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Q7 13 Points Consider the decisions of a representative consumer whose preferences are given by $u(C, l) = \alpha C + \beta \log l$, in which $C$ is the quantity of consumption and $l$ is the quantity of leisure. The parameters $\alpha$ and $\beta$ are positive. The consumer faces two constraints. The time constraint is given by $l + N^s = 1$ with $N^s$ as the time spent working (or the labor supply). Further, consumers take wages as given (outside of their control) and obtain wage income equal to $wN^s$. The budget constraint is $C = w(1 - l) + \pi - T$, with $\pi$ as the real dividend income received from the representative firm and $T$ as the real lump- sum taxes paid to the government. Assume for simplicity that $T = 0$. Q7.1 2 Points What is the optimal labor supply of the representative consumer? $N^{s} = 0$ $N^{s} = 1 - \frac{\omega \beta}{\alpha}$ $N^{s} = 1 - \frac{\beta}{\alpha w}$ $N^{s} = 1$

          Q7
13 Points
Consider the decisions of a representative consumer whose preferences are given by $u(C, l) = \alpha C + \beta \log l$, in which $C$ is the quantity of consumption and $l$ is the quantity of leisure. The
parameters $\alpha$ and $\beta$ are positive.
The consumer faces two constraints. The time constraint is given by $l + N^s = 1$ with $N^s$ as the
time spent working (or the labor supply). Further, consumers take wages as given (outside of their
control) and obtain wage income equal to $wN^s$. The budget constraint is $C = w(1 - l) + \pi - T$,
with $\pi$ as the real dividend income received from the representative firm and $T$ as the real lump-
sum taxes paid to the government. Assume for simplicity that $T = 0$.
Q7.1
2 Points
What is the optimal labor supply of the representative consumer?
$N^{s*} = 0$
$N^{s*} = 1 - \frac{\omega \beta}{\alpha}$
$N^{s*} = 1 - \frac{\beta}{\alpha w}$
$N^{s*} = 1$

Q7
13 Points
Consider the decisions of a representative consumer whose preferences are given by u(C, l) = α C + βlog l, in which C is the quantity of consumption and l is the quantity of leisure. The
parameters α and β are positive.
The consumer faces two constraints. The time constraint is given by l + N^s = 1 with N^s as the
time spent working (or the labor supply). Further, consumers take wages as given (outside of their
control) and obtain wage income equal to wN^s. The budget constraint is C = w(1 - l) + π - T,
with π as the real dividend income received from the representative firm and T as the real lump-
sum taxes paid to the government. Assume for simplicity that T = 0.
Q7.1
2 Points
What is the optimal labor supply of the representative consumer?
N^s* = 0
N^s* = 1 - (ωβ)/(α)
N^s* = 1 - (β)/(α w)
N^s* = 1

Added by Chad S.

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