Answered: marginal utilities

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Existence of representative consumer Suppose households 1 and 2 have one-period utility functions u(c₁) and w(c₂), respectively, where u and w are both increasing, strictly concave, twice-differentiable functions of a scalar consumption rate. Consider the Pareto problem:

Subject to the constraint c¹ + c² = c. Show that the solution of this problem has the form of a concave utility function v_θ(c), which depends on the Pareto weight θ. Show that v_θ(c) = θ_u (c₁) = (1 − θ)w (c₂). The function v_θ(c) is the utility function of the representative consumer. Such a representative consumer always lurks within a complete markets competitive equilibrium even with heterogeneous preferences. At a competitive equilibrium, the marginal utilities of the representative agent and each and every agent are proportional.

Definition Video Formula Definition Phenomenon in which market supply and demand balance each other. Market equilibrium is the economic state in which the market demand curve intersects the market supply curve, giving us the equilibrium price and equilibrium quantity for which a commodity can be sold and purchased in an economy. When market equilibrium is achieved, it suggests that all resources have been allocated efficiently and that there is just a distribution of income and resources in the economy. Video Formula

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