HISTORY VS EXPECTATIONS -- PAUL KRUGMAN PRESENTATION BY -KOSHA MODI -PALLAVI JINDAL

In the presence of external economies, it will often happen that the return to committing resources to some activity is higher, the greater the resources committed. This may naturally lead to multiple equilibria. There is an obvious question: which equilibrium actually gets established? On one side is the belief that the choice among multiple equilibria is essentially resolved by history: that past events set the preconditions that drive the economy to one or another steady state. On the other side is the view that the key determinant of choice of equilibrium is expectations: that there is a decisive element of self-fulfilling prophecy. Introduction

ASSUMPTIONS A one-factor (labour, L) economy which is able to produce two goods: C; a good produced with constant returns; X; a good whose production is subject to an externality. Small-country assumption: This economy is able to sell both C and X at fixed prices on world markets. Normalization: P C = 1 i.e, everything is in terms of the C good Further we assume, that one unit of labour produces one unit of the C good => w = 1 (w is the wage rate) A Simple Model with Multiple Equilibria

Since the (positive) economies of scale are external in the X sector, the average productivity of each labour unit increases as more and more labour work in the sector X. Now, the wage rate will be given by the average value of what each labour unit produces. w = (P x.X)/L =, ‘’ ‘’ > 0 (1) For an interesting case, let where is the total labour supply in the economy. A worker will go wherever he receives a higher wage.

Multiple equilibrium : 1. Nobody is employed in X : (L X = 0 ) A worker considering producing X would find that she would receive a lower wage than she receives producing C. There is an equilibrium in which the economy is specialized in the production of C. 2. Everyone is employed in the X sector (L X = L): A worker considering producing C would nd that this would involve a wage cut. Specialization in X is also an equilibrium.

Which equilibrium does the economy go to? L X * denotes the employment in X when w = 1: If the labor force in X is initially larger than L X * the X sector will snowball until the economy is specialized in X. If the labor force in X is initially smaller than L X *, the X sector will unravel, and the economy will end up specializing in C. Thus history, which determines the initial conditions, determines the ultimate outcome. NOTE: All that the workers are considering in choosing which sector to work for are the current wage earnings.

Problems with the quasi-dynamic story: Essentially the question is why labor should adjust slowly. Is there some kind of cost involved to move in between the sectors? Suppose first that labor can move costlessly between the X and C sectors. Then there is no reason why the initial distribution of labor should matter. Whatever the initial position, all workers can coordinate and move to the sector that they expect to yield the higher wage, which is the sector that they expect all the other workers to move to. Thus, in the absence of some cost of shifting labor, either equilibrium can be obtained as a self-fulfilling prophecy, whatever the initial position. History should not matter

Let us introduce some cost of shifting between sectors. As soon as we introduce this cost of adjustment, a worker’s decision to shift between sectors becomes an investment decision, which depends not only on the current wage differential but on expected future wage rates as well. But these future wage rates depend on the decisions of other workers; if everyone expects many workers to move from C to X over time, this will increase the attractiveness of moving from C to X even if there is no immediate effect on relative wage rates. Thus, one can see that expectations play a role in this model, and hence there is in this kind of model the possibility of self-fulfilling prophecy. Let us now introduce dynamics in the model, in which the speed of adjustment is related to the cost of adjustment, and model how workers will decide which sector to work for.

Making The Model Dynamic Cost of shifting labour is a quadratic function of the rate at which labour is moved between sectors Cost is : Where, It is also a measure of the speed of shifting (the lower the cost,the higher is the speed of adjustment)

The national income of the economy at instant t is : People can borrow or lend freely in the world markets at a given interest rate r. The objective is to maximize the present value of the aggregate output over the lifetime, given by:

Labour movement is determined by the equation:

Integrating the first order linear differential equation, we get = rq=return if asset of value q is invested elsewhere -1= like a dividend amount= wage differential between the 2 sectors V

The path could either be S shaped passing through Lx *

Or the path could look like spirals that originate from Lx* but never cut each other

In general,there will be infinitely many such S shaped or spiral curves originating from L x * but only those that go and intersect E x or E c are stable. The others will violate the transversality conditions.

If the path is S shaped,then for any initial L x,there exists only one value of q that can take the economy to equilibrium (either it will be E c (completely specialize in C) or E x (completely specialize in X). Which equilibrium will (if any) be reached depends on the initial value of L x and q. So HISTORY matters. If the path is spiral, then for each initial value of L x Є (L x c,L x x ),there are many values of q which can take the economy to either equilibrium E c or E x,which value of q actually will be chosen will depend on the EXPECTATIONS. The value of q depends on the expectation about how much labour will work in which sector in future. However, if L x ≤ L x c, or if L x ≥ L x x,then only history matters due to a unique value of q corresponding to every value of L x that can give an equilibrium.

When do we get the S shaped curve and the spirals?

Economic meaning of Figure III

Can oscillation be an equilibrium? If adjustment costs are very low, then it can be an equilibrium. All the workers will want to work in the same sector as everyone else and could switch sectors in alternate periods as per their beliefs. We can also have stochastic paths that will choose the deterministic paths with certain probabilities. Say L x < L x * and q=0. This implies that current wage is higher in the C sector. So, on a deterministic path, q should increase. However, we can have a stochastic equilibrium where there people stick to the X sector despite the above scenario.

This could be when there exists a constant probability that q will suddenly jump up to the upper arm of the spiral leading to E x, with this probability being high enough to compensate for the lower wage at present. This could equalize the expected rate of change of q. So L x remains constant until some random instant when it suddenly starts to rise. Economic interpretation: People working in the X sector don’t shift to C despite high wages there because they expect that, at some point in the future, everyone will shift to work in X sector and (L x ) will rise. We cannot rule out such possibilities in this model.

Existence and Size of Overlap