by Jim Rose in applied price theory, labour economics, unemployment Tags: Alfred Marshall, Armen Alchian, comparative statics, labour market shortages, search and matching, second law of demand, second law of supply, skill shortages, unemployment

Could you define both a severe skills shortage and a skills shortage?

How do these concepts differ from concepts such as rising demand, rapidly rising demand, and reduced and sharply reduced supply?

Are the phrases severe skills shortage and a skills shortage more precise than the phrases rising demand, rapidly rising demand, and reduced and sharply reduced supply?

Are the phrases severe skill shortage and a skill shortage more informative than referring to the short and long run elasticity of demand and supply as summed up in the second laws of demand and supply?

Why are rising demand, rapidly rising demand, and reduced and sharply reduced supply considered to be social problems. What causes rising demand, rapidly rising demand, and reduced and sharply reduced supply?

For whom are rising demand, rapidly rising demand, and reduced and sharply reduced supply considered to be problems? Employers? Employees? Others?

Should governments intervene to stop employers from competing to set wages to reflect increases in the marginal revenue product of labour?

Is not the purpose of short and long-term upward changes in relative prices or wages to induce people to buy less of a now scarcer resource and search for substitutes and additional sources of supply, and for new suppliers to enter the market in response to the higher prices or wages?

As a starter, I thought I would update Alchian and Arrow’s timeless 1958 analysis for the Rand Corporation of the purported shortage of engineers and scientists at the height of the missile gap in the cold war.

Alchian and Arrow tested the robustness of claims of a labour market shortage of scientists and engineers by investigating the sudden appearance of a servant shortage during World War II.

I will update this idea of a servant shortage to a purported shortage of nannies, as shown in figure 1 below which sets out the initial equilibrium and then an increase in demand.

Figure 1: the demand and supply for nannies by the old rich and power couples







In the diagram above, the initial equilibrium has the old rich hiring Q 1 nannies at a wage W 1 with demand curve D 1 , and the supply curve for nannies.

Power couples then enter the nannies market pushing total demand out to D 2 with wages increasing to W 2 and quantity supplied increasing a little to Q 2 ; The old rich can now afforded to buy only Q s in nannies and power couples hire (Q 2 – Q s ) in nannies.

By construction, the quantity of nannies supplied increases slightly in the short-run, with a large increase in wages for nannies! (Q 2 – Q 1 ) new nannies enter the market, lured in by the higher wages.

The old rich now face a shortage of nannies equal to the quantity (Q 1 – Q s ) . These nannies having switched to work for power couples on much better pay. (In the case of the original analysis Alchian and Arrow analysis, they switched into defence work or backfilled jobs of those that moved into defence work).



As with the wartime servant shortage, the old rich are unwilling to admit they are no longer able to keep themselves in the style they were accustomed too because the demand for domestic labour has increased.

Better to blame their loss of social status on a skills shortage in a poorly functioning market rather than accept the rise of middle class power couples outbidding them in the hire of domestic help. As Alchian and Arrow (1958, pp. 39-40) explain:

… Many people who formerly consumed some of the commodity or service in question and now find the price so high that they no longer want as much (or any) would describe the situation is one of “shortage”. Actually, this is merely one way of saying that they can’t get the given commodity at its old price. We can think of many examples of this use of the word “shortage”. For example, the “servant shortage” during World War II was a case in point. Those with whom the increase in household servants wages were more than they could afford to pay, apparently found it more convenient to describe their change in circumstances as a result of a “shortage” than to admit baldly that they couldn’t afford to keep the servants… It seems reasonable to explain a good deal of the current complaint about a shortage of scientists and engineers is a variant of the “servant shortage” phenomena. Employers who find themselves losing engineers to other firms and at the same time find it uneconomic to try and keep these employees by offering them substantial salary increases may see the situation as a “shortage” rather than recognise that other firms can put these skills to more valuable uses… While we lack specific evidence, we have the impression that the firms who have complained most consistently about “shortage” have been those whose demand has not increased or at least not increased as rapidly as that of other firms in their industry.

Why are people priced out of any market? Given a fixed income and the many other alternative uses of their incomes, any rise in price makes buying the old quantity no longer the best bargain.

Who will admit that they can no longer keep themselves in the style they were accustomed to when they complain of market failure, skill shortages and lack of government investment in skill formation.

Alfred Marshall’s comparative statics of price adjustment



The analysis of the time path of price adjustment for any commodity was developed by Alfred Marshall in 1890. He was concerned that time was an important factor in how the markets adjusted to demand and supply changes:

… markets vary with regard to the period of time which is allowed to the forces of demand and supply to bring themselves into equilibrium with one another, as well as with regard to the area over which they extend. And this element of Time requires more careful attention just now than does that of Space. For the nature of the equilibrium itself, and that of the causes by which it is determined, depend on the length of the period over which the market is taken to extend. We shall find that if the period is short, the supply is limited to the stores which happen to be at hand: if the period is longer, the supply will be influenced, more or less, by the cost of producing the commodity in question; and if the period is very long, this cost will in its turn be influenced, more or less, by the cost of producing the labour and the material things required for producing the commodity.

Marshall divided the price adjustment process into the market period, the short run, and the long run.

In the market period, production is fixed; and all factors of production are fixed in supply during this time period. The burden of price adjustment is on the demand side.

As the supply is fixed in the market period, it is shown as a vertical line S MP . It is also called as inelastic supply curve. When demand increases from DD to D 1 D 1 , price increases from P to P 1 . Similarly, a fall in demand from DD to D 2 D 2 pull the price down from P to P 2 .

In the short run, supply to be partially adaptable, in the sense that increased production can occur but capital equipment and certain other overhead items are held constant.

S SP is elastic implying that supply can be increased by changing a variable input. Note that the corresponding increase in price from P to P 1 for a given increase in demand from D to D 1 is less than in the market period. It is because the increase in demand is partially met by the increase in supply from q to q 1 .

The short run is the conceptual time period in which at least one factor of production is fixed in amount and others are variable in amount. In the short run, a profit-maximising firm will:

increase production if marginal cost marginal revenue

decrease production if marginal cost is greater than marginal revenue;

marginal cost is greater than marginal revenue; continue producing if average variable cost is less than price per unit, even if average total cost is greater than price;

average variable cost is less than price per unit, even if average total cost is greater than price; Shut-down if average variable cost price at each level of output.

In the long run, supply is fully flexible – there are no fixed factors of production. The Marshallian long-run allows for optimal capital stock adjustment.

The long period supply curve S LP is more elastic and flatter than that of the S SP . This implies the greater extent of flexibility of the firms to change the supply.

The price increases from P to P 2 in response to an increase in demand from D to D 1 and it is less than that of the market period (P 1 ) and short period (P 2 ). It is because the increase in demand is fully met by the required increase in supply. Hence, supply plays a significant role in determining the lower equilibrium price in the long run.

The market is cleared in the long run within a framework in which supply can be considered to be fully adaptable because all factors have adjusted to the new situation. Alfred Marshall explains:

In long periods on the other hand all investments of capital and effort in providing the material plant and the organization of a business, and in acquiring trade knowledge and specialized ability, have time to be adjusted to the incomes which are expected to be earned by them: and the estimates of those incomes therefore directly govern supply, and are the true long-period normal supply price of the commodities produced.

In addition, in the market period, the short run, and the long run, foresight is not perfect, information is not free, and the cost of adjusting something is not independent of the speed in which you wish to do so.

The 2nd laws of supply and of demand



Another way to discuss how time interacts with responsiveness of supply and demand are the second laws of supply and demand.

The Second Law of Supply states that supply is more responsive to price in the long run. The Second Law of Supply relates to how flexible producers are in terms of how much of a good they produce.



Supply is more elastic in the long run because given more time, producers can more easily adapt to the change in the price.

Within shorter periods of time, producers cannot as easily change the amount of a good they produce (since changes in production often require adjustments within factories, with workers etc.)



The Second Law of Demand states that demand is more responsive to price in the long run than in the short run. Initially, when the price of a good increases or decreases, consumption does not change drastically. However, when consumers are given more time to react to the change in price, consumption can either increase or decrease more dramatically. Demand is not only determined by price but also factors such as: income, tastes, and the price of related goods.

In the market period, any adjustment must be made through changes in price. This means that there could be initially a large price increase.

In the short run, there are some capability for more supply to come forward. This additional supply will temper the initial large price increase.

In the long run, producers are fully able to adapt their circumstances to the changing market conditions and higher prices. This will reduce prices as compared to the initial price spike when market conditions first changed.

In the long run, new firms can enter the industry and old firms can exit as required by the price change and their entrepreneurial expectations of the future of the industry.

Search and matching in a decentralised labour market



To cover off the bases, the simultaneous existence of vacancies and unemployed in a labour market is no evidence of either of surplus or shortage. It takes time for workers to locate vacancies and assess their competing job options. It takes time for employers to locate suitable workers to fill vacancies.

The simultaneous existence of vacancies and unemployed is the result of, as mentioned earlier, imperfect foresight, the fact that information is not free, nor freely available, and the costs of doing anything is not independent of the speed in which you wish to act. Searching for suitable vacancies, or suitable employees, is costly, and neither jobseeker nor employer knows whether any match will work out.

The one-price (one-wage) market that clears instantly will occur only where the cost of information about the prices (wages) offered by buyers and sellers is zero. As George Stigler observed in the opening paragraph of his famous 1961 paper The Economics of Information:

One should hardly have to tell academicians that information is a valuable resource: knowledge is power. And yet it occupies a slum dwelling in the town of economics. Mostly it is ignored: the best technology is assumed to be known, the relationship of commodities to consumer preferences is a datum. And one of the information producing industries, advertising, is treated with a hostility that economists normally reserve for tariffs or monopolists.

Job search cost are of two types: direct costs of gathering information about competing opportunities and the opportunity cost of being unemployed or staying in your current job at your current pay.

The benefit from job search is the expected gain in earnings that will result from waiting for a better wage offer.

The rational job searcher searches for better offers until the marginal benefit and cost of additional search are equal.

A significant cost of continued job search is the earnings foregone by not taking the previous best opportunity.

Unemployment can be a cost-effective method of searching for better employment opportunities and higher wage offers as David Andolfatto observed:

One frequently reads that “unemployment represents wasted resources.” But if job search is an information-gathering activity, designed to locate a high quality job match, in what sense does such an activity necessarily constitute wasted resources? (Does the existence of single people in the marriage market also represent wasted resources?) If the unemployment rate were to suddenly plummet because a large number of workers aborted their job search activity–accepting crappy jobs, or exiting the labour force–is this a reason to celebrate?

The behavioural responses of employers and workers to change are so pronounced because the cost of acquiring new information is profound (Alchian 1969). Many such costs impede wages from instantly fluctuating to rebalance labour supply with demand. Hicks (1932) explained this uncertainty and state of flux as follows:

For although the industry as a whole is stationary, some firms in it will be closing down or contracting their sphere of operations, others will be arising or expanding to take their place. Some firms then will be dismissing, others taking on, labour; and when they are not situated close together, so that knowledge of opportunities is imperfect, and transference is attended by all the difficulties of finding housing accommodation, and the uprooting and transplanting of social ties, it is not surprising that an interval of time elapses between dismissal and re-engagement, during which the workman is unemployed.

A job seeker does not initially know the location of suitable vacancies, the wages for various skills, differences in job security and other factors. Job seekers must search for this information, keep this knowledge current and forecast whether better vacancies may open soon. Employers must search to learn the location, availability and asking wages of applicants. There is a tendency for unpredicted wage changes to induce costly additional job search. Long-term contracts arise to share risks and curb opportunism over sunken investments in relationship-specific human and organisation capital. These factors all lead to queues, unemployment, spare capacity, layoffs, shortages, inventories and non-price rationing in conjunction with wage stability (Alchian 1969; Alchian and Allen 1967, 1973; Klein 1984; Hashimoto and Yu 1980; Hall and Lazear 1979).

By acquiring more information, a job seeker learns more about their options and can improve their prospects of finding better-paid job matches. Job seekers and employers invest time and resources to find one another, size each other up and form a job match or try their luck elsewhere. A job match is a pairing of a worker with a particular employer.

Job seekers will apply for a portfolio of job vacancies that reflect their asking wage and their known alternatives. An asking wage is the minimum that a job seeker is willing to accept given their options.

The extent of job search depends on the costs of job-information production and acquisition, the income available to job seekers while searching, the frequency and the magnitude of shifts in the relative demand between different sectors, the costs of relocation and retraining, and the extent and frequency of declines in aggregate demand (Alchian and Allen 1967).

The more varied will be the potential job opportunities and the greater will be the gains to job seekers from continued job search, the greater are the rate of change in tastes and demand, the greater are the differences in the skills of job seekers and the requirements of job vacancies, and the greater are the costs of moving (Alchian and Allen 1967).

Employers face an information dilemma as well. If they wait a bit longer, hold a job vacancy open, a better job applicant may come a long and a more profitable and longer lasting job match may result.

Of course, the employer is taking a chance here on the job applicant pool improving with time. There are elements of luck involved for both employers and job seekers when filling vacancies and finding jobs.

The employer must balance the costs of holding the vacancy open with his estimation of the value and probability of a better applicant applying at a later date if he searches further the prospective recruits. But reducing your ignorance has costs as Stigler (1961) explained:

Ignorance is like sub-zero weather: by a significant expenditure its effects upon people can be kept within tolerable or even comfortable bounds, but it would be wholly uneconomical entirely to eliminate all its effects.

The rate at which job vacancies are filled and the rate at which people leave unemployment and change jobs is determined by the job search decisions of job seekers and the recruitment decisions of employers. The way in which the process works is well explained by Andolfatto’s analogy to the marriage market:

In many ways, the labour market resembles a matching market for couples. That is, one is generally aware that the opposite side of the market consists of better and worse matches (we seldom take the view that there are no potential matches). The exact location of the better matches is unknown, but may be discovered with some effort. In the meantime, it may make sense to refrain from matching with ‘substandard’ opportunities that are currently available. But since search is costly, it will generally not be optimal to wait for ones “soul mate” to come along. Furthermore, since relationships are not perfectly durable, there is no reason to expect the stock of singles to converge to zero over time

As in the labour market, there are marriages and divorces and young people come of age and look for the first time; people also link up for short-term relationships; and some relationships do better than others.

To say there is involuntary unemployment is to say there is also involuntarily unmarried people. But we can always marry the first person we meet in the street, if they’ll have us. Search and matching is a two sided affair. I doubt that our first encounter in the street would accept this offer of marriage from a stranger. I doubt that anyone would want to marry a stranger who would so willingly marry a stranger. I think both sides suspect that such a random pairing would not last long because the pairing occurred after so little mutual scrutiny and measured assessment of alternatives, current and prospective. The same principles apply to search and matching in the labour market.