Question

1.- Consider the following utility function $u = \sum_{j} \beta_j ln c_j$ where $j=1,...,i,...N$, $0 < \beta_j < 1$ and $\sum_{j} \beta_j = 1$. The budget constraint is $E = \sum_{j} p_j c_j$ where E is the expenditure. Show that the demand function for the consumed quantity of good i, $c_i$, is $c_i = \frac{\beta_i E}{p_i}$

          1.- Consider the following utility function $u = \sum_{j} \beta_j ln c_j$ where $j=1,...,i,...N$,
$0 < \beta_j < 1$ and $\sum_{j} \beta_j = 1$. The budget constraint is $E = \sum_{j} p_j c_j$ where E is the
expenditure. Show that the demand function for the consumed quantity of good
i, $c_i$, is
$c_i = \frac{\beta_i E}{p_i}$

1.- Consider the following utility function u = ∑j ln cj where j=1,...,i,...N,
0 < < 1 and ∑j = 1. The budget constraint is E = ∑j pj cj where E is the
expenditure. Show that the demand function for the consumed quantity of good
i, ci, is
ci = ( E)/(pi)

Added by Hannah S.

Principles of Economics

Gregory Mankiw 8th Edition

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1.- Consider the following utility function u = ∑ᵢ βⱼlncⱼ where j=1, ..., i, ..., N, 0 < βⱼ < 1 and ∑ᵢ βⱼ = 1. The budget constraint is E = ∑ᵢ pⱼcⱼ where E is the expenditure. Show that the demand function for the consumed quantity of good i, cᵢ, is cᵢ = (βᵢE)/(pᵢ) 1.- Consider the following utility function u = j lnci where j=1, ... i, ... N, 0 < <1 and =1. The budget constraint is E = PiCi where E is the expenditure. Show that the demand function for the consumed quantity of good i, ci, is B: E Ci Pi