Final answer:
A binding constraint in optimization has a non-zero shadow price, indicating that relaxing the constraint would improve the objective function value. This concept is integral to understanding how constraints operate in economic models, such as budget constraints and the PPF. Minimum and living wage can similarly act as binding or nonbinding price floors depending on their relation to the equilibrium wage.
Step-by-step explanation:
A binding constraint in the context of linear programming refers to a situation where one or more of the constraints in an optimization problem are satisfied exactly, and any change in this constraint would affect the optimal solution. Specifically, the correct option for the definition of a binding constraint is a. has a non-zero shadow price. This means that if the constraint is relaxed, the objective function value (such as profit or cost) would improve. The binding constraint's shadow price, also known as the dual value, represents the rate at which the objective function value would improve per unit increase in the constraint's right-hand side.
Conversely, options b and c are incorrect, as they describe what would be the case for a non-binding constraint: one where resources are not fully utilized (slack value is positive) and you have some leftover capacity or resources that are not being used up totally. Option d is also incorrect because a zero-shadow price implies that the constraint is non-binding, meaning that loosening the constraint would not improve the objective function value.
In economics, similar concepts are observed in different contexts such as with budget constraints and the production possibility frontier (PPF). Both depict the limitations within which choices are made and illustrate trade-offs and opportunity costs. Regarding minimum wage and living wage scenarios, a minimum wage is a nonbinding price floor when it is set below the equilibrium wage — it does not affect the market wage. A living wage could be a binding price floor if it is set above the market-clearing level, thus becoming enforceable and affecting employment and wages in the market.