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foundations of microeconomics

Questions and Answers of Foundations Of Microeconomics

Are unions good or bad for investment? Intuitively one would think the latter. The argument might go as follows. When capital is a variable production factor, the demand for labour becomes more
8.5.2 Unions and investment
the average tax rate (tA ) rises. These conclusions are very similar to those that were obtained for the efficiency wage model in Chapter 7.
From (8.43) we can see that the gross wage w (and thus unemployment U) rises if the unemployment benefit (B) rises, the degree of progressivity falls (s rises), and
function is given by U(.) log (.). Then the markup equation (8.42) is simplified to:log w(1 - tA) = log B+sIED w= B e ED. 1 - tA
where s (1 - tm)I(1 - tA) is the index of progressivity of the tax system. For a progressive tax system, tM > tA, so that s < 1. Recall from Chapter 7 that an increase in progressivity of the tax
This expression can be simplified by using the result that wdtA/dw = tM - to and using the labour demand elasticity ED (defined below (8.9)):u(w(1 - tA)) - u(B) = s w(1 - tA)Uw(1-tA)(8.42)
The Foundation of Modern Macroeconomics(from (8.1)) to include income taxes:v(w, L) (R) u(w(1 - tA)) + [1 - (Ki)]u(B), so that the first-order condition for the optimal wage is:(B)A L dtA 1 = D,v +
=FL(LI,Ko-
where r is the real it problem are:aL1 an all an ( 1 aL2 1 +\an
that the capital stoatinvestment levels in which is defined as:n = Tri + 1+r F(L i ,Ki) -
this function capture!an increasing rate) 1 the firm does not in a close at the end of
where 7rt is real proi is the real wage rate, 4)(.) is the install,:
equal to:7ni 7-- F(1.1, --= F(1,2, K1 +
in a simple two-periol and a firm. This exam(1987b). The firm t
the risk and impact of result, discussed for bility issues in Chapt can overcome (son:behaviour. 1 The remainder of ti
however, the firm is shifted easily so the u off a large part of the has this incentive to cl ment of smooth and n
swing. Labour demand is 205
vi models (see Chapter 7).e modest in his/her wage her job. Second, the threat-eaten current employees nployed workers.
Dr the unemployment rate.process. First, there is the
i quite easily. Following n and the group of insiders
clined to lower wages to get ds after a positive aggregate Dr empirical and theoretical ovment rates in the UK and utoregressive coefficient in ival to unity. Theoretically,,,, rs have all the
he unemployment rate foil('surprises are random, the no tendency for the unem-- ,iition behind this result is)y (8.35)). The unemployed
(8.3 "-ms of the unemployment(8.3(
Suppose that the system of income taxes is progressive, that unemployment benefits are untaxed, and that the tax function is given by T(w), so that the marginal tax rate is tM dT dw and the average
In order not to unduly test the reader's patience, only one tax experiment is conducted.
In this section some of the union models discussed in this chapter are used to study two issues. First, we continue our study of the effects of taxation on employment, wages, and unemployment.
The Foundation of Modern Macroeconomics more long-term unemployed, so that even if the original long-term unemployed have died (or found a job), the thinness of the labour market remains. A temporary
As a second comparative statics exercise we now consider the effects of an increase in the labour income tax, tL. The effects of this shock are illustrated in Figure 9.4.The increase in the labour
Equation (9.25) is the marginal productivity condition for capital, determining the optimal capital stock (and thus the optimal size of production) of each firm with a filled job. Since the marginal
The Foundation of Modern Macroeconomics an intricate connection between the process linking workers to jobs, and the one linking jobs to workers. This is obvious, since workers and vacancies meet in
(9.6)215
3 The trick is to write (9.1) as XN = GuUN + GvVN, which implies q = Gu 10 + Gv. Hence, 9(0) =Gu 1(q0) =1 — Gv /q, which is between 0 and 1 because 0 < Gv < q.negotiations take place to 1d matching
a shorter duration of unemployment) if 0 is high, i.e. if there are relatively many vacancies. The definitions of q(0) and f (9) in (9.2) and (9.5) show that there is
Since f (0) represents the instantaneous probability of an unemployed worker finding a job, the expected duration of unemployment equals 1/f (0) = 1/(0q(0)). This is intuitive, since unemployed
This instantaneous probability can be written in terms of 0 also:G(UN , VN) VNG(UN /VN, 1)UN UN = (V /U)G(U / V , 1) = 0q 0() fie)). (9.5)The f (0) function has the following elasticity:0 df=[q(0) +
where ?AO) is the absolute value of the elasticity of the q(0) function.3 Unemployed workers also find a match in a stochastic manner. For workers, the instantaneous probability of finding a firm
Chapter 9: Search in the Labour Market meetings occur between an unemployed worker and a firm with a job vacancy.Which particular worker meets which particular job vacancy is selected
where 8 V /U is the v analysis. Obviously, sh filled in the time in to7 of a vacancy being fille these results are deriN In view of the assun function can be demon dq Gu d0 = 02
2 Mortensen and Pissarides (1994) and Pissarides (2000, ch. 2) develop a matching model with an endogenous job destruction rate.a meetings occur bets%Which particular w, Consider a small matches and
1 The exposition given in this section closely follows Pissarides (1990, ch. 1).
XN is the total number of matches, so that X is the matching rate, and G(., .)is a linearly homogeneous function, with Gu > 0, Gv > 0, Guu < 0, Gvv < 0, and GuuGvv –GUS > 0. The intuitive idea
The number of successful matches each instant in time depends on UN and VN according to the matching function:XN = G(UN , VN), (9.1)
It is assumed that there are many firms and many workers, and that every agent behaves as a perfect competitor. The fixed labour force consists of N workers, and each worker who has a job supplies
The modern theory of search makes use of the so-called matching function. This is a hypothetical concept, not unlike the production function, which turns out to be very convenient analytically. A
9.1.1 A simple models
The Foundation of Modern Macroeconomics of output. When a worker and a job meet each other, negotiations take place to determine the wage.
D the insider-outsider literature.bargaining framework. Koskela union model. For good surveys z Pencavel (1991), and Booth es on hysteresis.
' 1 otherwise have done. This iketched is an example of the settings in macroeconomics.investment, see Grout (1984), and Devereux and Lockwood model of unemployment per-
explains, rather than assuming that the market is the mechanism by which workers and jobs are brought together, the modern approach assumes that there is a search process which stochastically brings
Chapter 7, US unemployment seems to be relatively low and stable. The modern theory of search behaviour in the labour market is specifically aimed at describing this matching process that takes place
US the flow of workers entering or leaving a job amounts to 7 million per month(Blanchard and Diamond, 1989, p. 1)! It would be tempting to argue that these enormous flows, due to the simultaneous
9.1 Search in the Labour Market The labour market in many countries is characterized by huge gross flows of workers leaving a job and entering unemployment and vice versa. For example, for the
3. How can the search-theoretic approach explain observed persistence in the unemployment rate?
2. How does taxation affect the equilibrium unemployment rate? How can we reduce the equilibrium unemployment rate?
1. How can we explain the duration of unemployment? We introduce a simple model of search in the labour market.
212 Search in the Labour Market The purpose of this chapter is to discuss the following issues:
Chapter 7, US unempk theory of search beha\this matching process 1 cally different from the notion of an aggregate explains, rather than as!and jobs are brought tt process which stochasti in a
9.1 Search in the The labour market in rr ers leaving a job and er US the flow of workers(Blanchard and Diamon mous flows, due to the s are bound to cause prof versa. At a macroecona labour market is
On the interaction between union wage setting and firm investment, see Grout (1984), van der Ploeg (1987b), Anderson and Devereux (1988), and Devereux and Lockwood(1991). Gottfries and Horn (1987)
3. How can the sea unemployment r.(as in a Western movie) the firm's capital stock. The firm will formulate its optimal investment and production plans in the full knowledge that it will be held up
2. How does taxatioi, the equilibrium un
1. How can we expla,, of search in the lab
The Foundation of Modern Macroeconomics Search in The purpose of this chap
211
As a final application of the union model, we study the effects of a monopoly union on the investment plans of firms. It turns out that unions may be bad for firm investment because of the hold-up
Another stylized fact that can be explained with the aid of a union model is the high degree of persistence in the unemployment rate (the near-hysteresis effect). The membership rule of the union
The efficient bargaining model solves this problem by assuming that the firm and the union bargain over both the wage and the employment level. The outcome of this bargaining process is a range of
that it is Pareto inefficient, i.e. it is possible to make one of the parties involved in the bargaining strictly better off without making the other party worse off.
Using the concept of generalized Nash bargaining, the resulting wage can again be written in a markup format. In addition to unemployment benefit and demand elasticity an additional component
and investment depends e firm will also invest less ie inconsistent wage profile ck to its promises is to stifle union behaviour have ght-to-manage model, and the union is the expected the discussion
Chapter 8: Trade Unions and the Labour Market(8.61)c terms), so that the union-. the first period, i.e. li/2 =1g to believe the union if it a more complete treatment zis a solution for our present
As a final applicatic union on the invest:firm investment becau to offer low wages in t not credible to the fir renege on its promise 210
Another stylized fac high degree of persist, .membership rule of tr ing hysteresis. If the then strict hysteresis a'ing process, via the r predicts a high degree
as the degree of cent:tant institution. Some either many very small the intermediate case. 1 ment rate but intermec harm, large nation-%%the outcomes of excess do not take into acct. ..macroeconomy.
When combined wit..the model predicts a u employment are h profits into jobs.going to labour, is bat moves closer to the c In the remainder of ious union models. I labour market is that ii ployment
The efficient bargaini the union bargain ON of this bargaining pros
Using the concept of gt written in a markup elasticity an addition&bargaining strength of t is that it contains the special (extreme) cases.that it is Pareto int :the bargaining strictly 1
In the right-to-manage model, the firm is still allowed to decide on employment but the wage is the outcome of a bargaining process between the union and the firm.
so that the model is consistent with real wage rigidity. (The proviso must be made because a union which is fully employed is only interested in higher wages so that positive productivity shocks do
the union can be represented as a simple markup expression involving unemployment benefit and the elasticity of the labour demand function. The union's choice implies that both the wage and the
In the monopoly union model, the union unilaterally picks a wage rate such that union utility is maximized subject to the proviso that the solution lies on the labour demand curve. The union thus
n this chapter the three most important models of trade union behaviour have been studied, namely the monopoly union model, the right-to-manage model, and the efficient bargaining model. The
So what is the solution to this conundrum? Although a more complete treatment will have to wait until Chapter 10, common sense suggests a solution for our present problem. The firm knows that it is
which is iso-elastic with wage elasticity ED (in absolute terms), so that the union sets the wage in the second period at the same level as in the first period, i.e. i'2 =wl > 14/2. The firms knows
The Foundation of Modern Macroeconomics demand curve:a ED LD = (---) [xi +in, (8.61)
(8.58)(8.59)(8.60)
when period 2 comes along. In technical terms, the optimal policy for the union is dynamically inconsistent. The reason why the firm does not believe that the union will set the wage at W2 in period
The problem with the optimal union wage profile (WI , W2) is that the firm will not believe that the union will stick to it! Indeed, if a legally binding agreement is impossible, the union will not
Comparing the optimal wage rates in the two periods (as given in (8.58) and (8.59)), it is clear that the wage is lower in the second period, i.e. w*i > w2. By offering low wages in the second
log w; = log B +ED +where is defined as:802 all w2 (aED ) (1— a ( a )0)(1+0 Ly + r w2> 0.ah aw2
Specifically, we can easily derive that:1 U (w 2) - U(B) = log w2 - log B ED + wzUw(w2)1
Equation (8.57) is slightly more involved. The union realizes that the wage that it chooses for the second period influences the firm's investment decision: the higher the wage in the second period,
Ni for the static case (see is indifference curve and)n of the representative union member is logarithmic (u(.) = log (.)) equation (8.56) can be rewritten by using (8.50) to yield:1u=(w1) - u(B) =
(8.55), and the unemployment n consists of choosing w1 labour demand functions firm problem are:(8.56)(8.57)
(8.54)r 6), and V(wt , Lt) is the lows:
in period t, and q is Tobin's(8.50)-(8.51) show that the!) shows that investment is r• on the exogenously given id period w2.utility function:
Chapter 8: Trade Unions and the Labour Market Irk with specific functional mctions, and the utility funcent cost function is quadratic iction is assumed to be Cobb--n ting output. By using
when period 2 comes dynamically inconsistent. Th will set the wage at w*, in I did believe the union, and with w2 substituted (call ti the firm has invested a I, :labour according to (8.51)this
firm when period 2 comL, the light of new informatio

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