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# The Invisible Hand and Allocative Efficiency

Module by: Steven Hinson. E-mail the author

Summary: This module introduces the concept of allocative efficiency and demonstrates how markets can approach an allocatively efficient allocation of resources. The first example is highly simplified to demonstrate the concept. The second utilizes a real world example and more standard supply and demand analysis. The final section presents limitations of real world markets in achieving allocative efficiency.

## The “Invisible Hand” and Allocative Efficiency

### Learning Outcomes

• Understand Allocative Efficiency as a Benchmark
• Understand how Undirected Markets Approach Allocative Efficiency
• Understand the limitations of Allocative Efficiency in the Real Economy

A fundamental problem facing every society is how to allocate its scarce resources (i.e. land, people, energy) so as to produce the most beneficial allocation of goods and services. This problem imposes two questions: first, what do we mean by the most ‘beneficial’ allocation of resources, and second, how is it possible to coordinate the activities of literally millions of individual decision makers to achieve this allocation?

There are many possible answers to the first question. Under Mercantilism, the economic efforts of the nation were generally understood to be toward the purpose of strengthening the power of the state (often in the personage of a monarch). With the enlightenment came a change in economic thinking that instead put the wellbeing of the citizenry first. But even then the economic interests of citizens are often in conflict (e.g. the importer of wine versus domestic vintners). And so, what criteria might be sufficiently objective?

Vilfredo Pareto, an economist at the turn of the last century, put forward that, at a minimum, the desired allocation of resources should be such that it would be impossible to make one person better off with out at least making one party worse off. Otherwise, a reallocation of the resources could lead to an unambiguously superior outcome. For example, consider a situation where all automobiles have been allocated to one individual, Tom. Obviously, Tom doesn’t value any particular one of his many automobiles very much. George, on the other hand, doesn’t have any automobile at all and therefore would greatly value one. In this case, it would be entirely possible for George to trade some other good that Tom lacks (e.g. food) for one of his cars and both parties feel better off.

Building on this notion, we can define an ‘allocatively efficient’ outcome as one where no mutually beneficial trades are possible, or where total consumer valuation (defined in the next section) is maximized. But while ‘Pareto Efficiency’ assumes that any reallocation of resources will be accompanied by appropriate compensation for the losing party, ‘Allocative Efficiency’ (or its equivalent ‘Kaldor-Hicks Efficiency’), assumes only that the benefitting party from any reallocation could (but not necessarily would) compensate the losers so as to ensure no one is made worse off.

The second question to be addressed concerns how a modern industrial economy coordinates the activities of millions of independent economic agents. The following sections address this question.

### Scarcity Forces Choice

To first understand how markets achieve ‘allocative efficiency’, it’s useful to construct a vastly oversimplified economy to analyze. Our hypothetical island country, Absurdia, can produce only two goods: bottled water and soda. Further, at any given time it can produce a maximum of three bottles of either. Our bottling plants and workers are assumed to be equally adept at each and so the opportunity cost of producing either is one foregone bottle of the other. (Yes, vastly oversimplified.)

The ‘Production Possibilities Frontier’ is demonstrated by figure 1. Absurdia can produce three bottles of water and no soda, three bottles of soda and no water, or any linear combination of the two. There are four possible combinations to choose from indicated by points. (I connected the four points simply to visually reference the more standard treatment of a frontier.)

### Demand

So how might our society choose between these four combinations? In a market economy, like we have on our island, the answer depends on consumers’ relative demand for water and soda. On Absurdia, three consumers value bottled water: Kym, Tom, and Sue. Economists often use the concept of a ‘reservation price’ as a convenient proxy for how much a consumer values something like a bottle of water. As you can see in figure 2, our three Absurdians value water differently. Kym’s reservation price is $1. This means that she is willing to pay any amount up to and including$1, but no more. (She doesn’t get thirsty very often.) Tom on the other hand is willing to pay as much as $5. If we assume (only for now) that Kym and Tom have the same amount of money available, then it appears reasonable that Tom values water more, as he is willing to make the greater sacrifice in order to buy a bottle. Finally, Sue values a bottle of water at$3.

To see the relationship between reservation prices and demand, let’s next explore different pricing possibilities. First, let’s assume that the water company prices bottles of water at $5. This price exceeds the reservations prices of both Kym and Sue so they won’t buy any. Only Tom will buy a bottle of water at$5. Now let’s assume that the price is lowered to $3. The water company will now sell two: again one to Tom but also one to Sue. Finally, if the price reaches$1 or lower, they’ll sell three bottles. In figure 3, I’ve simply rearranged the bar graphs in descending order and indicated on the horizontal axis how many would be sold at each price.

The other product available in Absurdia is soda. Three different Absurdian consumers value Soda: Pat, Vim, and Tia. Their respective reservation prices are indicated in figure 4. (I went ahead and put them in descending order this time.)

As with bottled water, the quantity demanded will increase as the product price decreases. If the soda company charges $6, they will sell only one. If the price decreases to$4, they will sell two. And if the price decreases to $2 (or less) they will sell three. This is indicated in figure 5. ### Opportunity Cost Now we have some information regarding the relative value of the two goods, we can select the optimal combination of water and soda so as to maximize consumer value. In this particular example, this isn’t very hard to do. But let’s pretend it’s not so easy so I can cover one of economists’ favorite techniques, ‘marginal analysis’. Consider the first bottle of water. Do we want the water company to produce it? It depends. First, how much would a first bottle of water be valued by consumers? Assuming, for simplicity, that the bottling company uses some sort of bidding mechanism, it will almost certainly be purchased by Tom who values it at$5. But to decide whether we think it ought to be produced we also need to consider its opportunity cost (i.e. what we have to forego to produce it.) If a first bottle of water is produced, then a third bottle of soda is no longer possible. And how much was this foregone bottle of soda worth to consumers? Again assuming some type of bidding mechanism, Pat and Vim would likely purchase the first two and so it would be Tia (who valued soda at $2) that would have to do without. And so, the opportunity cost of producing the first bottle of water is$2. Should the first bottle of water be produced? Based on the information at hand, the answer is yes, it should. The value of the first bottle of water exceeds the value of the foregone bottle of soda. In figure 6, the darker bar indicates the value of the first bottle of water and the lighter bar indicates the opportunity cost of producing it.

Okay, so the first bottle of water is worth more than the third bottle of soda that must be given up in order to produce it. But how do these two independent companies, the water company and the soda company, figure this out? Well, consider the third bottle of soda. Tia is willing to pay $2 for it. So what is the very most the soda company is going to be willing to pay its workers and other suppliers to produce this third bottle of soda? The answer is certainly no more than$2. On the other hand, the water company can charge up to $5 for the first bottle of water. How much will it pay its workers and other suppliers to produce it? Exactly, they will pay up to$5. So who is going to be willing to pay the most for and therefore will be successful in hiring these resources? The water company will be.

What about the second and third bottles of water? The second bottle of water will necessitate giving up the second bottle of soda. And the third bottle of water would mean that not even the first bottle of soda could be produced. Will the water company produce the second and third bottles of water? No. The value of the foregone soda is higher in each case and so the soda company will outbid the water company for the necessary resources. And so, in the end, only one bottle of water will be produced. (See figure 7)

And what about the market for soda? Figure 8 indicates the value of each successive bottle of soda (dark bars) and the value of the foregone bottle of water (lighter bars.) The soda company will outbid the water company for the resources necessary to produce the first and second bottles of soda but not the third. Therefore two bottles of soda will be produced.

### Allocative Efficiency

So on our island of Absurdia, the water company chooses to produce one bottle of water. To produce anymore would require it to pay more for the additional resources than it would be able to charge for the added bottles of water. To produce less would be to walk away from a profitable transaction. Likewise, the soda company chooses to produce two bottles of soda. We have an answer to our original question regarding where on the production possibilities frontier to produce. But in what sense is this ‘allocatively efficient’?

Recall that ‘allocative efficiency’ implies that resources in society are allocated in such a way that combined consumer valuation is maximized. In our example this is relatively easy to see. The total value of the consumers’ reservation prices is $15 (i.e. two bottles of soda at$6 and $4 and one bottle of water at$5). Since total value is maximized, no mutually beneficial trades are possible.

By contrast consider the alternative where two bottles of water are produced and only one bottle of soda. Combined consumer value would be only $14. The loss comes from producing the second bottle of water that added$3 in value for Sue (who would buy the second bottle of water) but at a loss of $4 for Vim (who would’ve bought the second bottle of soda.) A reallocation of resources from the production of water to soda would therefore increase combined market value. The additional consumer of soda could (in theory) compensate the consumer who lost a bottle of water and both feel better off. ### The ‘Invisible Hand’ at Work on Absurdia The real ‘magic’ to the market mechanism is its ability to coordinate the activities of literally millions of economic participants without the need for any one central planning authority. To see this consider how the island of Absurdia would coordinate the necessary change in the allocation of resources if consumers decided to drink more water. Realizing the health benefits of water consumption, Tom, Kym, and Sue each increase their respective reservation prices by$2. (Notice how the dark blue bars increased in figure 9 relative to those in figure 7.) The water company will continue to produce the first bottle as before. But now, they will also profit by competing the resources necessary for a second bottle away from the soda company and therefore produce the second bottle as well. It will not however produce the third bottle, as the cost of acquiring the resources will exceed the \$3 that it can at most hope to sell it for.

And the soda company? They’ll still outbid the water company for the resources to produce the first bottle of soda. But they’ll not be able to afford the resources to produce the second bottle (nor the third as before) and will therefore produce only one bottle now. And so without any one individual directing the reallocation of resources, the island of Absurdia has successfully reallocated resources from soda to water consistent with the change in consumer demand.

### The ‘Invisible Hand’ and Tortilla Riots in Mexico

In a 2007 headline, BBC News reported that ‘Tens of thousands of people have marched through Mexico City in protest against the rising price of tortillas.” The price of tortillas, which are made from corn, had increased dramatically (by over 400% the BBC reports in the same article) severely impacting lower income Mexicans who depend on tortillas for a significant proportion of their diet. At the time the world pointed its finger at the United States, which had enacted federal policy that diverted a significant amount of corn to the production of corn-based ethanol (a more environmentally benign auto fuel.) While today, blame is also attributed to price speculators who withheld supply from the market, the example is still a good example of the ‘Invisible Hand’ at work as well as, as we’ll explore at the end, one of the most significant limitations of markets and the concept of ‘Allocative Efficiency’.

First consider the production possibilities frontier in figure 11. Corn can be used to produce either food products or ethanol for fuel. For simplicity, I used a straight-line frontier. This implies that the resources used for ethanol and food productions are perfectly substitutable. This isn’t really the case but the assumption does no harm for the purpose of this example.

Now consider the demand for ethanol depicted on the left hand side of figure 12. This stylized demand curve represents the inverse relationship between the quantity demanded of ethanol and the prevailing market price. While no names or reservation pricess are explicitly indicated, the height of the demand curve at any quantity of ethanol represents the value to some consumer of that particular gallon of ethanol.

The right hand side of the diagram represents the opportunity cost of using corn to produce food. Recall from figure 6, in the previous section, that the (marginal) cost of the first unit of water was the loss of the third unit of soda. Likewise in this example, the opportunity cost of producing the first unit of food is the loss of the last unit(s) of ethanol. As production of food continues to increase, successively more highly valued units of ethanol must be foregone (as represented by moving back up along the demand curve). And so the opportunity cost diagram on the right hand (most appropriately referred to as a supply or marginal cost curve) is simply the mirror image of the demand curve for ethanol. Similarly, the opportunity cost of producing ethanol is the lost ability to produce food. And so the supply (or marginal cost) curve for ethanol is the mirror image of the demand curve for corn.

In figure 13, the two diagrams are combined to represent the markets for food and ethanol. For units up to EA, the value of ethanol (represented by the height of the demand curve) exceeds the value of the foregone food (represented by the height of the supply curve) and so EA gallons of ethanol will be produced. However beyond EA, the value of the foregone food exceeds the value of any additional ethanol. And so the ethanol producer will find it unprofitable to compete for additional resources beyond that point. Similarly, the food producer will produce FA units of food but no more. These two quantities correspond to Point A in figure 11.

Now, consider the impact of the United States policy that diverted corn to the production of ethanol. The subsidies created by the federal government increased the value of corn in the production of ethanol. So the demand curve for ethanol shifted up. To understand the effect on the market for food, consider the situation for the corn wholesaler. The price being offered by ethanol producers has increased. Consequently, the wholesaler, who is also interested in maximizing profit, is going to demand a higher price from food producers to compensate for the loss of the sale to the ethanol producer. So the food producer will see its cost increase causing the supply curve (or better, its marginal cost curve) shift upward. The result, as seen in figure 14, is an increase in ethanol production and corresponding decrease in food production. These shifts correspond to a movement from Point A to Point B in figure 11.

### Last Thoughts

Had Adam Smith’s ‘Invisible Hand’ been a purposeful invention, it would have paralleled the steam engine and the printing press with regard to its importance to the rise of the modern industrial economy. Markets are remarkable in their use of prices to transmit information throughout an economy to a multitude of independent economic actors who, acting in their own self-interest, inadvertently continually adjust the allocation of society’s scarce resources so as to maximize combined consumer value.

However, it is important for you to also understand that this extraordinary outcome is only approximated in the real world. The neat demand and supply diagrams are based on a particular combination of market conditions that rarely hold in real markets. Relative to Smith’s late eighteenth century pre-industrial economy, today’s industrial economies are much less competitive. Further, significantly higher population density has increased the potential for and resulting costs of what economists refer to as externalities (e.g. pollution).

But there is a more significant caveat that must be understood. Consider the example of corn again. The market place led to the reallocation of corn from food production to ethanol production because consumers indicated that their relative valuation of ethanol had increased. Under the simplifying assumption that all consumers share the same amount of disposable income this should have increased combined consumer value and therefore been an allocatively efficient adjustment. But in reality, this is not the case. US consumers are clearly more affluent than the Mexican poor who depend on tortillas as a food staple. So how can we know that the last unit of ethanol produced was really worth more to some US consumer than the foregone unit of food to a lower-income Mexican? We can’t. We only know that someone was willing to pay more for it.

Simply put, the only way to know that any allocation of resources is truly ‘allocatively efficient’ is to have perfect income equity. Then we would know that the highest bidder for the use of resources is truly the highest valuing user. But this imposes a conundrum. The eloquence of the ‘Invisible Hand’ is its ability to direct self-interest for the general good. The ethanol maker will produce every unit that is more highly valued than the foregone corn (but no more) because this is what will maximize her or his profit. But if incomes are guaranteed equal, this incentive is undermined and the ethanol producer will have no incentive to pay proper heed to price signals. Unfortunately, the result of this dilemma is an eloquent system that at best only approximates allocatively efficient outcomes and at worst leads to substantially, and sometimes disastrously, inefficient allocations.

### References

Feldman, A. M. (1998). Kaldo-hicks compensation. In P. Newman (Ed.), The new palgrave dictionary of economics and the law (pp. 417-421). New York, New York: Stockton Press.

Hayek, ,F.A. (1945). The use of knowledge in society. The American Economic Review, 35(4)

Heilbroner, R. L. (1987). The essential adam smith. New York, New York: W.W. Norton and Comany.

Mexicans stage tortilla protest. (2007). Retrieved January 24, 2012, from http://news.bbc.co.uk/2/hi/6319093.stm

Reinhardt, Uwe E. (2010). When Value Judgements Masquerade as Science Economix (New York Times). Retrieved January 31, 2012, from http://economix.blogs.nytimes.com/2010/08/27/when-value-judgments-masquerade-as-science/

Stiglitz, Joseph E. "The Invisible Hand and Modern Welfare Economics" (March 1991). NBER Working Paper Series, Vol. w3641

Thomson, A. (2010). Tortilla riots' give foretaste of food challenge Financial Times. Retrieved January 24, 2012, from http://www.ft.com/intl/cms/s/0/a0aa9ef0-d618-11df-81f0-00144feabdc0.html

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