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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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

The wage-setting model demonstrates how firms can set wages to fulfill two key objectives: to recruit and retain the necessary workforce, and to provide employees with a strong incentive to work hard. This model, depicted in diagrams like Figure 6.15, is used to find a firm's profit-maximizing wage and employment level by overlaying its isoprofit curves onto its feasible set of (N, w) combinations. The feasible set consists of all points on or above the no-shirking wage curve, and the optimal choice for the firm is the combination of wage and employment on the highest possible isoprofit curve within this set.

The Wage-Setting 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/.

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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

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.

Increased Wages and Employment from a Binding Minimum Wage

A Binding Minimum Wage Reduces Firm's Profit in the No-Shirking Model

In the no-shirking wage model, a low minimum wage (represented as min_w) is a wage floor set below the firm's original profit-maximizing wage (w_0). This is illustrated on the model's diagram by a horizontal line that starts at the min_w level on the vertical wage axis and connects to the upward-sloping no-shirking wage curve.

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

In the wage-setting model, the zero-profit line represents combinations of wage and employment where the firm's economic profit is zero, marking the boundary of economic viability. For a firm where revenue per employee is €800, this line is composed of two segments: a vertical line along the wage axis from the origin (0, 0) up to (0, 800), which then becomes a horizontal line extending from that point onwards.

The Zero-Profit Line in the Wage-Setting Model

In the wage-setting model, there exists a group of unemployed individuals who are not classified as involuntarily unemployed. This is because their personal reservation wage is higher than the wage the firm is offering (w1). Since they would not accept a job at a wage that other workers find acceptable, they fall outside the standard definition of involuntary unemployment.

Workers Not Involuntarily Unemployed in the Wage-Setting Model

The wage-setting model for a single firm can be extended to represent an entire economy. This transition is accomplished by postulating that the economy consists of a fixed number of identical firms, each facing the same market and operational conditions.

Scaling the Single-Firm Model to an Economy-Wide Model

A firm's ability to achieve a certain profit level is determined by whether the corresponding isoprofit curve intersects with its feasible set. Some profit levels may be unattainable because their isoprofit curves lie entirely outside the feasible region, as illustrated by a €5,000 profit curve. In contrast, other profit levels, such as €3,000, are attainable because their isoprofit curves pass through the feasible set, although these may not represent the maximum possible profit.

Attainable vs. Unattainable Profits Based on Feasibility

The reason a profit-maximizing firm operates on the no-shirking wage curve is rooted in cost minimization. For any given level of employment ($N$), the firm must pay at least the no-shirking wage, $W(N)$, to ensure employee effort. This requirement is represented by the inequality $w \ge W(N)$. To maximize its profits, the firm has no incentive to pay more than this necessary minimum. Therefore, it will set the wage precisely at the lowest possible level that prevents shirking. This decision effectively transforms the no-shirking condition from an inequality into a mathematical equality: $w = W(N)$. As a result, the firm's optimal wage-employment choice will always lie on the no-shirking wage curve.

Why a Profit-Maximizing Firm Operates on the No-Shirking Wage Curve

The wage-setting model is applied to examine how a firm's optimal wage and employment levels are affected by shifts in broader economic conditions. This analysis explores the implications of these external changes on the outcomes of the model.

Implications of the Wage-Setting Model for Changing Economic Conditions

In the context of the wage-setting model, the feasible set includes all combinations of wage ($w$) and employment ($N$) that a firm can possibly choose. This set is mathematically defined by the inequality $w \ge W(N)$, where $W(N)$ represents the no-shirking wage curve. Consequently, any wage-employment combination situated on or above the no-shirking wage curve is a viable option for the firm.

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