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foundations of microeconomics

Questions and Answers of Foundations Of Microeconomics

✷ What are five foundations of economics? (p. 18)
✷ What is economics? (p. 18)
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:
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
The problem with the c, not believe that the union impossible, the union %N
Comparing the optimal it is clear that the wage is wages in the second period
e.g. (8.8)). A point of tangency is found between a union's indifference curve and the labour demand curve. Assuming that the utility function of the representative
(8.50)-(8.51). The necessary conditions for this optimization problem are:ac = av av =0, (8.56) awl awl 8L1 awl as.2 av av (aLy av2) ail 0g ) = + + 0. (8.57) aw2 awe awe aq aw2 Equation (8.56) has a
which indicates that membership of the union is fixed at N, and the unemployment benefit is constant over time. The optimal plan for the union consists of choosing w1 and w2 such that (8.54) is
where p is the pure rate of time preference (see Chapter 6), and V (wt , Lt ) is the instantaneous utility of the union, that is defined as follows:Lt V (wt, Lt) Lt(—N) u(wt) + [1 - (-Au(B), (8.55)
Equation (8.57) is slightly chooses for the second pt., the wage in the second pet pared to the static case vthe second period is more I Specifically, we can easily d V(wi,Li) -1- 1+ P )V(w2,L2),
where ED 1/(1 - a), Lp is the firm's demand for labour in period t, and q is Tobin's q-ratio discussed extensively in Chapter 4. Equations (8.50)-(8.51) show that the elasticity of labour demand is
(8.53)
Douglas, i.e. Yt = 41g -a , with 0 < a < 1 and Yt representing output. By using these specific functions, (8.47)-(8.49) can be written as:ED 1,113 = (°-) Kl, Wi A, ED LD =W2[Ki + 11= -b 2 1 FK(142,
The Foundation of Modern Macroeconomics In order to keep the model as simple as possible, we work with specific functional forms for the firm's production and adjustment cost functions, and the
ED + 0 w2Uw(w2)log w2 = log B + 1 ED - -where 0 is defined as:
where r is the real interest rate. The first-order conditions for the optimization problem are:an, ir = aL i aIi =a II aL2 an,-14,1= 0, 8.47)( 1 + = 0, (8.48)+1-[FL(L2,Ki 0 — w21 = r) 0. (8.49)207
investment levels in order to maximize the present value of its stream of profits, which is defined as:n= 7r2 + 1 + r F(Li ,Ki ) — wiLi —(pal) (F(L2,Ki + — w2L2 )1 + r(8.46)
the firm does not invest in the second period because our stylized world comes to a close at the end of that period. Furthermore, we have assumed for convenience that the capital stock does not
this function captures the existence of internal adjustment costs that are rising (at an increasing rate) in the rate of investment, i.e. (1)1 > 0 and (1)ll > 0. Obviously
where Trt is real profit in period t (= 1, 2), Lt is employment, It is investment, wt is the real wage rate, F(., .) is a constant returns to scale production function, and(I)(.) is the installation
The remainder of this section serves to demonstrate the underinvestment result in a simple two-period model of the interaction between a monopoly trade union and a firm. This example is a
however, the firm is a "sitting duck" for the union. The capital stock cannot be shifted easily so the union can renege on its promise of moderate wages and skim off a large part of the firm's
Aire will be comparable. A Ia credibility problem assothat investment is largely 1• 1 follow a smooth (and nce the firm has invested,
(8.43)unemployment U) rises if ressivity falls (s rises), and similar to those that were. -ould think the latter. The ble production factor, the conflict between what is un. Take, for example, the
tv of the tax system. For from Chapter 7 that an by a decrease in s.i member's indirect utility ation (8.42) is simplified to:
Chapter 8: Trade Unions and the Labour Márket(8.40)w dtA =0— dw . (8.41)at wdtA /dw = tM — to and 0):(8.42)
T4/ = [14(wa tA» -(8.40)8.41)(8.43)206
firm will not invest too much, so that the wage in the future will be comparable. A kind of wage smoothing behaviour may emerge.This is not the end of the story, however, since there is a credibility
short-sighted union will push for high wages and suffer the consequences in the future as firms accumulate capital and labour demand becomes more elastic. Farsighted unions, on the other hand, will

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