INTER-INDUSTRY WAGE DIFFERENTIALS: Sector Model 2

High effort saves capital costs. These savings are offset by the wage premiums necessary to compensate workers for high levels of effort. Multiple shifts and other forms of capital sharing can also save capital costs. When two workers share the same capital the intercept of the zero-profit line for each worker shifts upward towards the origin by the factor of two. This allows firms to offer better wage-effort contracts. But capital sharing doesn’t come without costs. Among the costs of capital sharing are wage premia for second and graveyard shifts, transitional down-times and increased non-capital fixed costs such as training and benefits, as well as moral hazard problems and coordination costs. Competition among firms will lead to efficient work practices that optimally trade off the gains from capital sharing with the costs.

Endogenous Effort with Cobb-Douglas Technologies

If the capital/labor ratio in a sector is not fixed technologically, the wage-effort offer curve loses its flat segments, but otherwise there is no material change in the model. For example a Cobb-Douglas production function is
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This sets wage offers proportional to effort raised to a power that exceeds one and that increases with the capital-intensity of the sector. A two-sector equilibrium with Cobb-Douglas production functions is displayed in Figure 2.2. It is very similar to the equilibrium seen in Figure 2.1. In fact it is easy to demonstrate that if the line tangent to the offer curves was traced back to the у-axis the intercept would be the negative cost of capital, r к .

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Changes in Product Prices

A change in the relative price in the two sectors twists the wage-effort offer curve. Figure 2.3 depicts the initial effect of a simultaneous rise in p2 and fall in pj that leaves the overall price level P constant. What this does is rotate upward the wage-effort offer line in the capital-intensive sector and rotate downward the wage-effort offer line in the labor-intensive sector. These changes render the low effort-low wage contract in the labor-intensive sector less attractive and causes income and substitution effects in opposite directions for the two contracts. The high-wage workers experience a favorable income effect and a substitution effect in favor of higher effort (steeper wage-effort offer line). The low-wage workers experience an unfavorable income effect and a substitution effect in favor of lower effort.