The Problem the Individual Solves to Derive the Labor Supply $\max _ { c , L } U ( c , L ) = \log c - 1 / 2 \frac { 1 } { \bar { \ell } } L ^ { 1 / 3 } \text { subject to } c + \bar { S } = w L$

Multiple Choice

The problem the individual solves to derive the labor supply is:

A) $\max _ { c , L } U ( c , L ) = \log c - 1 / 2 \frac { 1 } { \bar { \ell } } L ^ { 1 / 3 } \text { subject to } c + \bar { S } = w L$
B) $\max _ { c _ { \text {tody } } c _ { \text {farr } } } U \left( c _ { \text {toduy } } c _ { \text {future } } \right) = \log c _ { \text {today } } + \beta \log c _ { \text {future } } \text { subject toc } c _ { \text {today } } + \frac { c _ { \text {future } } } { 1 + R } = \bar { W }$
C) $\max _ { c }U ( c ) = \log c \text { subject to } P c = w L$

D) $\max _ { c , t } U ( c , \bar { \ell } ) = \alpha \cdot \log c + ( 1 - \alpha ) \cdot \bar { \ell } \text { subject to } c - w \bar { \ell } = w L$
E) $\max _ { k , L } U ( K , L ) = \bar { A } K ^ { \frac { 1 } { 3 } } L ^ { \frac { 2 } { 3 } } \text { subject to } C = r K + w L$