Tariffs, the Terms of Trade & the Distribution of National Income

Lloyd A. Metzler

Introduction:

The law of comparative advantage:

The law of comparative advantage allows all countries to consume more of all commodities through international trade. Mills added to this, stating how international trade affects the distribution of world income among countries.
However, this does not consider the impact that international trade has on the distribution of income between the factors of production. This has resulted in the discussion of income distribution having been separated from discussion of productivity and of gains and losses to a country. Despite this separation it is clear that a country’s terms of trade have an effect on the distribution of national income.
For example, country Alpha has a large amount of land per worker, in comparison with country Beta. Therefore land will be relatively cheaper in Alpha. Both produce wheat & textiles, wheat is relatively land intensive & textiles relatively labour intensive. Therefore the unit cost of producing wheat will be lower in Alpha; Alpha has a comparative advantage in wheat production. If international trade occurs Alpha will export wheat & Beta textiles. The wheat industry expands in Alpha & textiles contract. The shift from textiles to wheat increases the relative scarcity of land in Alpha. As a result, wages per unit labour fall relative to rent per unit of land. Therefore land now has a larger share of total product. Int’l trade increases demand for each country’s abundant factors, thereby equalising the relative returns to the factors of production.


Elasticity of Demand:

The ratio of the percentage change in demand for an item to the percentage change in its price. Demand is elastic if this ratio has a value of greater than one, and inelastic if it is less than one.






Section II

Tariff:

A tariff is a tax on foreign goods upon importation.

Owners of the factor of Production which is relatively scarce want to introduce tariffs so as to restrict trade. The tariff preserves the relative scarce factor i.e. in Alpha this would be labour (textiles), textiles from abroad (which are imported) are more expensive. One of the problems with this is that it only takes account of the relative position of a factor of production and not the absolute position i.e. the absolute return may decrease even though the relative return increase. This leaves the scarce factor of production (which in Alpha is labour) with a larger share of a reduced total, which is placing them in a worse off position than before.

Stolpher & Samuelson have shown that this is not a major concern as real and relative returns move in the same directions. So Alpha could increase the real wage rate by the introduction of the tariff even though national income would decrease. The negative effect of the tariff moves onto the abundant factor i.e. in Alpha this is land. Tariff causes the factors of productions to be moved from export industries (Alpha wheat) to industries competing with imports (textiles)

It is assumed that the marginal product of a factor declines as the ratio of that factor to others in a particular industry is increased. i.e. if you have a lot of land an extra acre will not make much difference whereas if you have very few employees and you get one more that will make a lot of difference.

When wages rise relative to rents its causes a substitution of land for labour i.e. more money in labour, thus causing the ratio of labour to land to decline in all industries.


Impact on World Markets:

If a country’s exports and imports are important influences on world markets and a tariff reduces the external prices of imports, relative to the prices of exports, to such and extent that real income for the country as a whole is clearly increased. Assuming the country has a scarcity of labour and so imports goods that require a high labour content it may seem that real wages would increase. But it must be remembered that the improvement in terms of trades affects real income as well as degree of scarcity of the scarce factor of production. So when changes in the terms of trade are taken into consideration, tariffs do not always protect the scarce factor.








Case 1: Elastic Demand for Alpha’s Exports (Fig 1)


• Beta’s demand for exports of Alpha is elastic.

• Alpha imposes 50% tariff on imported textiles from Beta. Demand schedule falls from A to A’.

• Equilibrium now moves to P’. The world price of textiles (exclusive of tariff) has fallen since

OT’/OW’ > OT/OW

• But, domestic price of textiles has increased since

OT’/OW’’ < OT/OW

• P’P’’ is 50% of T’P’ i.e. P’P’’ is tariff revenue

Impact on Dist of Income:

As a result, resources shift away from the wheat industry to textiles and the relative share of labour increases, as does the wage rate. This situation holds only if Beta’s demand is elastic and the tariff revenue is assumed to be spent on domestic goods. The improvement in terms of trade is not sufficient to offset the tariff, therefore resources shift to the protected industry and this becomes relatively more profitable.

Fig 1:















Case 2: Inelastic Demand for Alpha’s Exports (Fig 2)


• Beta’s demand is now inelastic. Therefore, when the world price of textiles falls (as it does after the imposition of a tariff) Beta will offer an increasing amount of textiles for a lower amount of wheat.

• Movement of equilibrium to P’, this improves Alphas terms of trade as they can now import OT’ units of textiles for only OW’ units of wheat.

• This ∆ in terms of trade is so large that the domestic price of textiles (including tariff) actually falls in Alpha.

• This can be seen by the fact that:
OT’/OW’’ > OT/OW

• As a result, the ‘protected’ industry actually suffers with resources shifting to the export industry, wheat.

Impact on Dist of Income:

The scarce factor of production (in this case labour) actually suffers both a relative and an absolute decline in income if export demand is sufficiently inelastic. The Gov. of Alpha use the tariff revenue to soak up the excess supply of wheat (W’W’’).

Fig 2:

















Case 3: Tariff Revenue Spent Entirely on Imports (Fig 3)

• In last two situations the tariff revenue was spent entirely on domestic goods.

• What happens if tariff revenue is spent entirely on imports?

• If tariff is not spent on imports Alpha’s demand curve falls to A’.

• At P’’ traders in Alpha give OW’ units of wheat for OT’’ units of textiles (Tariff revenue is SP’’).

• Assuming OSP’ is exchange rate line Alpha gives T’’S units of wheat to Beta for OT’’ units of textiles & SP’’ to Gov. in tariff revenue.

• If Gov. of Alpha spends entire tariff revenue on imports they receive P’’P’ units of textiles for SP’’ units of wheat.

• Terms of Trade of Alpha have improved (OT’ textiles for only OW’ wheat), however, domestic price of textiles has increased as trades in Alpha only receive OT’’ units of textiles for OW’ units of wheat.

• Therefore, if tariff revenue is spent entirely on imports, resources shift to the protected industry regardless of the foreign elasticity of demand.

• Impact on Dist of Income:

Resources shift from wheat to textiles & the relative share and absolute return to the scarce factor of production (Labour) increases.

Fig 3:
















Case 4: Tariff Revenue used to Reduce Domestic Taxes

• In a more realistic world the tariff revenue will be spent on both imports & exports.

• Tariff revenue now divided in the proportions of k and 1-k between purchase of imports & exports.

• Where:
k = Marginal Propensity to Import in Alpha
n= price elasticity of demand for Alpha’s exports.

• In this case ∆ in terms of trade offsets tariff revenue; therefore domestic price ratio remains unchanged.

• OP’ is the world rate of exchange, Alpha imports OT of textiles for TU of wheat, but Gov. receive wheat = UP.

• The amount UP is returned to citizens of Alpha through reductions in income taxes & a proportion of this is now used to purchase extra imports, i.e. US/UP = k

• Traders in Alpha now receive additional textiles = SP’ & equilibrium moves to P’ on A’’.

• Alpha’s terms of trade have clearly improved (Import OT’ for only OW’ wheat).

• However, domestic price ratio remains at P since this point is 50% above U. Therefore, no shift in resources between the industries & distribution of income remains the same.

Fig 4:


How can Alpha import more if domestic price ratio remains unchanged?

This occurs because the tariff revenue allows the Gov. of Alpha to reduce other taxes, there is now more disposable income in Alpha and this is used to purchase both goods that would ordinarily have been exported and also increase imports. Therefore imports rise by TT’ & exports fall by W’W as output remains unchanged.







Generalised Model: Can tariffs be implemented without impacting on the domestic price ratio?

• Can a tariff leave the domestic price ratio unchanged?

• If the price ratio is to remain the same the ∆ in the domestic price of imports must exactly offset the ∆ in terms of trade.

• The relative increase in demand for imports = kr

• Where:
k= Marginal Propensity to Import
r = Tariff Rate

• Assuming that demand in Beta is inelastic, the relative increase in supply of textiles from Beta = TT’/OT

• This is equal to –β(W’W/OW)

o Where β is the elasticity of the reciprocal demand schedule B.

• But, W’W/OW = (1-k)r since the increased consumption of wheat is the indirect result of the tariff.

• Therefore the increase in supply of textiles:

= –β(1-k)r

• If supply equals demand:
kr = –β(1-k)r

• Divide across by r:
k = –(1-k)β

But: β = 1 – 1/n

• Where n = elasticity of the ordinary money demand schedule.

Therefore k = -(1-k)(1-1/n)

Simplifying:

n = 1-k

• Therefore, if a tariff is to have no effect on the domestic price ratio, the foreign elasticity of demand for the country’s exports must be equal to the difference between unity & the Marginal Propensity to Import of the tariff charging country.


Section III: Real World Applications

Australia

• Argued reducing tariffs would shift resources from manufacturing to agriculture.
• Metzler argued that the reduction would in fact shift resources into manufacturing.
• Australia increased tariffs in 1921.
• Long term negative effect on exchange rates and relative costs.
• Tendency to look at immediate effects of tariffs vs. long term effects.

Latin America

• These governments encourage domestic manufacturing by means of tariffs on importing competing products.
• A good means of achieving more favourable terms of trade.
• Metzler argued that any benefits they confer upon one industry will be at the expense of another.
• Inelastic demand for their exports as they are generally agricultural in nature.

Friedrich List

• Believed in general protective duties on manufacturers were a useful means of promoting industrial growth.
• Divided economic growth into 4 periods.
• Found that in only 2 of these periods protective duties were beneficial to manufacturers (2nd and 3rd).

• Period 1: Agriculture is encouraged by importation of manufactured articles.
• Period 2: Manufacturers begin to increase at home.
• Period 3: Home manufactures mainly supply home market.
• Period 4: They export and import raw materials and agricultural products.

• List concludes like Metzler that a policy of protection is a questionable method of increasing manufacturing in an undeveloped country.

• Conclusion: Changes in duties have much less effect upon protected industries than is generally supposed.









Conclusions:

(i) A shift in resources from one industry to another will increase the real income & relative share of the total income of the resource that is required in relatively large amounts (i.e. the scarce resource).

(ii) A tariff has two effects:

(a). It causes a direct increase in import prices.

(b). It causes a reduction in the world price of the goods.

The overall impact on domestic prices depends on which force is stronger.

(iii) If MPI = 0 a tariff does not increase domestic price of imports unless foreign elasticity of demand for exports >1

(iv) If MPI = 1 a tariff always increases domestic price of imports regardless of n

(v) If 1-k < 1 and n is elastic a tariff always increases domestic import prices.

(vi) However, if foreign demand is inelastic a tariff may actually cause a shift in resources from the ‘protected’ industry to the export industry.

Summary of Godley Chapter 4

Government Money with Portfolio Choice

Overview
Government Money with Portfolio Choice introduces a model which enhances and expands on Model SIM developed and explained in the previous chapter. The new model, Model PC as it is called is that which introduces a new sector, the central bank, which hitherto had implicitly been part of government in Model SIM.

With respect to the updated transactions-flow matrix which now reflect the addition of this new participant, the central bank has two accounts: current and capital. It’s current account refers to inflows/outflows which happen as part of it’s day-to-day business. The capital account refers to changes which may results from alterations to the central banks balance sheet.

Another enhancement is the introduction of government bills (commonly called Treasury Bills ) which households and the central bank can purchase. The government pays holders of these bills interest and as a consequence household income increases to reflect this. Taxable income also increases to reflect this additional income and so “The state takes back with one hand part of what it has paid out with the other” as Godley et. al put it. The central bank also receives interest for holding government bills, but any profits made are returned to government coffers.

Equations and portfolio decisions
Households make a two-stage decision in how much they will save out of their income (consumption decision) and secondly how to allocate their wealth (allocation decision). A households total wealth is the sum of it’s wealth in the last period plus the difference in disposable income and consumption:

V = V-1 + (YD-C)
Where C = α1.YD + α2.V-1

In Model PC a decision must be made by households on how to allocate their wealth between money and bonds. The equations (Brainard-Tobin formula) which describe a households allocation of wealth to bills and money can be described as follows:

Hh/V = (1 - λ0) – λ1 . r + λ2 . (YD/V)

Bh/V = λ0 + λ1 . r - λ2 . (YD/V)

Households will hold a certain proportion (λ0) of wealth as bills and a certain proportion (1 - λ0 ) as money. The two mitigating factors which determine these proportions are: Interest rates and level of disposable income YD. This has a strong intuitive appeal. Higher interest rates results in higher bill coupon payments and as a result households may wish to allocate more of their wealth to bills than to money. Also, the lower the households level of disposable income, the lower the proportion of wealth that will be held in bills.

With respect to the government and central bank sectors, government deficits are financed by newly issued bills. Also, the central bank sector purchases any bills which households do not wish to hold for that particular rate of interest. In this sense, the central bank sector is said to provide cash money on demand. Cash money is therefore endogenous (internal) to the system. Interest rates on the other hand are said to be exogenous (external) or to put it another way it is a facet of monetary policy.

Expectations
In terms of the expectations of Model PC, as was the case with Model SIM, the notion that consumption depends on expected income applies but also that expectations of income can turn out to be incorrect. Since households cannot know in advance what their income will be at the end of any given period, those equations which describe portfolio allocations must be updated to reflect those expectations. The updated equations are as follows (subscript ‘d’ is utilised for assets demanded at the beginning of the period, superscript ‘e’ refers to expectations)


Hd/Ve = (1 - λ0) – λ1 . r + λ2 . (YDe/Ve)

Bd/Ve = λ0 + λ1 . r - λ2 . (YDe/Ve)

What Godley et. al describe as a ‘crucial assumption’ made when expectations of income are incorrect, and hence expectations of wealth are incorrect at the end of a period is that “money balances are the element of flexibility in a monetary system of production” in which money balances are the “buffer that absorbs unexpected flows of funds”. This can explained by way of example. If say disposable income is higher than expected, this model assumes that the unexpected income is saved in the form of cash money balances. Thus any unexpected change in disposable income is absorbed by a similar unexpected change in money balances. Ultimately, this means that households invest in bills with respect to their expectations of disposable income at the beginning of period.

If even there is a random element thrown into the mix such that expected disposable income YDe = YD . (1 + Ra) where Ra is a random process, then the difference between the amount of money held by households and the amount demanded by them is equal to the difference between realised and expected income or to put it another way: Hh – Hd = YD - YDe. Finally, the cash held by a household at the end of any given period should provide a telling signal as to how they should modify their consumption in the next period.

Steady State
When Model PC is simulated numerically, some interesting observations are to be made. Firstly, as interest rates tend higher, households tend to own more bills. This has a sound intuitive grounding: higher rates of return per unit risk on an asset would encourage further investment one would imagine. However, it can also be observed that as interest rates tend higher so too do disposable income and consumption. This does tend to fly in the face of conventional wisdom which would suggest that consumption would tend to decrease as a result of higher interest rates. To explain what is observed in the model, the steady-state solution for national income and consumption need to be examined:

Y* = G + r.Bh*.(1 - θ)/θ
C* = YD* = Y* + r.Bh* - T* = Y* + r.Bh* - θ.(Y* + r.Bh*)

Both equations (note that the asterisk refers to steady-state solutions) are increasing functions of interest rates. Increasing interest rates result in higher national income and consumption. Model PC interest rates do not have an effect on aggregate demand (the model assumes that supply meets demand instantaneously), and as a result a fall off in consumption is not observed in this case. Finally, a steady-state solution is derived and takes the form:

Y* = (G/ θ) { (1 + α3.( 1- θ ). rbar ) / ( θ / (1 - θ) – α3 . rbar) }

where α3 = (1 – α1)/α2

Implications
In examining the above steady-state solution to national income and by varying the parameters, some further observations can be made:

1.An increase in government expenditure G leads to an increase in the national income.
2.A decrease in the overall tax rate θ leads to an increase in the national income.
3.An increase in interest rates, leads to an increase in national income. This is somewhat counter intuitive as explained above, but with reasoning with respect to the model is reasonable.
4.A reduction in liquidity preference (an increase in the desire to hold bills) leads to an increase in national income. This is because any increase in the desire to hold bills leads to an increase in interest rates.
5.When the propensities to consume from income and wealth (α1, α2) become increasingly smaller, α3 or the propensity to invest in bills become larger, then national income becomes larger.

Also to note is that when household consumption is plotted along with expected disposable income and lagged wealth, it is observed that national income rises in the short run for a given amount of accumulated wealth; the increase in consumption expenditure out of current income leads to an increase in aggregate demand; this affect is only short-lived however. As the propensity to save decreases, so too does overall wealth. As wealth decreases, consumption also decreases, and eventually impacts on national income. Household wealth and government debt decrease together by the same amount in this model. This effect may continue until a new steady-state is reached.

Re-examining the curious relationship between higher interest rates and higher national income, the assumption that the propensity to save is constant is quashed. α1
is redefined such that it assumes a value which is negatively dependant on rate of interest.

α1 = α10 –i. r-1

Substituting into the previous equation for α3 :

α3 = (1 - α10 –i. r-1 )/ α2

Simulating the model PC with this new definition causes an initial decrease in economic activity. Consumption falls as does national income. This is consistent with existing short-run economic models. However, with the reduction in propensity to consume and the increase in target wealth to income ratio, there is a gradual increase in the level of wealth. While interest rates do have a negative impact in the short run, it is shown in the long run that the income flow is still a function of interest rates. The negative impact of higher taxes which results in a decrease in consumption leads to a decrease in government tax take – this creates a government deficit until a new steady-state is reached. This adjustment to the model shows the curious short-run effect of a higher interest rates on government fiscal position.

Debt/Income Ratio
Godley et. al finish this chapter by discussing the debt-to-income ratio. Firstly, this ratio is usually measured by dividing public debt by the GDP. In the Model PC however, this can be defined as V/ Y where V is the wealth of households which corresponds to government debt. This ratio is determined by the behaviour of households and as such there is nothing the government can to alter this ratio. However, in reality governments can reduce interests or increase tax rates either of which will lead to a decrease in income. This is incompatible with maintaining full employment in the long run however and consequently it is advised debt-to-income ratio be ignored.

Summary
To summarise, Model PC has been introduced as an enhancement to Model SIM explained in chapter 3. A new participant has been added: the central bank, which is comprised of two accounts under the transaction flow matrix. Also, Treasury bills are introduced into the Model. Households and the central banks can purchase these bills; the government must pay interest to holders of the bills. Households now have further decisions to make in order to determine how much money to allocate to cash and how much to bills. Influencing this decision are interest rates and disposable income. The model was simulated and the implications changing it’s parameters were examined. Interestingly, it was shown that higher interest rates lead to higher national income which though counter intuitive, could be explained by examining the steady-state solution to national income. Finally, the debt-to-income ratio was discussed and it was advised that seeking to alter this ratio was incompatible with maintaining full employment.

Class Work 26/03/07

(i) Godley/ Lavoie Table 3.4 Period 2:

G = 20

Y = G/[1-α1{1-θ}] = (20)/[1-0.6{0.8}] = 38.5

T = θ.Y = (0.2)(38.5) = 7.7

YD = Y – T = 30.8

C = α1(YD) + α2(H -1) = 0.6(30.8) + 0.4(0) = 18.5

∆Hs = G – T = 12.3

∆Hh = YD – C = 12.3

H = ∆H + H -1 = 12.3



(ii) Period 3:


G = 20

Y = (G + α2.H -1) /[1-α1{1-θ}] = (20 + 0.4*12.3)/[1-0.6{0.8}] = 47.9

T = θ.Y = (0.2)(47.9) = 9.6

YD = Y – T = 38.3

C = α1(YD) + α2(H -1) = 0.6(38.3) + 0.4(12.3) = 27.9

∆Hs = G – T = 10.4

∆Hh = YD – C = 10.4

H = ∆H + H -1 = 10.4 + 12.3 = 22.7







(iii) Tax Rate now set at 30% Period 2:


G = 20

Y = G/[1-α1{1-θ}] = (20)/[1-0.6{0.7}] = 34.5

T = θ.Y = (0.3)(34.5) = 10.35

YD = Y – T = 24.15

C = α1(YD) + α2(H -1) = 0.6(24.15) + 0.4(0) = 14.5

∆Hs = G – T = 9.65

∆Hh = YD – C = 9.65

H = ∆H + H -1 = 9.65



(iv) Tax Rate now set at 30% Period 3:


G = 20

Y = (G + α2.H -1) /[1-α1{1-θ}] = (20 + 0.4*9.65)/[1-0.6{0.7}] = 41.13

T = θ.Y = (0.3)(41.13) = 12.34

YD = Y – T = 28.79

C = α1(YD) + α2(H -1) = 0.6(28.79) + 0.4(9.65) = 21.13

∆Hs = G – T = 7.66

∆Hh = YD – C = 7.66

H = ∆H + H -1 = 9.65 + 7.66 = 17.31