The Transfer Problem and Exchange Stability
Definition:
“Consider a unilateral payment from one country to the other. This involves two parts: a financial (monetary) transfer and a real transfer. The monetary transfer refers to the accumulation and liquidation of debt on the part of individuals or governments in each country, while the real transfer refers to the induced movement of goods.
...Assume that A is the transferring country. Whatever the type of transfer ... domestic expenditure in A is reduced, and in B (transferor) is increased, by the amount of the transfer. These changes in expenditure induce changes in demand that, at constant terms of trade, create disequilibrium in the balance of payments. The transfer problem may then be posed as the problem of determining the direction and extent of the change in the terms of trade required to eliminate”.
http://www.columbia.edu/~ram15/ie/ie-02.html
Examples:
U.S.A:-. In order to transfer resources in real (non-financial) terms from the rest of the world, the U.S. runs very large trade deficits in manufactures from surplus-saving industrial economies such as China, Japan etc. This “real” transfer of manufactures needed to cover the shortfall in American saving speeds the contraction in employment in U.S. manufacturing beyond the “natural” rate of decline experienced by other mature industrial economies.
Why is this a problem?
The upshot is a protectionist backlash in the United States, particularly by members of Congress with manufacturing constituencies. These people incorrectly blame “unfair” foreign trading practices—undervalued currencies, substandard labor practices,or “dumping” of subsidized exports in American markets—instead of America’s own deficient saving covered by foreign borrowing.
http://www.aeaweb.org/annual_mtg_papers/2007/0106_1015_0702.pdf
Thailand:- The reversal in the current account: the country was forced by the reversal of capital flows to go from a deficit of some 10 percent of GDP in 1996 to a surplus of 8 percent in 1998. The need to effect such a huge change in the current account represents what may be history's most spectacular example of the classic “transfer problem” debated by Keynes and Ohlin in the 1920s. In practice this swing has been achieved partly through massive real depreciation, partly though severe recession that produces a compression of imports.
http://web.mit.edu/krugman/www/FLOOD.pdf
Classical approach – equality between income and expenditure equating to full employment of resources.
Keynesian approach – economy has perfectly elastic supply of labour and demand for labour and commodities at fixed wage and price level.
Two Problems:
(a) Will method of transfer finance affect each countries demand for imports enough to create trade surplus/deficit needed to affect transfer?
· Finance will reduce As demand for goods and increase Bs. This improves As balance of trade and worsens Bs.
· This usually implies disequilibrium which must be adjusted. How?
Classical - price inflation/deflation to change terms of trade.
Keynesian – price inflation/deflation to change terms of trade or devaluation.
(b) Will adjustment mechanism restore equilibrium? Factors:
· Direction – will a small downgrade in A or Bs terms of trade improve or worsen its’ trade balance? Stability Problem!
· Magnitude of influence – if such a downgrade does improve terms of trade, can trade balance increase be enough to achieve surplus?
Classical approach – we assume full employment. So if a decrease in As expenditure = increase in Bs expenditure this means no multiplier effect. A’s balance of trade improves due to decrease in demand for imports & increase in demand for exports.
• Total improvement = ∑ As Import expenditure change + Bs Import expenditure change
• If ∑ As Import expenditure change + Bs Import expenditure change > unity => Transfer is undereffected so terms of trade will change against A – and vice versa also applies
Focusing on proportions of expenditure change, we assume expenditure proportions can be related to A and Bs marginal propensities to spend on imports/exports. We highlight 3 cases:
1. Free Trade: A receives all proceeds from exporting to B.
2. Tariffs but no transport costs: Under Classical approach, we assume tariffs are redistributed and spent by B. As such proportions of expenditure change on exports is greater than marginal propensity to spend on exports.
3. Transfer costs but no tariffs: Transfer costs are receipts for A. Hence transport costs are an indirect demand for goods. So proportion of expenditure change on exports is greater than marginal propensities to spend on exports.
What does classical approach mean for countries involved? Let’s assume transfer undereffected if – when both A and B have an increase in income - A has greater spending power.
In case 1, free Trade A and B pay same prices. For Classical theory to hold, if both countries have similar “tastes” for goods, the country with the higher income per head produces more “luxurious” goods for export i.e. goods differ in degree of necessity.
Where tariffs and transport costs exist, goods are cheaper in the exporting country. For classical approach to hold, a country must favour its’ exports over imports and country with lower income per head must produce necessary goods.
What about indirect consumption?
For the case of tariffs but no transport costs, we assume indirect consumption of tariffs is same as direct so classical approach holds.
Where we have both transport costs and free trade, if transport costs are added fully to imported goods, then consumers are more likely to purchase similar home produced goods. And vice versa.
Additional factors to consider?
1. Varying the home production of similar imported good? Not relevant as it’s the price ratio that’s the crucial factor here.
2. Non-traded goods? Is a factor as demand for such goods changes total demand for imports/exports.
More countries? Is a factor since balance of trade between A and B are no longer
eual or opposite
II. The Keynesian Transfer Problem
Assumptions:
- economy consists of a perfectly elastic supply of labour and commodities at a fixed wage and price level so that output, income and employment are determined by aggregate demand (AD)
- exchange rates & interest rates are fixed by monetary policy
- international capital movements are independent of national income.
Multiplier Equations: (for country A and B)
- these equations relate changes in national income and balance of payments to changes in demand
- all marginal propensities are positive to guarantee stability in the system
Notation:
· Ya,b total change in national income
· Ba total change in country A’s balance of payments
· Ia,b change in demand for country’s own output
· Ma,b change in demand for each other’s output
· T change in capital movements from A to B
· ca,b marginal propensity to spend on domestic output
· ma,b marginal propensity to spend on imports
· sa,b marginal propensity to save in each country
Equations:
Ya = Ia + caYa + Mb + mbYb
Yb = Ib + cbYb + Ma + maYa
Ba = Mb + mbYb - Ma - maYa - T
Keynesian Problem:
Unlike the classical (real) case we do not assume that aggregate expenditure of A and B will change equal to the amount expensed on financing and disposal of the transfer. Any such changes in expenditure will have multiplier effects on the balance of trade between A and B. The problem therefore is whether the transferor’s balance of payments worsens or improves as a direct result of the transfer.
Solution:
To solve this problem we simply substitute for the change in demand in the multiplier equations with the proportion of the transfer whereby demand for domestic and foreign goods is reduced in A and increased in B (or vice versa).
We will work with the change in demand for imports and the saving associated with the transfer since the transfer must alter demand for domestic goods and imports or the accumulation of assets through saving.
m` change in demand for imports (as a proportion of amount transferred)
s` change in saving (as a proportion of amount transferred)
quations:
Ya = 1 / sa (Ba + s`a T)
Yb = - 1 / sb (Ba + s`b T)
Ba = (m`a + m`b - ma / sa (s`a) - mb / sb (s`b) – 1) X (sasb / Δ) T
where Δ = sasb + samb + sbma
From these equations we concur that the transfer will be undereffected or overeffected where m`a + m`b (sum of proportions of transfer by which expenditure on imports is altered by financing and disposal of transfer) is less than or greater than
ma / sa (s`a) + mb / sb (s`b) + 1
This criterion allows the transfer to be either undereffected or overeffected according to the scales of various parameters. The behaviour of income therefore, is determined by whether the transfer is undereffected or overeffected.
Generally, there seems to be less reason in the Keynesian model than in the classical model to identify the direct effects of the transfer on demand with those of any other economic change.
III – Application of transfer theory
Transfer theory applied in the analysis of:
Reparation payments
International flows of long term capital.
Also more importantly in overcoming any Balance of Payment (BOP) disequilibrium through either automatic mechanisms of adjustment or planned government policies.
Both the floating and fixed rate regimes are "automatic" free-market mechanisms for international payments. With a "clean" floating rate, a monetary authority sets a monetary policy, but has no exchange-rate policy—the exchange rate you might say is on autopilot. In effect, the monetary base is determined domestically by a monetary authority. In other words, when a central bank purchases bonds or bills and increases its net domestic assets, the monetary base increases and vice versa. Whereas, with a fixed rate, a monetary authority sets the exchange rate, but has no monetary policy—monetary policy is on autopilot. In consequence, under a fixed-rate regime, the monetary base is determined by the balance of payments. In other words, when a country's official net foreign reserves increase, its monetary base increases and vice versa. With both of these free-market exchange-rate mechanisms, there cannot be conflicts between exchange-rate and monetary policies, and balance-of-payments crises cannot occur. Market forces automatically rebalance financial flows and avert balance-of-payments crises.
Government policies are important in overcoming the above mentioned imbalance. For example the UK government might intervenr to raise or lower the value of sterling. This can be done through short term interest rates: usually raising them attracts investors into buying sterling while lowering encourages selling. Another option is to utilize its foreign currency reserves to push up its value or at least hold it steady.
BOP imbalance occurs due to some form of transfer from the surplus to deficit country. This can be solved by creating a transfer of equal amount in opposite direction.
For example, with ‘full employment’ in deficit country, deterioration in terms of trade will be less (or improvement greater) the more deflation of expenditure in deficit country and inflation of expenditure in surplus country is spent on imports as opposed to on exportable goods. Terms of trade refers to the purchasing power of a country’s exports in terms of the imports it buys; it indicates how much of goods and services one country can buy from abroad with the goods and services it sells abroad. The terms of trade shift whenever a country’s exports will buy more or fewer imports. An improvement in the terms of trade occurs when export prices rise relative to import prices.
In the Keynesian transfer analysis:
With a positive Marginal prop to save (MPS) in both countries changes in income taxation adequate to yield change in budget surpluses or deficits equal to original BOP deficits will not solve the disequilibrium issue. However changes in government expenditure of this amount may do so. This example involves adjustments to aggregate income and expenditure.
A more important application looks at effects of changes in relative price levels on the BOP’s. Change by deflation or inflation of domestic currency prices of fixed exchange rates or by alteration of exchange rate.
Problem formulated in terms of
Effects of devaluation on trade balance
Stability of foreign exchange markets
The Central theoretical problem
Conditions under which a relative reduction in export prices would tend to improve a countries trade balance?
Volume of exports determined by demand from abroad which in turn depends on the state of importing country, price of exports which are dependant on inflation and exchange rate and finally the quality of products.
Look at the exchange stability problem in terms of transfer theory. We assume that trade is balanced and no barriers exist.
What happens in terms of country A if there is a reduction in the price of A’s exportables relative to B?
Transfer from A to B = in amount to the increase in the cost of A’s initial volume of exports.
And in terms of B to the reduction in the costs of B’s initial volume of imports.
With initial balance and small price change these two transfers are approximately equal.
Transfer is ‘financed’ and ‘disposed of’ through effects of the relative price change which will have income and substitution effects on the demands of the countries for their own and each others goods.
The income effect – real income falls as prices increase
The substitution effect – price change that causes the consumer to substitute away from the comparatively more expensive one.
Price change will affect two countries aggregate expenditure and expenditure on imports.
Exchange stability problem takes into account whether effects of price change on expenditure will be sufficient to effect the transfer implicit in the price change itself.
With regard to classical case All income is spent insuring that transfer is accompanied by equal change in the two countries expenditure.
Transfer will be over or under-effected or market stable or unstable according to whether sum of the proportion of the transfer by which two countries expenditure on imports change is greater or less than unity.
Unit elasticity describes a supply or demand curve which is perfectly responsive to change in price. That is quantity supplied or demanded changes according to the same percentage as the change in price.
These proportions, equal to the price of demand for imports of the countries so that the market is stable depend on whether the sum of these elasticities is greater or less than unity. Transfer analysis leads to stable or unstable dependant on whether elasticities greater of less than
1+ S’a (ma / Sa) + S’b (mb / Sb)
Sa - marginal propensity to save
m – marginal propensity to import
S’a – proportion of transfer by which saving from pre-transfer level of income is reduced in A by increase in price of A’s imports.
S’b – proportion of transfer by which saving from pre-transfer level of income is increased in B by decrease in the price of B’s imports.
S’s above represent the consequence of a fall in the price of imports on saving or increase in the price of imports on expenditure from initial income divided by initial value of imports.
When elasticity is less than unity (inelastic demand) higher prices bring larger outlays.
When elasticity is greater than unity (elastic demand) higher prices bring smaller outlays.
Laursen and Metzler – highlight that in the short run of the cycle, a rising proportion of real income is saved to the conclusion that an increase in price of imports would increase expenditure thus making critical sum of elasticities import demand greater than unity.
Harberger looks at effect of an increase in imports prices on savings. He assumed that saving is measured in exports goods and depends on real income only, and that changes in prices inducing no substitution between Savings and Consumption.
Therefore it can be deduced that the criteria of exchange stability becomes whether sum of elasticities of import demand is greater or less than 1 plus the sum of Marginal propensity to import.
Assumptions of this criticized for a number of reasons.
Day, Savings and Imports might be substitutes (as imports may be consumer durables yielding flow of satisfaction comparable to interest on saving)
Pearce, shows Day overlooks effects of change in price of Imports on real value of interest.
Spraos, shows MPS from a change in real income due to change in real income due to change in Import prices is likely to be substantially greater than MPS from change in output at constant prices.
Spraos and Pearce, show Harberger implies presence of money illusion since they ignore effects of an increase in price of Imports in reducing value of saving.
If substitution effects between imports and savings and Pigou’s effect of import prices on savings are ignored then Harberger analysis on assumption that real rather than money saving depends on real income to yield
S’ = (Average propensity to save / 1-APS) X ( €s -1)
$s is income elasticity of demand for real saving. I – APS is the equivalent of the average propensity to consume.
The above formula proposes that the effect of a fall in the price of imports on saving = (APS / APS) X (Income elasticity of demand for real saving – 1)
This alteration reconciles Harberger’s and Metzler and Laursen’s approach. It also confirms the workings below in deducing the effect of devaluation on expenditure from the relationship between the savings ratio (MPS) and income.
Average propensity to save = Savings / Volume of domestic Output.
(Savings here is equivalent to Volume of domestic output minus Consumption at home and abroad.)
However it assumes that imports are demanded for consumption only. If some imports are required for investment as would be reasonable and investment expenditure is fixed in real terms a fall in import prices affects money saving both by increasing consumers real income and by reducing the cost of investment imports.
The preceding result is than changed to
S’ = mc (APS / 1-APS)($s – 1) + mi
Mc and Mi are proportions of the original volume of imports devoted to consumption and investment, respectively. Even though the assumption that the critical value of the sum of the elasticities of import demand is greater than unity implies a slightly unrealistic assumption about the behavior of the savings ratio this last result can be supported by the introduction of investment imports.
Tuesday, April 24, 2007
Tuesday, April 10, 2007
Chapter 4 – Government Money with Portfolio Choice
This posting is outside the 700 word boundary. It was decided that to reduce any further would mean losing clarity of summary, and the omittance of important facets of the theory.
Model portfolio choice (PC) adds T-Bills (US Treasury Bills) and interest payments into model SIM while also making the assumption that there is no production sector thus the household makes up the whole private sector. T-Bills are issued on a discount basis. At maturity you are offered the face value of the bill. The amount paid for the right to the face value at time T is lower i.e. at a discount, the difference being the interest rate.
The new balance sheet matrix shows that households can either hold cash or bills the sum of the two being the net worth. The total public debt is then equal to the bills held by the households and the bills held by the central bank. The central bank also takes deposits from the households.
The flow matrix in this chapter has two main changes to the previous chapter. Firstly the change in bills figures are added to the flow of funds accounts. Also there are now interest payments arising from government debt which must be accounted for. The central bank sector is now divided into current account and capital account. The current account deals with the inflows and outflows from the current operations of the central bank while the capital account describes any changes in the balance sheet of the central bank e.g. the purchase of new bills.
The Equations
The equations are built on the presumption that producers sell whatever is demanded and that householders have correct expectations regarding their incomes.
Y = C + G
Production is equal to consumption + government expenditure.
YD = Y – T + r-1 . Bh-1
Disposable income is enlarged by adding interest payments on government debt.
T = Ø . (Y + r-1 . Bh-1)
Taxable income is enlarged by adding interest payments on bills held by households.
The Portfolio Decision
Two decisions households face – How much they will save and how they will allocate wealth. The second decision is dependant on the first.
V = V-1 + (YD – C)
Difference between disposable income and consumption is equal to total change in wealth.
C = α1 . YD + α2. V-1, 0< α2 < α1 < 1
Money is replaced by wealth.
4.6A)
Households want to hold a certain amount (λ0) of wealth in bills and the rest (λ0-1) in money. The proportions are dependant on the level of interest on bills and the level of disposable income relative to wealth.
4.7)
Follows from equation 4.6A to show what has to be the share that people hold in the form of bills.
The endogeneity of the money supply
∆BS = Bs – Bs-1 = (G + r-1 . Bs-1) – (T + r-1 . Bcb-1)
The government deficit is financed by bills issued by the treasury department.
∆Hs = Hs - Hs-1 = ∆Bcb
Additions to the stock of high powered money are equal to the additional demand for bills by the central bank.
Bcb = Bs - Bh
r = r¯
The central bank is the residual purchaser of bills. It purchases all the bills offered by the government that the householders are not will to purchase at a given interest rate.
Hh = Hs
The amount of cash that households hold is equal to the amount of cash supplied by the central bank.
4.5 The Steady State Solutions Of The Model
4.5.1 The Puzzling Impact Of Interest Rates
By adding 100 Basis points to the interest rate the Banks set out in Model PC we can identify the difference between it and Model SIM. This results in an expected increase in Households holding more interest paying bills and an unexpected rise in disposable income and consumption. On this occasion when getting steady state solutions of the model government balances means that state revenues plus the profits of the central banks must be equal to pure government expenditures on goods and services plus the cost of servicing the government debt. We arrive at: (4.18)
Y* = G + r.B*h . (1 – θ) / θ = GnT/ θ
This is the steady-state value for national income. Likewise the steady-state solution for disposable income can be obtained by assuming consumption here equals disposable income and substituting Y* for its value in 4.18 we arrive at: (4.19)
C* = YD* = (G + r.N*h).[(1 – θ)/θ]
Both equations are, in full stationary state, an increasing function of the interest rate. This explains the earlier higher interest rates are associated with a higher steady-state national income. Ultimately higher interest rates mean larger absolute amount of bills and households are encouraged to hold a larger proportion of their wealth in the form of bills both leading to larger interest payments on debt.
4.5.2 Fully Developed Steady State Solutions
To formally demonstrate that an increase in the rate of interest will lead to an increase in the amount of bills held by households and an increase in the overall interest payments received by households we must find the value of B*h and substitute it into equations 4.18 amd 4.19. We first turn the consumption function (4.5) into a wealth accumulation function and combine equations 4.4 and 4.5 to get:
∆V = α2 . (α3 . YD – V – 1)
After identifying the value of ∆V = 0 and getting the ratio for wealth and disposable income we combine equations 4.21 and 4.7 we get a value for B*h. After much manipulation we arrive at:
Y* = (G/ θ) { 1 + α3. (1 – θ) . ѓ/[θ/(1- θ)] - α3 . ѓ }
4.6 Implications of changes in parameter values for temporary and steady-state income
4.6.1 Some Puzzling results
If there were an increase in the permanent level of government expenditures G or any permanent decrease in the overall tax rate θ would lead to an increase in the stationary level of income and disposable income: dY/dθ < 0 . Higher rates of interest leads to an increase in the flow of payments that arise from the government sector which leads to an increase of the steady-state level of disposable income and households holding more interest paying government debt. Also increases in the α3 parameter also eventually leads to an increase in stationary income or disposable income.
4.6.2 A Graphical Analysis
As discussed earlier, an increase in any of the propensities to consume means a decrease in the target wealth to disposable income ratio will result. Godley goes on to state that the effect of a higher propensity to consume out of expected disposable income is positive in the short-term, with GDP rising, but, on the other hand, GDP congregates to a new steady-state value in the long run, which is lower than the original steady-state.
Furthermore, National Income rises in the short-term, but then again this effect is only momentary. A lower propensity to save by individuals results in the stock of wealth decreasing, because consumption exceeds disposable income. However, the reduced consumption ultimately compensates for the higher consumption out of current income, so as the wealth continues to decrease, consumption and the interest income on government debt also continue to drop; until it reaches a “new stationary state”, which is lower than the previous steady-state.
Since this is a simplified model, both the household wealth and government debt decrease together, because households are consuming more and therefore, dissaving; while the government benefits from this boost in economic activity, through the generation of increased tax revenues.
In Model PC the relationship between disposable income (YD) and national income (Y) is more complicated than Model SIM, as it goes beyond taxes and takes into account interest payments on debt:
Y = r-1 * Bh-1 + YD /(1- θ)
This equation shows that any increase in the interest rate, or in the propensity to consume leads to a temporary increase in disposable income and national income.
Godley then goes on to state that when one is comparing steady-states, the aggregate income flow is still an increasing function of the interest rate, albeit the short-term impact of interest rates is to reduce consumption and hence income.
Finally, Godley explains that if government officials want to decrease the public debt-to-GDP ratio, they would need to increase tax rates or reduce interest rates, which would lead to a lower level of stationary income. Therefore, they should disregard the debt-to-income ratio if they want to maintain full-employment income.
Model portfolio choice (PC) adds T-Bills (US Treasury Bills) and interest payments into model SIM while also making the assumption that there is no production sector thus the household makes up the whole private sector. T-Bills are issued on a discount basis. At maturity you are offered the face value of the bill. The amount paid for the right to the face value at time T is lower i.e. at a discount, the difference being the interest rate.
The new balance sheet matrix shows that households can either hold cash or bills the sum of the two being the net worth. The total public debt is then equal to the bills held by the households and the bills held by the central bank. The central bank also takes deposits from the households.
The flow matrix in this chapter has two main changes to the previous chapter. Firstly the change in bills figures are added to the flow of funds accounts. Also there are now interest payments arising from government debt which must be accounted for. The central bank sector is now divided into current account and capital account. The current account deals with the inflows and outflows from the current operations of the central bank while the capital account describes any changes in the balance sheet of the central bank e.g. the purchase of new bills.
The Equations
The equations are built on the presumption that producers sell whatever is demanded and that householders have correct expectations regarding their incomes.
Y = C + G
Production is equal to consumption + government expenditure.
YD = Y – T + r-1 . Bh-1
Disposable income is enlarged by adding interest payments on government debt.
T = Ø . (Y + r-1 . Bh-1)
Taxable income is enlarged by adding interest payments on bills held by households.
The Portfolio Decision
Two decisions households face – How much they will save and how they will allocate wealth. The second decision is dependant on the first.
V = V-1 + (YD – C)
Difference between disposable income and consumption is equal to total change in wealth.
C = α1 . YD + α2. V-1, 0< α2 < α1 < 1
Money is replaced by wealth.
4.6A)
Households want to hold a certain amount (λ0) of wealth in bills and the rest (λ0-1) in money. The proportions are dependant on the level of interest on bills and the level of disposable income relative to wealth.
4.7)
Follows from equation 4.6A to show what has to be the share that people hold in the form of bills.
The endogeneity of the money supply
∆BS = Bs – Bs-1 = (G + r-1 . Bs-1) – (T + r-1 . Bcb-1)
The government deficit is financed by bills issued by the treasury department.
∆Hs = Hs - Hs-1 = ∆Bcb
Additions to the stock of high powered money are equal to the additional demand for bills by the central bank.
Bcb = Bs - Bh
r = r¯
The central bank is the residual purchaser of bills. It purchases all the bills offered by the government that the householders are not will to purchase at a given interest rate.
Hh = Hs
The amount of cash that households hold is equal to the amount of cash supplied by the central bank.
4.5 The Steady State Solutions Of The Model
4.5.1 The Puzzling Impact Of Interest Rates
By adding 100 Basis points to the interest rate the Banks set out in Model PC we can identify the difference between it and Model SIM. This results in an expected increase in Households holding more interest paying bills and an unexpected rise in disposable income and consumption. On this occasion when getting steady state solutions of the model government balances means that state revenues plus the profits of the central banks must be equal to pure government expenditures on goods and services plus the cost of servicing the government debt. We arrive at: (4.18)
Y* = G + r.B*h . (1 – θ) / θ = GnT/ θ
This is the steady-state value for national income. Likewise the steady-state solution for disposable income can be obtained by assuming consumption here equals disposable income and substituting Y* for its value in 4.18 we arrive at: (4.19)
C* = YD* = (G + r.N*h).[(1 – θ)/θ]
Both equations are, in full stationary state, an increasing function of the interest rate. This explains the earlier higher interest rates are associated with a higher steady-state national income. Ultimately higher interest rates mean larger absolute amount of bills and households are encouraged to hold a larger proportion of their wealth in the form of bills both leading to larger interest payments on debt.
4.5.2 Fully Developed Steady State Solutions
To formally demonstrate that an increase in the rate of interest will lead to an increase in the amount of bills held by households and an increase in the overall interest payments received by households we must find the value of B*h and substitute it into equations 4.18 amd 4.19. We first turn the consumption function (4.5) into a wealth accumulation function and combine equations 4.4 and 4.5 to get:
∆V = α2 . (α3 . YD – V – 1)
After identifying the value of ∆V = 0 and getting the ratio for wealth and disposable income we combine equations 4.21 and 4.7 we get a value for B*h. After much manipulation we arrive at:
Y* = (G/ θ) { 1 + α3. (1 – θ) . ѓ/[θ/(1- θ)] - α3 . ѓ }
4.6 Implications of changes in parameter values for temporary and steady-state income
4.6.1 Some Puzzling results
If there were an increase in the permanent level of government expenditures G or any permanent decrease in the overall tax rate θ would lead to an increase in the stationary level of income and disposable income: dY/dθ < 0 . Higher rates of interest leads to an increase in the flow of payments that arise from the government sector which leads to an increase of the steady-state level of disposable income and households holding more interest paying government debt. Also increases in the α3 parameter also eventually leads to an increase in stationary income or disposable income.
4.6.2 A Graphical Analysis
As discussed earlier, an increase in any of the propensities to consume means a decrease in the target wealth to disposable income ratio will result. Godley goes on to state that the effect of a higher propensity to consume out of expected disposable income is positive in the short-term, with GDP rising, but, on the other hand, GDP congregates to a new steady-state value in the long run, which is lower than the original steady-state.
Furthermore, National Income rises in the short-term, but then again this effect is only momentary. A lower propensity to save by individuals results in the stock of wealth decreasing, because consumption exceeds disposable income. However, the reduced consumption ultimately compensates for the higher consumption out of current income, so as the wealth continues to decrease, consumption and the interest income on government debt also continue to drop; until it reaches a “new stationary state”, which is lower than the previous steady-state.
Since this is a simplified model, both the household wealth and government debt decrease together, because households are consuming more and therefore, dissaving; while the government benefits from this boost in economic activity, through the generation of increased tax revenues.
In Model PC the relationship between disposable income (YD) and national income (Y) is more complicated than Model SIM, as it goes beyond taxes and takes into account interest payments on debt:
Y = r-1 * Bh-1 + YD /(1- θ)
This equation shows that any increase in the interest rate, or in the propensity to consume leads to a temporary increase in disposable income and national income.
Godley then goes on to state that when one is comparing steady-states, the aggregate income flow is still an increasing function of the interest rate, albeit the short-term impact of interest rates is to reduce consumption and hence income.
Finally, Godley explains that if government officials want to decrease the public debt-to-GDP ratio, they would need to increase tax rates or reduce interest rates, which would lead to a lower level of stationary income. Therefore, they should disregard the debt-to-income ratio if they want to maintain full-employment income.
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