1. The General Equilibrium system of economic integration
2. The Production Possibility Frontier and its Implications
3. Concluding Comments
   

We will concentrate on the simplest economy we can think of: one which is only interested in producing and consuming two goods (food (+fibre); clothes (+ shelter)).  These two goods, which can be thought of composites as indicated, comprise all the necessities of life, and are all this simple economy produces, or, for the present, wants to produce.  It is self contained and self-sufficient as a whole. Our economy is a self-contained collection of producers and consumers - everyone is either one or both. In other words, it can be considered as a Household.

Notice - we are talking of an economy here - which might be the world,  a country, or a region, or a community or locality or village, or whatever. In the limit, such an economy could be as small as a self-sufficient, single and subsistence household.  It doesn't matter how big or small it is.  All that matters - for the moment - is that it is self-contained.  We will come to what can happen when two such economies meet and trade with each other below.  For the present, we just consider the logic of this single and simple economy as separate and self contained entity.  And, we are only considering this community as an  economy, not (yet) as a society, or a political entity.

How does our simple economy organise itself?

• to produce food (and fibre), or clothes, or (more likely) a mixture of the two.
• to consume (use) food and fibre or clothes, or almost certainly a mixture of the two.

Consider the production possibilities (the supply side) and the consumption preferences (the demand side) for the two goods (which makes up the totality of our simple economy).  We are going to draw a diagram, which allows us to picture the economy, and also allows us to determine certain logical properties of the choices our economy makes.

The diagram we will use relates production and consumption of one good (food (and fibre)) to the production and consumption of the other (clothes (and shelter)).  So we measure (illustrate) quantities of each good on the two axes:  quantity of clothes on the vertical axis and food on the horizontal axis - though it could just as easily be the other way round, it doesn't matter.  Get a bit of paper and draw this diagram for yourselves now.  Then read the following and trace the argument (logic) out on your diagram as you follow it through.

The supply side:

Consider the production or supply side first.  What options does our economy have?  To use all available production factors (land and labour) to produce food;  or to use all its factors to produce clothes; or to produce some combination of the two goods. And, because our citizens are sensible, they will organise themselves to produce as much as possible of each good.  What?  What about leisure and living?  Don't they take time and effort?  Yes, so our production possibility set will represent the quantities of the two goods our citizens are prepared to, are willing to produce, given that any production involves use of scarce (limited) time and effort, for which there are competing leisure (consumption) and recuperation (investment - see below) demands

So, there is some upper limit to the amount (quantity) of each good our citizens are prepared to produce in this economy.  We can mark these two upper limits (F* and C*) on each of the axes of our diagram of the economy.  Producing F* means that will not produce any C at all, so quantity of C is zero when Food production is at F*, and vice versa. OK?

But neither of these extremes is likely to be a sensible choice for our people - they are much more likely to choose a combination of the two goods.  What are the production possibilities for mixtures of the two goods?  Suppose we start with the economy producing all food and no clothes (at point F*on the horizontal axis), and now ask ourselves how much clothing this economy could produce if it diverted some of its resources from food to clothes production.  How much food production would have to be given up to produce the first few units of clothes?  Probably not very much, since some factors of production (land and labour etc.) are not very good for food production and would be much better at producing clothes.  Furthermore, some of our people would prefer to make clothes than produce food, so are likely to be better at producing clothes than food.

So, to begin with, moving from F* upwards and to the left to produce more clothes and less food, our economy could gain quite a lot of clothes without having to give up much food production.  Eventually, though, as we progressively cut back on food production in order to produce more clothes, we will find that we are having to give up more and more food for each extra unit of clothing production - as the extra resources we need to produce clothes are progressively better at producing food than clothes.  Eventually, we would wind up producing all clothes and no food - at point C*.

So, our production possibility relationship will be curved between F* and C*.  Make sure you follow this logic and the representation of it as the production possibility frontier (PPF) on the diagram .  This should be what you got on your own diagram as you followed the argument through.  If you didn't, why not?  Notice, it is frontier because this curve represents the maximum possible combinations of food and clothes that our citizens are willing to produce, given the land, skills, technologies and work preferences they have.

Notice, too, what this PPF means.  Suppose we start at point C* and then ask how many clothes we have to give up to produce some food.  Move along the PPF, and watch how much extra food we get as we give up limited quantities of clothes. At first, we only have to give up a little clothes for a lot of food - the slope of the PPF is quite flat.  In other words, the supply price (cost) of more food in terms of clothes given up (the opportunity cost, which here is the total cost of food production) is low.

But, as we progress down the PPF, the real cost of food  (its cost relative to everything else in the economy, which in our case is clothes) increases - the slope of the PPF gets steeper.  The cost of food production increases the more food we try and produce - the real supply curve for food slopes upwards.

Repeat this argument (logic) for the price of clothes in terms of food - you will get the same answer - the real supply curve of clothes also slopes upwards: the more we want to produce, the higher the cost in terms of foregone food production - the higher the real (relative) cost of clothes.

PPF Conclusions:

• The PPF shows the full employment capacity of the economy: inside it means unemployment; outside it is impossible (unless, that is, we add to the capacity of the economy - see below)
• So, it also shows the maximum real income our economy can generate, in terms of food and clothes mixtures.  Our producers are here not producing these things just for fun, they are producing them because they and their neighbours want them - the products are their income, their return for the work they do.
• The slope of the PPF measures the real supply price (the real cost) of producing both goods.
• The supply curves for both products slope upwards - greater quantities supplied cost more per unit.
• Notice, too, that this shape implies some considerable specialisation  - the first of the two key insights of economics into the effective organisation of societies (we come to the second below). The PPF is curved precisely because it makes sense for people (and all other resources) to do what they are best at relative to what they themselves might otherwise do, so people and resources are employed according to their comparative advantage, and specialise in doing what they do best, compared with what they might otherwise do.
  

• By "investing in human capital" - improving the health, skills and productivity of our people - the labour, (and the consumers), or simply gettting more people.
  
• By investing in land to make it more productive (draining it etc.)
• By improving the effectiveness of our production systems - getting more out for the same level of land and labour input - improving efficiency, which means one or both of better management (perhaps, ideally less management, since management by itself produces nothing), and better technologies.
• By investing in capital (tools, plant and equipment) which labour can use with the land to produce the goods.
• By combining these things so that work (production) becomes more fun and more respectable, so that people are more willing to work than before (a point seldom, if ever recognised in the textbooks)

The demand side:

What about the consumption or demand side?  Now we have to think about how to represent consumer choices about how much of each (food and clothes) they would like to have and enjoy.  Go back to your paper diagram.  Start with some mix of the two which represents one particular (and observable) choice (F1 of food and C1 of clothes) - a point (x) which will be in the middle of our diagram somewhere - it doesn't really matter exactly where. If we imagine that we are  observing this simple economy,they will have already made a choice about this, and we will see it in their output/activity mix. But, if you are drawing this on the diagram with the PPF on it (which you should now have labelled), you had better put your x somewhere on this frontier, hadn't you?   Why?

Otherwise you will be trying to consume mixes of the two goods you cannot possibly produce (x lies outside the PPF).  Or you will be wasting resources - x lies inside the PPF, which means leaving people and land unemployed when they could be working, and working at something they would like to do, and earning a living, and producing something we want, and thus earning respect.

So, put your x on the PPF - anywhere else is daft, (or, as economists say, inefficient), so we would not expect people to choose it, unless they are so stupid as not to be human.  This point x represents the one the people in our simple economy choose for themselves - it is the one we would observe them at, if we could find this simple economy to look at.

Now ask yourself how the consumers in the economy might judge other combinations or mixes of the two goods that they might have chosen instead of x (F1 and C1)?  How might they compare other possible points on this diagram with x?

Within reason, more of each good would typically be considered preferable to less of each of the two goods, especially as we have included capital in each, - right?  So we can identify the north east quadrant (all points above and to the right of point x) as a preferred set or zone of possible consumption mixes or 'baskets' of goods.  Draw this zone on your diagram now.  And the south west quadrant (all points or good combinations consisting of less and F1 food and C1 clothes) will be considered inferior choices or combinations for our consumer population.  Otherwise they would have chosen one of the points in this zone, and they did not.  Shade in this inferior zone in now.

So, somewhere in the top left (north west) and bottom right (south east) quadrants will lie a boundary which separates the preferred set of consumption mixes from the inferior set, compared with our initial combination x.  There will be a separation between mixes which are preferred and mixes of goods which are considered inferior - a separation zone or boundary along which our citizens cannot make up their minds about which mix is better and which worse - they are, in effect, indifferent between any of the mixes defined by this boundary or indiference zone.

This boundary will (has to) slope downwards and to the right, passing through our reference point, x.  So, draw such a boundary on your diagram.

You have just drawn what economists call an indifference curve (or boundary) (let's label it I2, we'll see why in a minute) which indicates all those combinations of food and clothes which the consumers cannot judge to either worse or better than the one they chose initially (x) - they are indifferent between any of the combinations which lie on this boundary or curve.  So, you can now extend the shading of both the preferred zone and the inferior zone up to this boundary. Got that?  If not, go back and re-read the logic and re-draw your own diagram.

You should have got (most of) this diagram.  ( I have left off the production possibility frontier, to make it clearer.)  But you didn't get three curves, you only got I2.  So what are the other curves?  Well, what we are drawing here is a map of consumer preferences.  The further north east we go this map, the more preferable the bundles of goods become (within reason) - bundles to the north east of x have a higher value to the consumers than bundles to the south west.  The indifference curve we have drawn is a contour line on this preference "hill" - a line joining together all those points (bundles of the two goods) which are considered of equal value by the consumers, the citizens of our economy.  So there are as many other contour lines as we care to draw on this preference map.  I have just drawn in two others, of lower value than I2, so I have labeled them I1 and Io respectively.

Now go back to point x.  Ask yourself how much food our citizens would be willing to give up in exchange for a little more clothes - move upwards and to the left of point x along the indifference curve, I2.

Why along the curve?  Because, if we move upwards and to the right of this curve, we are assuming that our consumers consider themselves to have suddenly become richer.  How come?  Because they can get to a preferred mix of both goods anywhere above and to the right of I2 - (I2 marks the boundary between the preferred set of goods and the set considered inferior.)  They choose x - because they could not get any mix of goods above and to the right (outside) I2.  If they could have, they would have, and x would be in a different place than we supposed. [This sort of analysis is known, in the textbooks as revealed preference theory for this reason - the choices people actually make reveal their preferences for what they want, and about how much effort they are prepared to put in to get it]

Indifference Curve Conclusions:

An indifference curve also shows a constant real income level for our economy, where income is now defined as command over consumption (and investment) mixes ("demand income"), rather than as the returns from production.  Note, again, that this is not a distinction that the textbooks identify.  Why not?  The answer takes us into some even deeper conceptual water than we are already in, and I don't think is necessary here, but you can follow it if you like.  It may help you in potential arguments with others who have followed textbook courses in this subject.

So, if we want to know how much food our consumers will be prepared to give up (pay) for an additional quantity of clothes, we had better hold their demand incomes constant - otherwise we will confuse ourselves about why they are willing to pay more or less for more clothes.  So we move up the indifference curve I2.  As we do so, what do we see?  That our consumers are willing to give up progressively less and less food for more and more clothes.  The indifference curve gets steeper.  The more clothes they want, the less food they are prepared to trade (pay) for them, the demand curve for clothes is downward sloping.

Alternatively, move down the indifference curve from point x.  The consumers are willing to give up less and less clothes for more and more food.  The indifference curve gets flatter.  The more food they want the lower the price in terms of clothes (the real price) they are prepared to pay.  The demand curve for food is downward sloping.

The slope of the Indifference Curve shows the real demand prices (the prices consumers are willing to pay) for the two goods. These are indeed real prices - each is priced relative to the other (which is all there is in this economy).

General Market equilibrium:  the PPF meets the Indifference Curve. (or the lecturer meets the class?).  We have now isolated the fundamental dilemma for our simple economy: how can we reconcile the production value of goods, as the things our people are prepared to do for others in return for income or payment, represented by the PPF, with the consumption value of goods, as the values people attach to consuming or having the goods for themselves, represented by the indifference curve?

Economics textbooks traditionally start with the partial answer to this question - the intersection of supply and demand curves in a single-good market. As the markets (the possible trade-offs) for each of the two goods settle down to their equilibrium positions, each will settle on a particular quantity and a particular price - at which the supply cost equals the demand price (where the supply curve and demand curve intersect).  Where will this equilibrium quantity mix (of food and clothes) be on our production possibility frontier (PPF) and consumer preference map (indifference curve map) diagram?  What combinations (quantities) of the two goods would you expect this single simple economy to choose?  Think, before you read on.

Answer: first, it has to be a mix that our citizens are willing to produce - so the combination has to lie somewhere on the PPF.  But where? Where the consumers think they are getting the best value from their consumption - i.e. as high up the preference map as possible  - on the highest possible indifference contour or curve.  Which is a single unique point (X) as a combination of C1 clothes and F1 food.  This economy, or community, cannot do better than this on its own. At this point, and only at this point, the production value of each of the goods (their supply prices) are equal to the consumption (demand or use) value of each of these goods (their demand prices) - exactly  what the traditional market diagrams show, onlyhere for all possible markets.

We should expect a sensible, coherent and communicative, and cooperative community to come up with this, given time and no interference from anywhere else.  This is how we would expect people to learn to behave, if left to themselves.  What?  No, you wouldn't expect this?  They will fight and bicker?  They will steal and thieve?  They will behave like children, then?  They won't grow up and be sensible and wise?  Why not, if we leave them alone, wouldn't we expect them to grow up and learn from their mistakes and work out how to do things better?  Isn't this what humans do, if we leave them alone?  If they don't, they will wipe each other out.  These people, in case you hadn't noticed, are our ancestors - so they didn't wipe themselves out.

OK, so I have altered the shape of the PPF here - the reason will become obvious in a minute.  For the present, just notice that this different shape reflects the capacity of the community, and its willingness to work at these particular activities - this one is better at producing clothes than food compared to the previous one.  Why?  because it has more labour and less land, perhaps, and clothing (and shelter) production is more labour intensive and less land intensive than food and fibre production. Or because theylive in colder climates, and have discovered that not only is it more difficult to produce food in such a climate, but also that they don't need asmuch food if they keep themselves warmer.

At this unique point, this single optimum combination of food and clothes, the indifference curve and the PPF will be tangential to each other - they will have the same slopes.  In other words, at this point, the rate at which consumers are willing to give up one good in terms of the other (the slope of the indifference curve), which is the consumer demand price for each good, will equal the rate at which it is possible to supply one good in terms of the other - the supply cost of each good - the slope of the PPF.  At this point, and this point alone, the production value of the two goods will equal the consumption value.

What are these rates?  They are the real (relative) prices of each good in terms of the other.  The supply prices are equal to the demand prices at this general equilibrium in our two markets.  And the price ratio of one good in terms of the other is the slope of the tangent - the ratio of C0 to F0 in the diagram opposite -  the supply price ratio of the slope of the PPF equals the demand price ratio of the indifference curve.  So, this country's markets will settle down at a general equilibrium of producing and consuming at point X, = C1 of clothes and F1 of food.

General Equilibrium (GE) Conclusions:
This conclusion now demonstrates the second key insight of economics - specialisation (in production) only makes sense if the products are traded between producers and consumers, so that needs (demands) can be most effectively met from the sensibly specialised production activities.  This  picture of general equilibrium requires specialisation (according to comparative advantage) and trade (exchange or gift).

The Case for Markets and free trade?  However, GE does NOT necessarily require explicit markets to achieve this equilibrium.  As it stands, this theoretical discussion of the implications of sensible societies  determining how to make the best use of available resources (assets) does not require any formal markets, and does not rely on money - it could work with barter, and it could (and obviously did in the past) work through patronage, dictatorship, or simple community action. Although much of the outline explanation provided above has been in terms of real prices (the price of one good in terms of the other, or the rate at which one can be exchanged for another, either in production or in consumption), this does not mean anything more than the rate of barter exchange, where goods are physically exchanged for each other. Only in the most primitive sense can such barter exchanges be considered as genuine markets. The prices referred to above can be, and often are in so-called primitive societies, implict rather than explicit.

Are markets the only way of achieving this optimum allocation of resources and goods? Good question.  See here for a discussion of this important question.

Simply making these points highlights the obvious difficulties of organising societies so as to be as effective and efficient as possible without organised and trustworthy markets. In any real society, GE implies some highly enlightened organisation, achieved in the first instance no doubt by considerable trial and error (which, of course, we are still making).

Nevertheless, Markets in principle can achieve the best of all possible worlds, in the real world in which we live. This is a fact of logic as well as a consequence of our socio-economic evolution, not just an assertion or an assumption.  It is true in principle and by demonstration of our history.   As humans, we are uniquely capable of turning our principles into practice (or, more usually, of developing best practices, and then working out why the best practice is the best practice, and trying to make it even better) - that is what we do that makes us different from the animals.  If the real world does not live up to this principle in its practice, then we will work to understand why, and then work to fix it.  This is science and reason.  Anything else is idle speculation or fantasy.  Simple, isn't it?  Tough, isn't it?  Is this why you don't like economics?

Implication:
The market system rewards the owners of the factors of production - those who have the most land, the most capital and the labour skills best fitted, most well matched to the wants of society (the consumer) will earn the most production income, and thus get to exercise the most money votes about what is produced.   If you (land, labour, capital, or management) are useless, you won't get paid in this system, and you won't get the chance to exercise your consumption income. To him that hath shall be given - from those who are most able, but not (necessarily) to those who are considered most deserving (except in the most happy (and fictitious) of societies - we still have a lot to learn, but then we haven't been practicing for very long in the wider scheme of the universe). Because markets tend to evolve into capitalism - the separation of ownership and control of the means of production (especially physical capital and  land) from the people involved in their use, and trade (exchange) of these assets between people, the economic system can result in the survival of the richest, rather than the survival of the fittest - so long as the poor are  sufficiently content (or cowed) to accept their lot without social revolution or exit (migration).

So we would also expect our sensible human community to show some humanity and seek to soften the harsh realities of natural selection (since that is what this system really is).  Our community will also develop governance and redistribution (care) systems alongside its market systems.  Why? Because, some form of government is an essential complement to this trading system - the long arm of the law is necessarily attached to Adam Smith's invisible hand of the market - to outlaw theft, enforce contracts and protect property rights (whether these are common rights or private rights).  Once in place, such governments will also become responsible for managing the natural selection of the market - including acting as judge to redistribute losses and gains, and protect or support the less well off.  The humane economy will naturally develop gifts from those who have to those who have not, which will be outside the system of specialisation and exchange portrayed here. But not independent of it, since the capacity to give depends on the resources one can accumulate and incomes one can generate.

We have not concentrated on either the sociology or the politics of our economy, our community, here - because this is the economic basis of trade and exchange.  But it is nonsense to pretend that these aspects of humanity do not exist, or that economics is fundamentally different and separated from them.  They have to fit, and the way they fit is through the governance (or management, if you prefer) of the market system. If they don't get these aspects right as well, then their markets cannot work either.

Finally, in this session - the benefits of Trade.
Now, at last, we are in a position to look at the benefits from trade.  Suppose, now, we have another community (or region, or tribe, or country, if you prefer).  This second country - country 2 - is different from country 1.  The PPF for country 2 shows that the country is better at food production and not so good at clothing production as country 1.  The preference maps are shown here as identical for the two countries, but they do not need to be.  On its own, then, country 2 would choose to produce and consume C2 clothes and F2 food, at a real price ratio of C3/F3.

Now suppose you are a trader. You have an opportunity to do business between these two communties (labeled countries here).  What are you going to do?  Buy clothes where they are cheap and sell them where they are expensive, and the same thing for food.  And where is food cheap?  In country 2 - you don't have to pay as much in clothes in country 2 as you do in country 1.  And clothes are cheap in country 1.  So there is money to be made shipping food from country 2 to 1 and clothes from 1 to 2 - right?  Just think about the meaning of the slopes of the "price lines" in each country - they show the price of one good in terms of the other.

And what happens when we start to trade - exporting food from 2 to 1 and clothes from 1 to 2?   The price of food will rise in country 2 (the food exporter), and thus the price of clothes will fall in 2.  Country 2's "price line" (C3 to F3) will get steeper.  The opposite will happen in country 1 - the line C0 - F0 will get flatter.

And what will limit this process of price changes as a consequence of trade between to two countries?  The free trade or "world price" will be the same in each country - the slopes of the price lines will be the same, flatter than 1's and steeper than 2's (ignoring the costs of the exchange or trade)   The trading price line will lie between the price lines of the two countries (or regions), as in the figure below (Ce - Fe). I have omitted the previous no-trade price lines from these diagrams, to make them clearer.  But you should be able to re-draw these for yourselves.

So what? At this price ratio, country 1's optimum consumption point is now C1c of clothes and C1f of food.  This is where the trade price line touches the highest possible indifference curve. A higher indifference curve than it can possibly get to without trade - a higher consumer or demand income - so it is definitely better off with trade.

How does it manage to consume this amount of food (which is more than it could possibly produce itself in this diagram - C1f lies outside the PPF)?  Answer - it imports food, and pays for these imports with exports of clothes.

How much food and clothes would it pay country 1 to produce?  Where the trade price line is the same slope as (lies tangential to) the PPF - since the slope of the PPF shows the supply price ratio of the two goods - the price ratio which matches the opportunity costs of producing each of the goods.  So, country 1 produces P1c of clothes, and P1f of food, and trades (P1c - C1c) clothes for (C1f - P1f) food, which it can do along the trade price line.

The exports [production minus consumption] of clothes pays for the imports (consumption minus production) of food, at the trading price ratio between the two products.  And country 1 is clearly better off with trade than without it, since it can now consume above (beyond) the limits of its production possibilities.  The same arguments apply to country 2.  Follow them through for country 2 for yourselves.

Conclusions from Trade:

• Country 1 is said to have a comparative advantage in clothing production - it can produce clothes relatively cheaply in terms of food, whereas country 2 has a comparative advantage in food production.  Notice, importantly, that one of these countries could be absolutely better at producing both goods - able to produce both more food and more clothes per person or per hectare.  But this would make absolutely no difference to its comparative advantage.  Unless both countries are absolutely identical (in which case their real prices would also be identical, and there would be no gain from trade, and thus no trade) , one must have a comparative advantage in one good and the other must have a comparative advantage in the other good - fact of logic; mathematical certainty; law of human nature - call it what you like. Notice - trade relies on differences - so, if globalisation is simply a trade phenomenon, it will not on its own produce a single global homogeneity - differentiation is much more sensible and likely.
  
• In particular - there is no way that one country can possibly have a comparative advantage in the production of both goods.  Having a comparative advantage in one good automatically means that the country has  comparative disadvantage in the other.  This result is perfectly general - it holds however many goods we might like to consider - any country (region) will have a comparative advantage in something - something which it is relatively good at compared with all the other things it might be able to do.
• Trade allows these countries to exploit their comparative advantages, buying (importing) things which are relatively cheap from elsewhere and paying for these imports with exports of things which are relatively cheap in this country, and thus relatively expensive elsewhere.
• It will pay countries to specialise in the things which they are relatively good at - the things in which they have a comparative advantage.  Country 1 here specialises in clothes - producing more than it is willing to consume, and country 2 specialises in food (& fibre) production.
• Trade prices equalise between countries as trade occurs, which encourage the appropriate supply and demand responses to exploit these opportunities for specialisation
• The results of this logical analysis are unambiguous - trade pays and is of benefit to everyone.  There is no doubt about this - it is a fact of logic - it stands to reason.  Not believing this is exactly equivalent to not believing that the earth is round and goes round the sun - it is daft, nonsensical, illogical, without foundation.
• It is also, I argue, a fact of life as well as a fact of logic - because the principle of specialisation and trade according to comparative advantage is a basic principle of evolution and natural selection.  Rabbits don't try to be wolves - they get better at being rabbits, and working better with the resources and conditions in which they find themselves. This is how natural ecosystems work, as well as how markets work.  But this is another story.

B.    The Production Possibility Frontier and its implications

If the rate at which the two outputs can be traded for each other in the market place is represented by the trade price line Z, (which indicates one of the more important links with the outside world), then the appropriate (economically efficient) production mix for the region is Q*1; Q*2 - which will define the economic structure and income earning ability of the region, and will be the outcome expected by the operation of an effectively competitive market place.

Notice - if the capital asset base of this region is increased, then the constraint lines shift outwards from the origin - the productive capacity or feasible set of outputs for the region is increased.  Notice, too, that we could also include measures of the other two major forms of capital (spatial and social), and could also further subdivide these major forms into their componant parts (with differing relative capacities in the production of the two goods (or services), which would tend to make the PPF (the Feasible region) even more convex to the origin (bowed outwards from the intersection of the axes).  We could also consider a greater number of outputs - though drawing the diagram would then become even more messy.  However, if we can draw the diagram, we can also express these relationships mathmatically, and thus remove the difficulties imposed by a two dimensional representation of the problem as a diagram.

One obvious problem with this representation of the capacity or capability of a region or community is that the production systems available to transform the capital assets (combined with appropriate inputs) into the potential products or outputs is not uniform - the representation of the use of capital assets to produce outputs 1 and 2 in this figure as if they could be trasferred between uses at a uniform rate (the constraints as straight lines) is a gross simplification.  However, this is not a serious problem.

Figure 2:  Consider the simplest relaxation of this initial assumption - that there are at least two different ways of producing a single output (Process 1 and Process 2).  Process 1 uses more of factor A (capital type A) than factor B in producing output 1, while Process 2 uses more of B than A.  If you like, Process 1 is the capital intensive production system, and 2 is the labour intensive alternative.  The choice of which process is the most appropriate (most efficient) depends on the alternative uses possible for each of the factors - what they could earn doing something else instead of producing output 1 (their opportunity costs).  If these opportunity costs are as represented by the ratio of values (prices) as price ratio x, then process 1 will be the most efficient use of these factors for output 1.  If the price ratio is y, then the most appropriate (efficient) process is process 2.

Furthermore, we can think of subdividing our major capital (factor) classes into those biits which are more suitable for the production of one good or service rather than another - output specific factor classes - which would introduce more constraints on the first of these two figures.  In the limit - a particular capital class which is only suitable for the production of one good, and completely useless for the production of another, makes the relevant constraint line in Figure 1 either vertical or horizontal (depending on which is the relevant output).

These conceptual relationships can be explicitly modelled using linear programming techniques, which replicate this logic for many outputs and many different factors (capital classes) and processes.

The fact that many of the particular ouputs and capitals relevant to the problems of rural development and sustainable resource use are difficult to measure accurately, and that the processes used to produce the relevant outputs are not well known or understood can be viewed from two rather different perspectives:

• It is therefore impossible to simplify the problems and issues in this manner, still less hope to model the various alternatives in a computable form - so this whole exercise is a waste of time.  However, if you take this stance, then you are obliged to advance an alternative framework which can be used to seriously address then problems and issues.
• These facts identify and emphasise the critical difficulties of managing (or even managing with) these complex systems - that of generating good understandings of the ways in which they actually work and could be conceived of as working differently.  The solution is then to make educated guesses about the capacities available and the process transformations which could be used, and experiment with their consequences.

Comments or suggestions to DRH