Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Emma has a utility function U(x1, x2, x3) = log x1 + 0.8 log x2 + 0.72 log x3 over her incomes x1, x2, x3 in the next three years. This is an example of
(A) expected value;
(B) quasi-hyperbolic utility function;
(C) standard discounted utility;
(D) none of the above.
Emma’s preferences can exhibit which of the following behavioral patterns?
(A) preference for flflexibility;
(B) context effffects;
(C) time inconsistency;
(D) intransitivity.
It is given that a typical consumer has a well-behaved preference structure for his consumption bundle, which includes only two goods, A and B. Further, assume that commodity A is normal and commodity B is Giffen. By keeping commodity A on the x-axis and commodity B on the y-axis, you are required to show the price decomposition for commodity B when $PB decreases exogenously relative to $PA.
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 vθ(c), which depends on the Pareto weight θ. Show that vθ(c) = θu (c1) = (1 − θ)w (c2). The function vθ(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.
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