The analysis of the wage-setting model demonstrates that a minimum wage, if set at a level high enough to be binding, can lead to beneficial outcomes for workers. Specifically, the firm's new optimal choice involves both a higher wage and a greater level of employment than was the case before the policy was introduced.

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In the context of the no-shirking wage model, a 'higher' minimum wage (`min_w`) is defined as a wage set above the firm's initial profit-maximizing wage (`w_0`). On the model's diagram, this is represented by a horizontal line drawn at the `min_w` level. This line originates from the vertical axis and intersects the no-shirking wage curve at a new point, designated as F.

Graphical Representation of a Higher Minimum Wage in the No-Shirking Model

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

CORE Econ - The Economy 2.0: Microeconomics

This activity guides the analysis of how a minimum wage affects a firm's choices in the no-shirking wage model, as depicted in Figure 6.19. A crucial technique to verify that a new point, such as F, is indeed the profit-maximizing choice is to visually trace the new lower boundary of the firm's feasible set. By observing the isoprofit curves that this boundary crosses, one can determine where the firm's profit is rising or falling, and thereby confirm the location of the new optimum.

Activity: Analyzing the Effect of a Minimum Wage Using the No-Shirking Wage Curve Model

The introduction of a minimum wage modifies a firm's feasible set of wage and employment combinations. For lower levels of employment, the new lower boundary of this set becomes a horizontal line at the minimum wage level. This horizontal boundary applies up to the point where it intersects the no-shirking wage curve, which then continues to define the boundary for all subsequent higher employment levels.

Alteration of the Feasible Set by a Minimum Wage

When a minimum wage is implemented at a level that makes the firm's original profit-maximizing combination of wage and employment infeasible (e.g., point E), the firm must alter its decision. It will select a new optimal point (e.g., point F) that represents the highest possible profit on its newly constrained feasible set.

Firm's Choice Shifts When Minimum Wage Renders Optimum Infeasible

Increased Wages and Employment from a Binding Minimum Wage

The introduction of a binding minimum wage, while potentially benefiting workers, reduces the firm's profit in the no-shirking model. This is because the new constrained profit-maximizing point (F) necessarily lies on a lower isoprofit curve than the original, unconstrained optimum (E).

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