"Europe" and the United States - University of St Andrews
"Europe" and the United States - University of St Andrews
"Europe" and the United States - University of St Andrews
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The terms b t <strong>and</strong> (Y t 1 = (n t 1 n n s )) represent <strong>and</strong> a modi…cation to <strong>the</strong> Danthine<br />
<strong>and</strong> Kurman (2004) cost <strong>of</strong> e¤ort function. b t denotes unemployment income.<br />
This will be chie‡y unemployment bene…ts <strong>and</strong> black market income. It tends to<br />
lower <strong>the</strong> level <strong>of</strong> e¤ort. 27 Workers want to be valued more than someone who receives<br />
bene…ts or does not have a legal job. b t is linked both to past real wages <strong>and</strong><br />
past productivity in <strong>the</strong> private sector, where Y t denotes private sector output. This<br />
may re‡ect both <strong>the</strong> structure <strong>of</strong> bene…ts <strong>and</strong> <strong>the</strong> manner in which <strong>the</strong> black market is<br />
linked to <strong>the</strong> o¢ cial economy. Productivity also has a direct e¤ect on morale <strong>and</strong> effort<br />
as employees desire <strong>the</strong>ir due share <strong>of</strong> <strong>the</strong> companies’success. Unions might play<br />
a role in this to <strong>the</strong> extent that <strong>the</strong>y instil a sense <strong>of</strong> entitlement among employees.<br />
The employer takes this relationship into account when setting <strong>the</strong> wage, as will<br />
be discussed fur<strong>the</strong>r below.<br />
7.2 Cost Minimisation <strong>and</strong> E¢ ciency Wages<br />
The production technology is a Cobb Douglas production function,<br />
Y t (i) = AK t (i) (T F P t e t (i) (n t (i) n)) 1 <br />
where <strong>the</strong> output <strong>of</strong> …rm i Y t (i) depends on <strong>the</strong> capital stock <strong>of</strong> …rm i K t (i), <strong>the</strong><br />
e¢ ciency <strong>of</strong> its workers e t (i) <strong>and</strong> <strong>the</strong> number <strong>of</strong> non-overhead workers n t (i) n: In<br />
<strong>the</strong> Danthine <strong>and</strong> Kurman model (2004), in a …rst stage <strong>the</strong> …rm minimises its cost <strong>of</strong><br />
producing a given amount <strong>of</strong> output. Capital <strong>and</strong> labour are hired in economy wide<br />
factor market. However, <strong>the</strong> …rm does not take <strong>the</strong> real wage as given but sets it<br />
taking into account <strong>the</strong> relationship between e¤ort <strong>and</strong> wages given by (27). 28 Hence<br />
<strong>the</strong> …rm’s problem is:<br />
min rt k K t (i)+w t (i)(n t (i) n)s:t:Y t (i) = AK t (i) (T F P t e t (i) (n t (i) n)) 1 <br />
K t(i);n t(i);w t(i);e t(i)<br />
<strong>and</strong> e t (i) = 0 + 1 log w t (i) + 2 (n t n) + 3 log w t<br />
+ 4 log w t 1 5 log b t 8 (Y t 1 = (n t 1 n n s ))<br />
The …rst order conditions for capital <strong>and</strong> labour are<br />
rt k = mc t (i) Y t(i)<br />
K t (i)<br />
Y t (i)<br />
w t (i) = (1 )mc t (i)<br />
n t (i)<br />
n<br />
(28)<br />
(29)<br />
27 Danthine <strong>and</strong> Kurman (2007) introduce <strong>the</strong> bene…t level as a factor which, ceteris paribus,<br />
reduces e¤ort.<br />
28 See Danthine <strong>and</strong> Kurman (2004), pp. 114-115.<br />
29
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