Question 1: Interest rate smoothing in the AS-AD model

A). the assumption made in deriving equation 2.5 that is there is static expectation from the population
is not reasonable since inflation in normal economy fluctuates from time to time therefore the current inflation will not always be the same as last years inflation(. However it should be said that inflation rate currently and the observed inflation will converge in the long-run when necessary action is taken by key players in the economy(Sorensen and Witta-Jacobsen, 2010). This will have the following trend

b).
,
,

,

,
,
=,

Then let us insert the equations 2.2,into equation i

Then let us insert the equations 2.3 and 2.5 into equation

Then let us insert the equations 2.5 into equation

The

,

,

In the more general AD-AS model, the effect of an increase in aggregate demand on real income depends on the shape of the AD curve. When the interest changes, the output and inflation are affected on the assumption that expectations are rational(Sorensen and Witta-Jacobsen, 2010).

c) since
, Is written as

,

And
and
,

Then let us eliminate

,
,
=,

SRAS:

These equations are inserted into

(Sorensen and Witta-Jacobsen, 2010).

The real output shows that the policy is effective in thus the model is held. The second model is more realistic than the first model. For
, we can see that if
increases, the equation would result in a lower value for the numerator. Thus if deficit increases it implies that national income would decrease. The same effect is experienced by the interest rate. That is if deficit increases then interest rate decreases as well. This analysis is easily linked to the aggregate supply-aggregate demand framework. In the case the long-run inflation rate is zero. For simplicity, suppose business-cycle fluctuations are brief enough that the short-run aggregate supply curve remains stable. The aggregate demand curve bounces up down, and output fluctuates between a high level,
, and a low level,
, on either side of the full-employment level
as the aggregate demand curve moves up, we have the expansion phase of the cycle, during which output and the price level both rise. The model shows that inflation is deeply ingrained(Sorensen and Witta-Jacobsen, 2010).

c). if the economy starts at period 0 when
then the short-run and eventual long-run equilibrium. The figure below shows the Long-run aggregate curve where the inflation is static and there are no shocks

From the graph it can be noted that short-run equilibrium is at point Eo where the actual output is lower than the natural output.

e) if the economy is hit by temporary negative shock the graph below shows how the equilibrium

From the graph it will be noted that the long-run aggregate supply curve is not affected because situation is temporary, however the short-run aggregate supply curve will be affected as shown in the graph. It will upwards from SRAS0 to SRAS1 . This changes the equilibrium from E to E1. However in the long-run it settles at E and short-run aggregate supply curve is SRAS2 . The aggregate supply curve is generally positively sloped. But, in the extreme Keynesian case, it is horizontal and in the extreme classical case, it is vertical. This is after reaching the full employment level of output, it is vertical. In the long run, aggregate supply curve is vertical. This is because, it is believed that in the long-run, there will be no unemployment of resources because markets will clear, thus whatever be the rate of inflation, firms will supply the maximum capacity of the economy(Sorensen and Witta-Jacobsen, 2010).

f) The graph below shows temporary negative demand and its effects. The aggregate demand curve shows the combinations of price level and the level of output at which the goods and the assets markets are simultaneously in equilibrium (Sorensen and Witta-Jacobsen, 2010).

When there is a negative demand the initial equilibrium which was E for Long-run supply curve and short-run supply curve shift from AD0 TO AD1 changing the new equilibrium to E1. At this point SRAS0 =SRAS2
where they meet with AD1. In this case, shock which shifts the AD curves from AD1 to AD2. In the short term, real income will rise from
and the price level will rise from
as we move along SRAS0. But this reduces unemployment below its ‘natural rate’ of unemployment, real income will return to
and the price level will rise(Sorensen and Witta-Jacobsen, 2010).

Question 2: Fiscal policy in a liquidity trap (chapter 20)

Usually rising prices create a feeling of optimism in the early stages and all businesspersons feel greatly encouraged to make heavy profits. However, rising prices hit people with fixed incomes, i.e. government employees. In the reverse direction, falling prices produce even more depressing and disastrous results. A fluctuating money standard at one time checks and at another time over-stimulates the production of wealth. Speculation prevails and efficiency in production suffers. Fluctuating prices create a feeling of uncertainty about the future (Sorensen and Witta-Jacobsen, 2010). The government acts on such situation using fiscal policy. This policy is made more flexible by the fact that governments do not need to keep ‘balanced budgets’-they can run a budget surplus by spending less than they raise in taxes. Under normal circumstances change in government spending causes income to rise and this, in turn, causes the transactions demand for money to increase; with a constant money stock, less is now is now available for speculative purposes, so that interest rates are pushed upwards and this causes private investment to be cut back, so offsetting to some extent the effect of the increase in government spending on income.

However, it is possible it is possible for fiscal policy to be completely ineffective so far as its influence over equilibrium national income is concerned. This when the level of income remains unchanged whichever fiscal policy is applied. This is point of liquidity trap. In liquidity trap, interest rates are unaffected by fiscal policy, but income rises by the full multiplier effect. (Sorensen and Witta-Jacobsen, 2010).

Figure 1: Fiscal policy completely ineffective figure 2: Fiscal policy very effective

From the two graphs above, the effectiveness of fiscal policy is shown by the steepness of the IS curve. The policy would be completely ineffective if the IS curve were horizontal, but would have its full effect if it were vertical. The steepness of the IS curve depends largely on the interest-elasticity of investment completely interest-elastic investment yields a horizontal IS curve, as shown in figure 1; increased government expenditure leaves the IS curve unchanged so that the policy has no effect on income. Perfectly interest-inelastic investment would yield a vertical IS curve, as shown in figure 2 and, in this case, an increase in government expenditure would have a full multiplier effect.

Generally, any increase in the spending made by the government authorities needs to be financed through other sources. Issuance of bonds or mere printing of new money to finance the expenditure will result in deficits of the government to the private parties. One policy, which is used often, is any increase in government spending is harmonized by an equal increase in government’s tax collection so as to keep the government’s budget incrementally balanced.

Figure 3: Fiscal policy completely ineffective figure 4: Fiscal policy very effective

Here, the government incurs no additional indebtedness. Given this equal increases in government expenditure and taxes, the change in the national income due to a change in government expenditure is referred as the balanced budget multiplier in macroeconomics. For deriving the balanced budget multiplier, one may consider the following national income identity(Sorensen, P.B. & Witta-Jacobsen, H,J. (2010).

So, the value of the balanced budget multiplier is unity. A multiplier of one implies that output expands precisely by the increase in government expenditure with no induced consumption spending. Here, the effect of higher taxes is exactly offset the effect of the income expansion. Consequently, disposable income, and consumption remain constant.

Government expenditure is harmonized by an equal increase in government’s borrowings so as to keep the government’s budget incrementally balanced. Here, the government incurs additional indebtedness. Due to expansionary fiscal policy a output level increases while the price level remains unchanged. It implies that, at a given price, more output is realized. This results into a shift in the AD curve(Sorensen, P.B. & Witta-Jacobsen, H,J. (2010).

References