ECON 704 Midterm: greenwood_704_spring_2013
Image an industry inhabited by a …rm and a union. The …rm chooses
how many workers, l, to hire at a given wage rate, w, and a given amount of
known e¤ort that each worker expends on job e. The union picks the amount
of e¤ort, e, that each worker puts in on the job and the wage rate, w. Wages
are paid for showing up and not for the amount of on-the-job e¤ort. All
workers are unionized and follow union dictates.
The …rm produces output, o, in line with the production function
o=le;with 0< ; ; + < 1;
as can be seen, output is a function of both the number of bodies hired and
the e¤ort each worker puts in. Production is subject to the …xed cost, ,
in terms of output. Output is sold at the …xed price p= 1. The union has
preferences of the following form:
w!l"e; with 0< =(1 )< ! < 1, and " > 0.
It values the wage, w, each worker receives, the amount of workers hired, l,
and the e¤ort, e, that each worker expends. (This question will be graded
both upon the economic intuition and the technical ability that you demon-
strate. Double space your answer.)
1. Formulate and solve the …rm’s problem.
2. Formulate and solve the union’s problem. Assume that (!) < .
(Hint: Try to express in the problem in terms of eonly.)
3. How are e¤ort, e, employment, l, and wages, w, linked with ? What
is the intuition here?
4. How are e¤ort, e, employment, l, and wages, w, linked with "? What
is the intuition here?
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