11. A worker derives utility from consumption, C and leisure, L U = U(C, L) and initially faces the constraints p.C = N+w.H H = 24 - L where p is the nominal price of consumption, N> 0 is unearned income, w is the nominal wage and H is hours worked. (a) Derive the budget constraint in terms of C and L and show on a diagram an initial optimal choice of C and L, in which both are positive. (b) State this equilibrium algebraically, and briefly explain how it can be derived. (c) Show that, assuming normality of leisure, for some value N*, if N> N*, the individual will choose not to work. Is the initial level of N in your answers to parts a) and b) greater or less than N*?
Utility:
Utility refers to the satisfaction, well-being, or happiness that an individual derives from consuming goods and services. In economics, utility is a concept used to measure and quantify the subjective benefits or preferences that individuals have for different combinations of goods and services. It is important to note that utility is a subjective concept, meaning it varies from person to person. Economists use utility functions to represent and analyze individuals' preferences and choices when making decisions about how to allocate their resources, such as income, to maximize their well-being.
Budget Constraint:
A budget constraint is a representation of the limitations or restrictions on an individual's spending or consumption choices due to their available income and the prices of goods and services. It defines the feasible set of consumption choices available to an individual based on their income and the prices of goods. In simple terms, it shows what an individual can afford given their financial resources. A budget constraint is typically represented as an equation that relates the quantity of goods and services an individual can purchase to their income and the prices of those goods and services. It helps individuals make decisions about how to allocate their income to maximize their utility while staying within their budget.
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