Todaro Migration Model: A Graphical Exposition with a Numerical Example
This is a graphical exposition of the model in Todaro's Economic Development text (5th edition, 1994).
1. Our economy has eight million workers, and consists of two sectors, rural and urban, with demand curves for labor that look like this.
2. Workers can move back and forth freely between town and country. Where will they go? Under conditions of wage flexibility, workers will always look for the highest wage, so that equilibrium will require wage equalization between the two sectors, with the entire workforce of 8 million employed.
This can be demonstrated by flipping the urban graph horizontally, like
and then superimposing it on the rural diagram:
|We flip and superimpose because this lets us see, in one graph, where all the workers are. We have 8 million workers -- the width of the bottom of our graph. For the agricultural/rural workers, start at the left-hand side of the graph, focus on the curve representing demand for labor in agriculture (the red one), and move rightward to where the agricultural wage gives you a number of workers employed in agriculture. For the manufacturing/urban workers, start at the right-hand edge, focus on the curve representing demand for labor in manufacturing (the blue one), and move leftward to where the manufacturing wage gives you a number of workers employed in manufacturing.|
In this equilibrium, both rural and urban employment will pay $1.50 a day, with 4.5 million people in agricultural employment and 3.5 million working in manufacturing. In this case then, the equilibrium condition is simply WA = WM.
3. Now let us suppose that the urban wage (WM) is institutionally set at $4 a day. In other words, the urban wage is no longer flexible. The rural wage remains flexible.
Reading off the demand curve for urban employment, you can see that only 2 million fortunate people will get manufacturing jobs at that wage. What will the remaining 6 million workers in the economy do? Under simple micro assumptions, they will take whatever work they can find in the agricultural sector. So 6 million unlucky people take rural jobs, and the rural wage is $1 a day.
Todaro's key insight is that under these conditions, a $4 a day wage looks awfully good to someone making $1 a day, and such a person might be willing to put up with the prospect of unemployment in order to have a chance at such a job. If that is the case the situation shown at right is not an equilibrium, and will not persist for long.
4. Todaro reasons as follows. Suppose that the person who is considering migrating compares the rural wage to an urban wage that is adjusted by the prospect of getting such a job. A simple way to represent the probability of getting urban employment is the total number of urban employed (LM) divided by the total urban labor force (LU). In other words the equilibrium condition -- the point at which a worker would be indifferent between being in the city or the countryside -- is actually:
number of employed manufacturing workers (LM)
WA = -------------------------------------------------------------- x WM
total number of urban workers (LU)
In this case the situation represented in (3), in which the entire urban workforce was employed, would suggest to a rural worker a pretty good chance of getting an urban job if he/she went to the city. So if we started with the situation in (3), people would migrate. As they migrated, two things would happen: the rural wage would rise, and the urban workforce (and with it urban unemployment) would also rise. The first change would raise the attractiveness of rural employment, and the second change would reduce the attractiveness of urban employment. Just to be sure we understand the mechanics of the model, suppose that we start with the situation in (3), and 1 million people then leave the countryside and arrive in the city.
The rural wage will rise to $1.25 a day. Two thirds of the urban workforce will now be employed (the number of employed urban workers does not change because the wage is fixed). Are we in equilibrium? Not yet, according to the model. Plugging in numbers, WA = $1.25 and WM = $4. But rural workers will perceive a 2/3 (LM/LU) chance of getting an urban job, yielding a benefit of $2.33 a day to being in the city. Rural-urban migration will continue.
5. The equilibrium condition WA = (LM/LU) x WM can actually generate for us a set of rural wage rates and rural/urban residence patterns that would make workers indifferent between being in the city or the country. This "locus" of equilibrium points is represented by the purple dashed line below.
As you work down the locus, lower rural wages are compatible, in equilibrium, with more people crowding into the city and creating lower urban employment rates. For example it would have required a rural wage of $2.33, in the example above, to produce an equilibrium (point A). But our rural sector, sadly, cannot employ 5 million workers at $2.33 a day, so that equilibrium is not attainable. The point represented at Z, where our equilibrium locus intersects the demand curve for rural labor, is attainable: at this point the rural wage of $2 a day and the urban employment rate of 50% fulfill the equilibrium condition stated above:
$2 = (2 million/4 million) x $4
No further workers will migrate.
(Note: The above generally follows the notation in Todaro pages 268-269. The "Lu" shown on Figure 8.3 in the Todaro text is a typo.)