# Combined Problem, No Equilibrium

In this graph, the market-clearing conditions aren't enforced. Play around with the real wage and see how there is only one wage at which the Producer's and Consumer's Decisions align.

Exogenous Parameters:
$$K$$:
$$z$$:
$$\alpha$$:
$$h$$:
$$G$$:
$$w$$:

Endogenous Parameters:
$$N_d$$: test
$$N_s$$: test
$$Y$$: test
$$\pi$$: test
$$C$$: test
$$l$$: test
$$U$$: test

### 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}