This section reviews Learner’s( 1997b) two-sector model with endogenous effort. The key building block is a production function defined as
where Q is the rate of output per unit of time, К and L are the (timeless) stocks of capital and labor inputs respectively, /(.,.) is a function homogeneous to degree one, s is the “intensity” of operation, h is the hours of operation, and e~s-h is the overall effort exerted by each worker. Intensity is influenced by speed of operations but includes also the level of care or attentiveness a worker must exert to reduce the likelihood of breakdowns and other costly delays in the production process.
We make two additional assumptions about effort. First we assume that labor cares about effort, but capital does not. In other words, long hours at high speed will not wear out equipment any faster than short hours at slow speed. The second assumption is that effort is continuous and completely variable, which is an assumption that affects the details but not the basic message of the model.2 For generating most of the diagrams we assume that each sector has fixed input technologies and the production function takes the form
where ei is the effort level in sector i and К and L are the capital and labor inputs. With the assumption that depreciation doesn’t depend on worker effort, a competitive labor market will award any marginal increase in output from greater effort to the workers. Expressed differently, it is as if the workers rented the capital equipment and received the excess earnings as compensation for the effort they decide to exert. The (net) wage rate wf(ef) applicable to effort e can be found from the zero profit condition pi ■ ei * /L) = w, (
where P is an overall price index. The wage-effort zero-profit lines for two different sectors are illustrated in Figure 2.1.
Both zero profit lines in Figure 2.1 have negative intercepts since at very low levels of effort the value of the output is not large enough to cover capital rental costs. Since the capital costs in the capital-intensive sector are higher, the intercept is more negative. As the effort increases, workers can be awarded higher wages in both sectors.4 The observed labor contracts will lie along the upper envelope of these wage-offer curves, highlighted as the heavy curve depicted in Figure 2.1. The marginal return to effort has to be lower in the labor-intensive sector since otherwise there would be no attractive contracts in the capital-intensive sector.
These intercepts and slopes dictate that the low effort-low wage contracts are offered in the labor-intensive sector while high wage-high effort contracts are offered in the capital-intensive sector. Also depicted in Figure 2.1 is an indifference curve tangent to the wage-effort offer curve at two points. This represents an equilibrium with identical workers who are indifferent between the two prevailing contracts: high effort-high wage and low effort-low wage.loan for bad credit utah