the equilibrium on the domestic money market. The LM curve for this economy is flat because a given increase in the output raises money demand by a smaller amount and, a return to money market equilibrium requires a small compensating interest rate increase. This shows that the income elasticity of MD is small. Fig.2 (a) and (b) show the diagrammatic derivation of the LM curve.
The equilibrium interest rate (i) and output (Y), is where the goods market and the money market are in equilibrium. Solving simultaneously gives;
i = 31 -Y [3] (IS curve)
i = Y - [4] (LM curve).
31 -Y = Y -
Y =
Y = 10272 & . This is the equilibrium output for both markets.
(Y = 10272.73 to 2.s.f)
Therefore i = 31 - (10272 & ).
i = 10 & . This is the equilibrium interest rate for both markets.
(i = 10.45 to 2.s.f).
The equilibrium point is where the IS and LM curves intersect and this is at E in Fig.3 and corresponds to equations [3] and [4]. This represents equilibrium for a closed economy.
(b) I shall now consider the implications of a lower foreign interest rate (i*) on the output level and on the domestic interest rate in an economy under a fixed exchange rate. In my analysis, I will assume that the domestic central bank (CB) has enough domestic currency reserves and foreign currency reserves for it to intervene in the money market effectively (http://weber.ucsd.edu/~dkim/110b/AD_open_ho.pdf). Under fixed exchange rates, changes in the foreign interest rates are transmitted directly into the domestic interest rate (Burda and Wyplosz 2003). This implies that i falls from 10.45 to 10 to equal i*.
i* = i = 10. [5]
Assuming that information is symmetric between the domestic and foreign country, and that there are no government controls on capital any interest rate disparities will lead to capital being perfectly mobile (). This implies that the financial integration line is horizontal.
GDP (Y) in the economy is market value of all final goods and services produced in a country in a given time period (http://staffwww.fullcoll.edu/aturner/ch19.doc). Hence to calculate the real GDP I will use the IS function, i = 31 -Y. Substituting [5] into [3] gives:
10 = 31- Y
Y = real GDP = 10500.
MS = 0.5Y - 300i + 500 where Y = 10500.
= 0.5(10500) – 300(10) + 500
= 2750
MS = 2750. This is the nominal value of MS at the new interest rate. The new LM curve is;
2750 = 0.5Y – 300i + 500
300i = 0.5Y – 2250
i = Y – [6].
I shall now explain the process involved in getting to the equilibrium i and Y using fig.4 (a) and (b). The financial integration line (BP curve) is at the foreign interest rate level (i* = 10). Now at A, the goods and money markets are in equilibrium but lie above the BP curve. The economy should thus be in balance of payments surplus, since the increase in capital inflows would outweigh the decrease in exports (CA > 0) due to the higher domestic interest rate (41IE lecture notes). The capital inflows that would result from an increase in demand for the domestic currency would put pressure on the domestic currency to appreciate. However, there is instantaneous adjustment of money supply as the CB increases MS, thus lowering the domestic interest rate to equal i*. The CB intervenes in the foreign exchange market selling domestic currency and buying foreign currency and thus increasing the money supply. The LM curve shifts rightwards from LM0 to LM1 along the IS curve. Fig.4 (b) shows this as an increase of MS from M0/P to M1/P. Now there is excess money supply at i = 10 given by AC, and so interest rates fall from 10.45 to 10. This maintains S = 1 and avoids any capital movements..
As the interest rate falls, this would lead to an increase in the domestic firms’ net worth because future revenues would be of more value in current terms. As the net worth increases, the risk premium decreases, inducing an increase in investment spending which leads to an increase in output. Output then increases from 10272.73 to 10500. This is the movement down along the IS curve to the point of intersection with the BP curve at B. The increase in output and decrease in interest rates which lower the opportunity cost of holding money, cause households to demand more money. This is shown as a movement down the liquidity preference curve from A to B. As the LM curve shifts rightwards, its intercept is changing and at equilibrium the resulting LM curve is i = Y – and has a lower intercept than LM0. The result is that output increases from 10272.73 to 10500 and MS increases from 2500 to 2750. Finally, the goods, money and international capital markets are in equilibrium at B with i = 10 and Y = 10500. If the CB just set i = 10, without changing the nominal money supply, MD > MS and so the money market would not be in equilibrium. Instead this would put pressure for interest rates to increase. It is therefore necessary that the CB increases the nominal money supply if it is to maintain interest rate parity. This shows that under fixed exchange rates money supply is endogenous
(c) Under fixed exchange rates, a fiscal expansion is very effective in changing output
(). The resulting increase in output will be greater than increase in government spending due to the government multiplier effect ( ∆Y = k∆G). I will assume that T is constant and its value is not affected by this particular ∆G.
T = 3000, i = 10
Y = 3000 + 0.8(Y – 3000) + 3500- 100i – 500(1)
100i = 3600- Y
i = 36 - Y [7] IS curve.
Y = 13000
MS = MD = 0.5 (13000) – 300(10)+ 50(10) = 4000
4000 = 0.5Y – 300i + 500
300i = 0.5Y – 3500
i = Y - [8] LM curve.
k = ∆Y/∆G k = (13000-10500)/ (3500-3000) = 5.
36 - Y = Y -
Y = 11863 & 7/11
i = 12 &3/11 (12.27). This is the interest rate at E1.
Fig.5 (a) and (b) show that the increase in government expenditure causes output to increase and output in turn leads to an increase in induced consumption. This causes the IS curve to shift from IS0 to IS1 along the LM curve. The increase in output raises the demand for money and so the liquidity preference curve shifts rightwards from L(i0,Y, c) to L(i1, Y, c). Excess money demand (E0E2) causes interests to rise to E1. The interest rate and output therefore rise to i = 12.27 and Y = 11863.64. The new IS-LM equilibrium point at E1, is above the financial integration line so the economy should be in surplus because the increase in capital inflows outweighs the decrease in exports. The increase in i raises the demand for the domestic currency, tending to appreciate its value. E1 does not support the interest rate parity condition, thus cannot be the final equilibrium point (41H6 lecture notes). However the CB remains committed to keeping the exchange rate at S and so the goods and money markets should always be in equilibrium with the international capital market.
The CB therefore instantaneously adjusts MS selling domestic currency and buying foreign currency to increase the money supply from 2750 to 4000. (https://netfiles.uiuc.edu/kdesmet/www/econ522/topic6.pdf). The LM curve (and M/P) therefore shifts rightwards from LM0 to LM1 (M0/P to M1/P). The excess money demand falls as liquidity increases and thus lowers the interest rate. Eventually the markets are back in equilibrium and this is at E2 where i = 10 and Y = 13000. The economy moves along the BP curve from E0 to E2.
The above calculations and dynamics are for a small open economy. It is necessary to know at what equilibrium point the economy lies when a fiscal expansion occurs. If we started off at full employment, the long run effect of a permanent fiscal policy increases MS, raises the price levels if prices were allowed to adjust, and then shifts back the IS and LM curves back to their original positions. If we started off in a recession, rather than at full employment, fiscal policy is very effective in stabilizing the economy and will take back the economy to Yf ().
Bibliography
M. Burda and C. Wyplosz (2003) Macroeconomics: A European text
41H6 lecture notes
41IE lecture notes
http://weber.ucsd.edu/~dkim/110b/AD_open_ho.pdf
