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Copyright 2013 Pearson Canada Inc.

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CHAPTER 6

Search and Unemployment

KEY IDEAS IN THIS CHAPTER

1. The model constructed in this chapter is intended to explain Statistics Canada labormarket data, and to organize our thinking about the role played by the labor market in

the macroeconomy.

2. Key labor market variables are the unemployment rate, the participation rate, and the

employment/population ratio.

3. In the Diamond-Mortensen-Pissarides (DMP) labor search model, on the supply sideof the labor market, there are N consumers who choose between home production and

labor market search. On the demand side of the labor market, firms can either be idleor can pay a cost to post vacancies. The number of searching would-be workers andthe number of searching firms determines the number of successful matches in the

labor market, through the matching function. Each successful match produces output.

4. For consumers, searching for work becomes more attractive the higher the market

wage, the higher is labor market tightness, and the higher is the unemployment

insurance benefit.

5. For firms, posting vacancies becomes more attractive the lower is the cost of posting

a vacancy, the lower is labor market tightness, the higher is productivity, and the

lower is the market wage.

6. In equilibrium, a higher unemployment insurance benefit increases the unemployment

rate, reduces labor market tightness, reduces the vacancy rate, and has an ambiguouseffect on the labor force.

7. In equilibrium, an increase in productivity increases labor market tightness, reducesthe unemployment rate, increases the vacancy rate, and increases the labor force.

8. In equilibrium, a decrease in matching efficiency reduces labor market tightness,

increases the unemployment rate, and may result in an increase or a decrease in the

vacancy rate. The labor force decreases.

9. A form of Keynesian analysis is introduced. In the DMP model, bargaining between amatched firm and worker determines the wage, but bargaining strength can be

sticky of the result of social norms, which leads to Keynesian indeterminacy. It is

possible to have a bad Keynesian equilibrium where the wage and the unemploymentrate are inefficiently high.


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Chapter 6: Search and Unemployment


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NEW IN THE FOURTH EDITION

1. The entire chapter is new.

TEACHING GOALS

Including a version of the DMP model in an intermediate macroeconomics text is a

novelty. Students should not have difficulty understanding the model, but they may need

some additional help, as the approach is somewhat different than what we use in standardcompetitive equilibrium models, for example in Chapter 5. However, it helps to think of

the labor market in terms of demand and supply sides. Then, it is possible to use what a

student knows from Chapter 5 to teach them about the DMP model. Workers and firmscare about the wage in the same way they do in a competitive model, but now the market

clears in a different way. Workers care not only about the wage, but the employment

insurance benefit (because their job search may be unsuccessful) and labor market

tightness (which determines the chances of finding a job). Would-be employers careabout labor market tightness and the cost of posting a vacancy, as well as the market

wage. The matching function, which determines the number of successful matches as a

function of matching efficiency and the numbers of firms and consumers searching, is animportant concept. In this case, appeal to what students know about the production

function, as the matching function has the same properties. Then, one can appeal by

analogy to production so that the student understands how the matching process takesplace.

It is important first to understand the labor market data. The DMP model is very nice, as

the variables in the model match up almost exactly with the labor market data as

measured. The unemployed are those who chose to search but were unsuccessful, thelabor force is the number of people who actively searched and found a job (employed)

plus the number who actively searched and were unsuccessful (the unemployed), etc.

The experiments in the model increase in the employment insurance benefit, increase inproductivity, decrease in matching efficiency are all useful in understanding recent

economic events and less-recent ones. A problem in Canada is that Statistics Canada does

not collect vacancy data, so sometimes it might be useful to bring in U.S. data. The

Beveridge curve correlation is particularly helpful.

The Keynesian DMP Model comes from ideas in work by Roger Farmer. This is a niceway to understand Keynesian ideas (for starters). With bargaining indeterminacy the

wage could be stuck at too high a level, with an unemployment rate that is too high. Wedont deal with Keynesian economic policies in this chapter, leaving that for laterchapters.


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Instructors Manual for Macroeconomics, Fourth Canadian Edition


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CLASSROOM DISCUSSION TOPICS

It should not be hard to get students talking about unemployment. Most of them should

know someone who has been unemployed, or they have read about unemployment as it

relates to the recent recession. However, students may not understand how

unemployment is actually defined, or how economists think about it. An importantfeature of the DMP model is that there will be unemployment under any circumstances,

and students should understand that we cannot make unemployment go away, nor shouldwe want it to.

It will be helpful if students understand why a search-model approach is necessary tounderstanding unemployment. Get them thinking about what an unemployed person is

actually doing, and what is motivating them. Unemployment is an economically

measurable activity, and we want to take a scientific approach to thinking about it.

Also, get the students to think about what motivates firms to search for workers to fill job

openings. Why is searching for workers costly? What difficulties does a firm face inhiring workers? How does matching between firms and workers take place? Why is themarket for labor similar to, and different from, the market for a good or service?

Students should be encouraged to think about government intervention and how it mattersfor labor market behavior. What will employment insurance do? How can the

government speed up or slow down the matching process in the labor market?

OUTLINE

1. The Behaviour of the Unemployment Rate, the Participation Rate, and the

Employment/Population Ratio in Canada a) Unemployment Rate, participation rate, and employment/population ratio: data.

b) Key determinants of the unemployment rate: aggregate economic activity,demographics, government intervention, mismatch

2. The Diamond-Mortensen-Pissarides Model of Search and Unemployment

a) Consumersb) Firms

c) Matching

d) Optimization by Consumerse) Optimization by Firms

f) Equilibriumg) An increase in the unemployment insurance benefith) An increase in productivity

i) A decrease in matching efficiency

j) The Beveridge curve

k) A Keynesian DMP model


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TEXTBOOK QUESTION SOLUTIONS

Problems

1. More labour-saving devices has the effect of reducing the payoff to working at homefor all consumers, which reduces v(Q)for each value of Q. As a result, the curve inpanel (a) of Figure 6.1 shifts up. In equilibrium, Q increases, but j remains

unchanged. The unemployment rate and the vacancy rate are unaffected, but the labor

force Qincreases. Since j = A/Q, therefore the number of firms Aincreases.Aggregate output Y = Qem(1,j), so Yincreases, as Q has risen and j is unchanged.

Labour saving devices makes searching for work more attractive relative to workingat home for consumers. With more consumers in the market, labour market tightness

tends to go down, which attracts more firms into the labour market. Ultimately, the

number of active firms increases proportionally to the number of consumers searching

for work, and there is no change in labour market tightness in equilibrium. Outputgoes up because there are more successful matches in the labour market.

Figure 6.1


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2. (i) With a subsidy sto hiring a worker, for a successful match, the surplus of the firm

is z+s-w, the surplus of the worker is w-b, total surplus is z+s-b, and the wage(from Nash bargaining) is w=a(z+s)+(1-a)b. Then, on the supply side of the

labour market, the equation determining the curve in panel (a) of Figure 6.2 is

given by

v(Q)=b+em(1,j)a(z+s-b),

and on the demand side of the market, the equation determining j is

(k/((1-a)(z+s-b)))=em((1/j),1)

Then, in Figure 6.2, comparing the equilibrium when s=0to one with s>0, the

subsidy acts to increase labour market tightness, j, and to increase the labour force, Q.

The subsidy acts to induce more firms to enter the labor market to search for workers,which makes j=(A/Q)higher. This in turn acts to make search more attractive for

workers, as it is now easier to find a job. As well, the subsidy increases the wage,which further increases the incentive to search for work. The unemployment rate is 1-

em(1,j), which falls when jincreases, so the subsidy reduces the unemployment rate.

(ii) If the government pays would-be workers to stay out of the labour market, this

has no effect on the demand side (firms' behavior). However, the supply side ofthe labour market is now characterized by the equation

q+v(Q)=b+em(1,j)a(z+s-b),

Therefore, when q>0, this shifts the curve in the upper panel of Figure 6.2 to theright. There is no effect on labour market tightness, j, and therefore no effect on the

unemployment rate. However, Qfalls. Since jdoes not change, this implies that A

falls as well, since j=(A/Q). Therefore, this policy has the effect not only of reducingthe number of would-be workers looking for work, but it reduces the number of firms

searching for workers. The policy has an unintended side effect and has no effect on

the unemployment rate.


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Figure 6.2

3. The lower recruiting cost, k, affects only the demand side of the labour market. InFigure 6.3, labour market tightness increases from j to j , and the labor forceincreases from Q to Q . The unemployment rate is 1-em(1,j), which decreasesbecause of the increase in j, and the vacancy rate is 1-em((1/j),1), which increases.Since j=(A/Q), and since Qand jincrease, Aalso increases. Aggregate output isQem(1,j)z, which increases, as Qand jboth increase. Thus, the lower cost ofrecruiting induces more firms to enter the labor market, which increases labour

market tightness, inducing more workers to enter the labour market to search forwork, as the chances are now better of finding a job.


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Figure 6.3

4. For this question, re-define labor market tightness as j = (A+G)/Q. Then, the diagramwe work with looks identical to Figure 6.10 in Chapter 6, and Qand jare determinedas in Figure 6.10. Note in particular that Gis irrelevant for determining Qand j, sogovernment activity is irrelevant for the size of the labor force and labor markettightness. Further, government activity will not matter for the unemployment rate, thevacancy rate, or aggregate output. However, since j and Qdo not change when Gchanges, A+G = jQ does not change either. But then an increase in Gmust reduce Aby the same amount. Therefore, government activity simply reduces the number ofprivate firms by an equal amount, and there is otherwise no effect on economicactivity. The key to this result is that the government was assumed to be no better orworse at producing output than private sector firms. Therefore, the scale ofgovernment activity could not matter for aggregate variables.

5. In the Keynesian DMP model, the wage wis indeterminate and, given w, equations(6.6) and (6.8) solve for Qand j, i.e.


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v(Q)=b+em(1,j)w, (1)

and

(k/(z-w))=em((1/j),1) (2)

Suppose that wis too high in equilibrium, which implies that Qand j are too lowrelative to what is socially efficient. If the government were to subsidize successful

matches by paying sto a firm when a match occurs, then equation (2) becomes

(k/(z-w+s))=em((1/j),1), (3)

since the firm's surplus from a match (the firm's profit) is now z-w+s. In Figure 6.4,this has the effect of increasing jand Q. As long as the government makes s

sufficiently large, it can correct the social inefficiency. The subsidy makes it more

attractive for firms to enter the labour market to search for workers, which in turnattracts more would-be workers into the labour market as it is now easier to get a job.

The labor force increases, the unemployment rate decreases, the vacancy rateincreases, and GDP increases. In Keynesian models, there always exists some price

distortion - goods and/or labor are mispriced - and this type of inefficiency can becorrected just as we would correct a standard type of inefficiency such as an

externality. Typically, we can correct a negative externality with a Pigouvian tax -

e.g. a tax on gasoline, as burning gas causes pollution. A positive externality can becorrected with a subsidy. If the government were to subsidize a firm for posting a

vacancy, then equation (2) becomes

((k-s)/(z-w))=em((1/j),1), (4)

as now the vacancy-posting cost is k-s. Qualitatively, this has the same effects as inFigure 6.4, so in that sense it does not matter if the subsidy is aimed at reducing

recruiting costs or subsidizing successful matches. In fact, it literally makes no

difference to the government which way the subsidy is implemented. Suppose that the

government wants to achieve a particular value for labor market tightness, j*, through

a subsidy. If government subsidizes successful matches with a subsidy s , then

equation (3) gives

k=(z-w+s )em(1/(j ),1), (5)

and if the government subsidizes recruiting with a subsidy s , then equation (4)

gives

k-s =(z-w)em(1/(j ),1). (6)

Then, subtract equation (6) from equation (5) to get

s =s em(1/(j ),1) (7)


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But in equation (7), the left-hand side is the cost of the subsidy program per active

firm, in the first case, and the right-hand side is the cost of the subsidy program per

active firm in the second case. Since j=j for both programs and Qis the same for

both programs, therefore A=j Qis the same for both programs, i.e. the number of

active firms is the same for each program. Therefore, to get the same effect (a given j)

each subsidy program has exactly the same cost for the government, so they areidentical.

6. If all social welfare programs simultaneously become more generous, suppose that we

represent this as a payment p to each person not in the labor force, and an increase by

p in the employment insurance benefit. Then, the equation that summarizes behavior

on the supply side of the labour market becomes

v(Q) + p = b + p + em(1,j)a(z-b-p),

or, simplifying,

v(Q) = b + em(1,j)a(z-b-p).

As well, the equation summarizing demand-side behaviour in the labour market can be

written as

em(1/j,1) = k/(1-a)(z-b-p)

Therefore, in Figure 6.4, labour market tightness falls from j1 to j2, and the labour

force falls from Q1 to Q2. As a result, the unemployment rate increases and thevacancy rate decreases. The number of firms is A=jQ, so Adecreases. As well, output

is Y=zQem(1,j), so output falls as well. Consumers are affected by two social

programs one which pays a benefit to people not in the labour force, and one that

pays an employment insurance benefit to the unemployed. Since the consumerreceives the employment insurance benefit only in the event that search for work is

unsuccessful, the increase in generosity of all social programs will on net discourage

consumers from searching for work. Further, more generous social programs reduces

the total surplus from a successful match, and this discourages firms from postingvacancies. On net, labour market tightness goes down, the labour force contracts, andaggregate output decreases, with the unemployment rate increasing and the vacancy

rate decreasing.


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chapter06 sol

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