for a given change in interest rate there is marginal change in (no change) investments.
(a) In a case where investments are very interest rate inelastic.
In this case the IS curve is almost vertical. This is because as r decreases investments will increase by a small amount. Alternatively, a small increase in output will require a huge drop in interest rate.
People do not want assets, as they do not trust them. In this case the LM curve is almost vertical. This is because as income (Y) increases money demand increases, so need a huge increase in interest rate to take money demand back to starting level.
(c) If money demand is extremely sensitive to the interest rate, then it takes a very small increase in the interest rate to reduce money demand and restore equilibrium in the money market. Hence, the LM curve is (nearly) horizontal, as shown in Figure below
Assume that the domestic demand for a good is QD = 100−P, and domestic supply is given by QS = 40 + P. The market for this good is perfectly competitive.
(b) Assume that the economy opens to trade and that the world price for this good is £50. What are the equilibrium price and quantity in the domestic market? Show them in a graph.
(c) Calculate the consumer and the producer surplus in both (a) and (b). Compare them and discuss your ï¬ndings, with special reference to whether it is beneï¬cial for the country to open to trade.
(b) At world price, quantity demanded is lesser than the quantity supplied when compared to the domestic price.
(c) As we see from the above graph that the consumer surplus is the highest followed by world price and domestic price in case of the equilibrium price which is the area above the price line and below the demand curve. Whereas, producer surplus is reduced after entering into the trade. It is the area below the price line and above the supply curve. Therefore, it is not beneficial to enter into trade.
Consider the following economy. Consumption, C, depends on income, Y , and private investment, I, is exogenous. There is no government:
C = 100 + 0.7Y
I = 40
This is an open economy, where imports, Z, increase with national income. Assume also that exports, X, increase with the national income, Y X, of the home country’s trading partner (the home country takes Y X as given):
Z = 10 + 0.1Y
X = 10 + 0.1Y X
(a) Write down the aggregate demand function for this economy and graph it in the Keynesian Cross.
(b) What is the equilibrium income of this economy? What value does it take if Y X = 100?
(c) Assume now that exports are described by X = 10 + 0.2Y X. Everything else remains unchanged. Calculate the new equilibrium income. How does this change aï¬€ect the multiplier? Explain.
(a) Aggregate Demand= C + I + (X-M)
= [100+0.7Y] +40+ [X-M]
= 140 + 0.7Y + 10 + 0.1YX
Aggregate Demand= 140 + 0.6y + 0.1 YX
(b) Y= Aggregate Demand
= 140 + 0.6y + 0.1 
- Aggregate Demand = 140 + 0.7Y +10 – 0.1y -10 + 0.2 YX
(c) Aggregate Demand = 140 + 0.6y + 0.2YX
Y= 140 + 0.2 (100)
Y = 400
When there is a change of 0.1 in marginal propensity to export e.g. now for a I unit change in YX it leads to 0.2 change in exports. Thus this leads to an increase in equilibrium income by 25.
The following questions deal with the IS−LM model of a closed economy and the concept of a “liquidity trap”:
(a) A liquidity trap is a scenario in which interest rates are very close to zero. Within the IS−LM model in which the nominal interest rate is equal to the real interest rate, discuss how such low interest rates relate to the willingness of people to hold money and to the elasticity of the LM curve. Draw the IS −LM equilibrium of an economy that is in a liquidity trap.
(b) Discuss the relative eï¬€ectiveness of ï¬scal vs. monetary policy for a country in a liquidity trap. Make use of relevant diagrams in your answer.
(c) In reality, nominal and real interest rates tend to diï¬€er by the rate of inï¬‚ation, π, such that i = r + π, where i is the nominal interest rate and r the real interest rate. On which of these interest rates should money demand principally depend on? How does this impact the existence of a liquidity trap and the eï¬€ectiveness of monetary policy?
(a) A liquidity trap is a scenario in which interest rates are very close to zero. In this situation, they would not be interested to part with their cash holdings as the amount that they would get during this time is not lucrative. They would rather prefer holding money in the form of cash rather than bank deposits.
(b). In such situation, no monetary policy would not be effective. Any attempts on the part of policy makers to convince the people to hold money in the form of no liquid assets will not work merely by increasing the money supply. Hence changing the demand for money merely by altering the interest rate was no more phenomenon to control the happenings in the economy. Here comes the expansionary fiscal policy into the picture to overcome liquidity trap. Here attempts is made by the government to increase aggregate demand which happens through government expenditure or lowering the taxes.
(c). Ideally the economy must count on the real interest rate as the nominal interest rate considers inflation. It is the real interest rate which shows the amount of actual investment happening in the economy. It also shows the real income generated as mere creation of money is only going to build an inflationary pressure without any actual increase in the real output. Hence, loose monetary policy would only add to inflationary pressure.
Discuss the following statements within a Keynesian cross model. Make use of economic theory to substantiate your claims.
(a) In a closed economy where the private sector invests more that it saves, the government must be running a budget deï¬cit.
(b) To increase economic income in an open economy, the government should ban imports.
(c) The government budget multiplier is bigger in a closed economy than in an open economy.
(a). When investment is more than savings that means that the interest rate offered would low as the investment is high. This would generate lesser revenue for the government. But as the country expenses are high and there have been no changes in the government expenditure, this would led to increase in budget deficit.
(b). Government must ban imports and enter into trade as this would lead to the specialization in the production of those commodity which is cheaper to produce and would import which is expensive to produce. Hence, net exports would increase leading to the increase in the income of the country.
(c ). Government multiplier is bigger in closed economy than the openeconomy because the role of the government in terms of expenditure and intervention is comparatively more than in case of open economy. So it is higher.
Consider the following model:
C = C0 + c(Y −T),
I = I0 −br,
where C is consumption, I investment, Y is income and T denotes lump sum taxes. C0 > 0 and I0 > 0 are autonomous consumption and investment respectively, 0 < c < 1 is the marginal propensity to consume out of disposable income, and b > 0 is sensitivity of investment with respect to the real interest rate (r). Denote government spending as G and assume that money demand is give by:
(M/P)d = k(Y −T)−hr,
where k > 0 and h > 0.
Using the IS −LM model, show and discuss how the inclusion of T into the money demand function will aï¬€ect the following:
(a) Derive the equilibrium levels of income and interest rate in this economy.
(b) If taxes were not included in the money demand function, ceteris paribus, equilibrium income and interest rate would be:
Y ∗ = h/bk + (1−c)h [C0 + I0 + G + b/h+M/P −cT]
r ∗ = k/bk + (1−c)h [C0 + I0 + G−cT]− (1−c/bk + (1−c)h M/P).
With this information, and your result in (a), discuss how the inclusion of taxes in the money demand function aï¬€ect the analysis of changes in government expenditure and taxes.
(a) We see that due to the introduction of taxes , the real income declines and interest rate also falls. Equilibrium income falls from Y*4 to Y*3
The rationale behind this is that due to the inclusion of taxes, consumption reduces due to the decreased in the disposable income. This causes reduction in the aggregate demand. Thus IS curve shifts to the left.
(b) Initially when the taxes are not included, aggregate demand is a function of consumption, investment, net of government purchases and taxes and net exports. It is assumed that except consumption everything is constant. Thus, any change in any these variable will cause shift in the IS curve. These shifts depends where there have been increase or decrease in the any of these variables. Thus, inclusion of government purchases would lead to the increase in the real income and interest rate of the economy. This will increase the aggregate demand and so the IS curve will shift to the right.
However, when taxes are included, income of the people falls. This leads to the reduction in the consumption causing downward shift in the aggregate demand curve. Ultimately leading the leftward shift in the IS curve.
Answer the following questions within a Keynesian Cross model. In your answer, make use of economic theory and state clearly any assumptions you make along the way.
(a) If the household saving rate in the UK was zero, what would be the impact of an increase in government spending?
(b) How does your answer to (a) change if the UK had a large trade deï¬cit with the rest of the world?
(c) How do your answers to (a) and (b) depend on how the UK raises tax revenues? In particular, does it matter whether the UK raises lump sum taxes, or proportional income taxes?
(a). If the savings rate is zero, the increase in government expenditure would lead to the shift in the planned expenditure curve upward causing an increase in income by [1/(1-mpc)] âˆ†G
(b). If there is trade deficit with the rest of the world, that means the government is spending more than its mean leading to higher increase in the expenditure. Thus, the extent of the increase in the expenditure will be more in this case.
(c). An increases in the taxes would reduce the disposable income by the amount t, (Y-t) and hence reduces the consumption by the amount MPC x âˆ†T. hence causing the planned expenditure to shift downward by MPC x âˆ†T.
An economy is described by the following relationships:
C = c0 + b(Y −T)
I = I
G = G
T = T
where C is consumption, I is investment, T are lump sum taxes, G is government spending, c0 is autonomous consumption, b is the marginal propensity to consume and Y is income.
(a) Derive the equation for equilibrium income, Y ∗. What is the government multiplier, i.e., the multiplier that shows by how much equilibrium income changes if government spending increases by 1 unit?
(b) Explain why the government multiplier is bigger than 1.
(c) Derive the tax multiplier in this economy, i.e., the multiplier that shows by how much equilibrium income changes if taxes increase by one unit.
(d) Discuss the relative sizes of the multipliers you derived in parts (a) and (c). What do they imply for the eï¬€ectiveness of government spending relative to taxation?
(a) To determine equilibrium income (i.e. Y*). We start with the following (algebraic) set of equations:
C = C0 + b(DI)
I = Io
G = Go
T = To
X = M = 0
(C = consumption spending, b = marginal propensity to consume, c0= autonomous consumption, DI = disposable income, I = investment expenditure, G = government spending, X = exports, M = imports, and T = tax revenue)
The "o" subscripts are provided to distinguish these variables as autonomous expenditures.
Step1 - Find equilibrium:
Equate Y with Aggregate Expenditure, solve for Y*:
C= c0 + b(Y-T)
AE = Y = [b(Y - To) + c0] + Io + Go + (0 - 0)
Y* = (-bTo + c0 + Io + Go)/(1 - b)
Step 2 - Consider a change in G
suppose we allow for a change in govt. spending. If so, then:
G = Go + DG
Step 3 - Recalculate the new equilbrium:
Equate Y with the new AE, solve for Y**:
AE = Y = [b(Y - To) + c0] + Io + [Go + DG] + (0 - 0)
Y** = (-bTo + c0 + Io + [Go + DG])/(1 - b)
Step 4 - Determine the change in Y:
Subtract Y* from Y**:
Y** - Y* = [(-bTo + c0 + Io + [Go + DG])/(1 - b)] - [(-bTo + c0 + Io + Go)/(1 - b)]
Y** - Y* = (DG)/(1 - b)
DY = (DG)/(1 - b)
DY/DG = 1/(1 - b)
(b). The first is reason to be its value greater than one is, the multiplier on changes in government spending is larger than the multiplier on changes in marginal propensity to consume and second one is that as its value is government spending times to 1/(1 - b), where b, 0<b<1.
(c). In this case, we want to know how much a change in the tax rate will affect total income. Our derivation follows the same lines as before. In this case we have:
Y= b(Y-T) + I + G
dY= b (dY –dT)
dY(1-b)= - b dT
In general government multiplier is greater than tax multiplier since marginal propensity to consume is less than & equal to 1.
If government reduces taxes by $1 unit, only the MPC x $1 unit is injected into the income stream.
(d). The size of the increase in GDP depends on the type of fiscal policy.
The multiplier on changes in government spending is larger than the multiplier on changes in taxation levels.
The taxation multiplier is smaller than the spending multiplier because part of any change in taxes is absorbed by savings.