The cobweb model and labour market shocks

The cobweb model describes an occupation that takes years of training to enter and whose students choose it by looking at today’s wage. A rise in demand then sets off a cycle of booms and busts: the wage overshoots, too many students enter, the wage falls, too few enter, and the market approaches its long-run equilibrium only gradually, if at all. Natural disasters and pandemics are analysed with the same supply and demand tools: they shift one or both curves, and wages and employment respond as the shifts predict.

Booms and busts for engineers

Suppose demand for new engineers rises. It takes years to train an engineer, so the number available this year is fixed, and the extra demand shows up entirely as higher starting salaries. Students choosing a program see those salaries and enrol in large numbers. When they graduate together, the market is flooded and salaries fall below their long-run level. The next group of students sees low salaries and stays away, so a shortage follows. Each cohort reacts to the salary when it enrols rather than the salary it will face when it graduates.

The model

Three assumptions drive the cycle:

1. Training takes time. Students decide this period and enter the market next period.
2. Short-run supply is perfectly inelastic. In any period the number of engineers is fixed by earlier enrolment.
3. Myopic expectations. Students expect today’s wage to persist. They do not account for the fact that other students are reacting to the same wage.

The long-run supply curve $S$ gives the number of graduates who will enter at each expected wage. Under myopic expectations the market follows

$$E_{t+1} = S(w_t), \qquad w_{t+1} = D^{-1}(E_{t+1}),$$

where $D^{-1}(E)$ is the wage at which firms want to hire $E$ engineers. Each period’s supply responds to last period’s wage, and each period’s wage is set by demand given that supply.

Periods since demand rose

5

Slope of long-run supply ÷ slope of demand

1.2

Starting salary this period

$84.4k

Engineers this period

45.6k

Gap from long-run salary

$4.4k

Open in Graph Lab

Figure 1. Demand for new engineers rises from $D_0$ to $D_1$. With the stock fixed in the short run ($S_{SR}$), the salary jumps; the next cohort is too large, the salary falls below its long-run level, and the path spirals toward $E^*$, 50 thousand engineers at $80 thousand. The cycles shrink when long-run supply is steeper than demand, repeat forever when the slopes are equal, and grow when supply is flatter.

Whether the cycle dies out depends on the slopes. With linear demand $w = a - bE$ and long-run supply $w = c + dE$, the gap between employment and its long-run level $E^*$ evolves as

$$E_{t+1} - E^* = -\frac{b}{d}\,(E_t - E^*).$$

If supply is steeper than demand ($d$ greater than $b$, so supply is less elastic), the gaps shrink and the market converges. If supply is flatter, they grow and the cobweb unravels. Equal slopes give a cycle that repeats forever.

Rational expectations. Students with rational expectations understand how the market works and correctly forecast the salary they will earn when they graduate. They anticipate that a high salary will draw many entrants, so enrolment rises only to the level consistent with the long-run equilibrium, and there is no cycle. The cobweb pattern arises only when people misread the future.

Salary in period 2, myopic

$74.7k

Salary in period 2, rational

$80.0k

Open in Graph Lab

Figure 2. Starting salaries after the same demand increase under myopic and rational expectations. Both jump from $68 thousand to $88 thousand while the stock of engineers is fixed. Myopic students then overshoot and the salary oscillates around $80 thousand; students with rational expectations enrol exactly enough to reach the long-run equilibrium, so the salary settles at $80 thousand immediately.

Key idea

The cobweb needs two ingredients: a training lag that makes short-run supply vertical, and myopic expectations. Remove either and the boom-bust cycle disappears.

Richard Freeman modelled the markets for new engineers and new lawyers in the United States as cobwebs, with the number of graduates depending on salaries when students enrolled.¹² Later work by Ryoo and Rosen found that engineering enrolment is highly sensitive to career prospects, and that a model in which students look ahead to future demand fits the data reasonably well, so students are less myopic than the simplest cobweb assumes.³

Supply shocks: natural disasters

A hurricane is close to a natural experiment, because which counties it hits depends on its path rather than on local labour market conditions. A direct hit destroys homes and displaces residents, which shifts labour supply left in the county. Many displaced residents move to nearby counties, which shifts labour supply right there. The model predicts a higher wage and lower employment in the county that was hit, and a lower wage and higher employment next door.

Workers displaced to the neighbouring county (thousands)

16k

Hit county: wage

$16.50

Hit county: employment

−10.0%

Neighbour: wage

$13.50

Neighbour: employment

10.0%

Open in Graph Lab

Figure 3. Two identical counties, one hit by a hurricane. Displaced workers shift supply left in the hit county and right in its neighbour. With 16 thousand displaced, the hit county's wage rises 10 percent to $16.50 and its employment falls 10 percent, while the neighbour's wage falls to $13.50 and its employment rises 10 percent.

Belasen and Polachek tested these predictions with quarterly county data on employment and earnings in Florida, which was struck by 19 hurricanes between 1988 and 2005. They compared counties hit directly, and their neighbours, with counties the storms left untouched.⁴ In the quarter of a direct hit by a category 4 or 5 hurricane, employment fell 4.8 percent and earnings per worker rose 4.4 percent relative to the average county; for a category 1 to 3 storm the effects were −1.5 percent and +1.3 percent. In neighbouring counties, earnings per worker fell 4.5 percent after a category 1 to 3 storm and 3.3 percent after a category 4 or 5 storm, relative to the average county, with no statistically significant change in employment.⁵ The signs match the supply-shock predictions. Disasters can also shift demand, by destroying businesses or by creating rebuilding work, so the supply-only model is a simplification.

Shocks to both sides: COVID-19

In spring 2020 public health restrictions closed restaurants, stores and offices, so the value of many workers’ output fell: labour demand shifted left. At the same time, health risks, school and daycare closures and new income support reduced the number of people willing to work at any given wage: labour supply shifted left. When both curves shift left, employment must fall, but the wage can go either way: it falls if the demand shift is larger and rises if the supply shift is larger.

Fall in labour demand (thousand hours at each wage)

20k

Fall in labour supply (thousand hours at each wage)

8k

Employment

44.5k hrs

Change in employment

−25.8%

Wage

$13.88

Change in wage

−7.5%

Open in Graph Lab

Figure 4. A large fall in labour demand combined with a smaller fall in labour supply. Employment falls from 60 to 44.5 thousand hours and the wage from $15.00 to $13.88. Employment falls under any combination of the two shifts; the wage rises only if the supply shift is the larger one.

Canada’s employment fell by more than three million between February and April 2020.⁶ The Canada Emergency Response Benefit paid eligible workers $2,000 for each four-week period from March 15 to September 26, 2020,⁷ which in the model raises recipients’ reservation wages and adds to the fall in labour supply. The Canada Emergency Wage Subsidy pushed the other way, shifting labour demand up; see employment subsidies.

Unemployment rate, Canada

Monthly, seasonally adjusted, population aged 15 and over

Canada's unemployment rate rose from 5.8 percent in February 2020 to 14.2 percent in May 2020 and was back below 6 percent by December 2021.Source: Statistics Canada, Table 14-10-0287-01, Labour force characteristics, monthly, seasonally adjusted and trend-cycle. Retrieved 2026-10-23.

Show the data and notes

Seasonally adjusted Labour Force Survey estimates, both genders; revised periodically. The Labour Force Survey covers the 10 provinces; it excludes the territories, people living on reserves, full-time members of the Canadian Armed Forces and people living in institutions.

Period	Unemployment rate
Jan 2019	5.7%
Feb 2019	5.8%
Mar 2019	5.8%
Apr 2019	5.7%
May 2019	5.5%
Jun 2019	5.6%
Jul 2019	5.7%
Aug 2019	5.7%
Sep 2019	5.6%
Oct 2019	5.6%
Nov 2019	5.9%
Dec 2019	5.6%
Jan 2020	5.5%
Feb 2020	5.8%
Mar 2020	8.5%
Apr 2020	13.7%
May 2020	14.2%
Jun 2020	12.6%
Jul 2020	10.9%
Aug 2020	10.1%
Sep 2020	9.1%
Oct 2020	9.0%
Nov 2020	8.6%
Dec 2020	8.9%
Jan 2021	9.2%
Feb 2021	8.5%
Mar 2021	7.7%
Apr 2021	8.2%
May 2021	8.3%
Jun 2021	7.9%
Jul 2021	7.4%
Aug 2021	7.1%
Sep 2021	7.0%
Oct 2021	6.5%
Nov 2021	6.1%
Dec 2021	5.9%
Jan 2022	6.4%
Feb 2022	5.5%
Mar 2022	5.4%
Apr 2022	5.4%
May 2022	5.2%
Jun 2022	4.9%
Jul 2022	4.8%
Aug 2022	5.2%
Sep 2022	5.1%
Oct 2022	5.1%
Nov 2022	5.0%
Dec 2022	5.0%

One statistic from April 2020 looks like a contradiction. Average hourly wages were 10.8 percent higher than a year earlier, partly because job losses were concentrated in low-paying industries.⁶ This is a composition effect: the average rose because the lowest-paid workers dropped out of the calculation, not because the market wage for any given job went up.

Worked example

Demand for new engineers rises to $w = 130 - E$, where $w$ is the starting salary in thousands of dollars and $E$ is thousands of engineers. Long-run supply is $w = 80 + 1.5(E - 50)$, so the long-run equilibrium is 50 thousand engineers at $80 thousand. Before the increase the market was at 42 thousand engineers and $68 thousand.

1. Short run. The stock is fixed at 42, so the salary jumps to $130 - 42 = 88$.

2. First response. Myopic students expect 88 to last and enrol until the supply price is 88: $80 + 1.5(E - 50) = 88$ gives $E = 55.3$.

3. Bust. With 55.3 thousand engineers, the salary falls to $130 - 55.3 = 74.7$.

4. Second response. Students now expect 74.7: $80 + 1.5(E - 50) = 74.7$ gives $E = 46.4$, and the salary rises to $130 - 46.4 = 83.6$.

5. Convergence. The gap from 50 thousand goes from −8 to +5.3 to −3.6: each gap is $-1 / 1.5$ times the last. Supply is steeper than demand, so the cycle dies out.

6. Rational expectations. Students who foresee the outcome enrol 50 thousand at once, and the salary goes from 88 straight to 80.

Common mistakes

Traps on exams

• Drawing the cobweb without the short-run supply curve. Each period’s wage comes from a vertical short-run supply curve meeting demand; the long-run supply curve only tells you next period’s enrolment.
• Reversing the convergence condition. The cycle shrinks when long-run supply is steeper than demand and grows when it is flatter.
• Treating the neighbouring county as unaffected. Displaced workers move there, so it receives a supply shock of the opposite sign; it is not a clean control group.
• Reading the April 2020 rise in average wages as a rise in demand. It was largely a change in who was still working.
• Predicting a definite wage change when both curves shift. With both demand and supply falling, only the fall in employment is certain.

On the exam

For the cobweb, draw demand, the long-run supply curve and a vertical short-run supply curve at the current stock. Number the points in order (wage jump, enrolment response, wage fall) and state the expectations assumption. For a shock question, say which curve shifts and why, then give the predicted direction of the wage and employment, with a caveat if both curves move.

Check yourself

1.

Demand for new engineers rises unexpectedly. Training takes four years. What happens in the first year?

1The starting salary rises and the number of engineers employed stays the same2The number of engineers rises and the starting salary stays the same3Both the starting salary and the number of engineers rise to their long-run levels4The starting salary falls because more students enrol

Check answer

2.

A hurricane destroys housing in a county and many residents leave. According to the supply and demand model, what happens to that county's labour market, holding labour demand fixed?

1Labour supply shifts left, so the wage rises and employment falls2Labour supply shifts right, so the wage falls and employment rises3Labour demand shifts left, so the wage and employment both fall4Nothing, because the displaced workers return once the storm passes

Check answer

3.

Early in the COVID-19 pandemic, lockdowns reduced labour demand while health risks, school closures and income support reduced labour supply. What does the supply and demand model predict?

1Employment falls; the wage rises or falls depending on which shift is larger2Employment and the wage both fall3The wage rises and employment is unchanged4Employment is unchanged because the two shifts cancel out

Check answer

Practise more questions on this topic

Sources

1. Freeman, R. B. (1976). A cobweb model of the supply and starting salary of new engineers. Industrial and Labor Relations Review, 29(2), 236 to 248. doi:10.1177/001979397602900204. ↩

2. Freeman, R. B. (1975). Legal “cobwebs”: A recursive model of the market for new lawyers. Review of Economics and Statistics, 57(2), 171 to 179. doi:10.2307/1923998. ↩

3. Ryoo, J. and S. Rosen (2004). The engineering labor market. Journal of Political Economy, 112(S1), S110 to S140. doi:10.1086/379946. ↩

4. Belasen, A. R. and S. W. Polachek (2009). How disasters affect local labor markets: The effects of hurricanes in Florida. Journal of Human Resources, 44(1), 251 to 276. doi:10.3368/jhr.44.1.251. ↩

5. Estimates from table 4 of the working paper version: Belasen, A. R. and S. W. Polachek (2007). How disasters affect local labor markets: The effects of hurricanes in Florida. IZA discussion paper 2976. ↩

6. Statistics Canada, Labour Force Survey, April 2020, The Daily, May 8, 2020. ↩ ↩²

7. Canada Revenue Agency, Canada Emergency Response Benefit with CRA, and Service Canada, Canada Emergency Response Benefit. ↩