The following is an interactive example showing both the consumer's problem and the producer's problem on the same graph:

Exogenous Variables and Parameters:

\(K\):

\(z\):

\(\alpha\):

\(h\):

\(G\):

Endogenous Parameters:

\(C\):

\(l\):

\(N_d=N_s\):

\(U\):

Details

The firm solves
\[\max_{N_s}\left[ zK^\alpha N_d^{1-\alpha} - wN_s\right]\]

The consumer solves
\[\max_{C,l}\;\left[\ln C + \ln l\right]\]
subject to the constraints:
\begin{gather}
c\geq 0, \quad \quad h \geq l \geq 0 \tag{NonNeg}\\
c \leq w\cdot(h-l) + \pi - T \tag{Budget}\\
\end{gather}

Market Clearing Conditions are \[Y=C+G\] \[N_d = N_s = h-l\]