10

The expression in question is in footnote $11$ of the referenced article. Reading the paper, we see that the decision variable here is "the payout rate", which is the reciprocal of $P$. So equivalently, we can solve the maximization problem with respect to $P$ (and not w.r.t. $Q$). More over, "price elasticity of demand" involves the derivative of $Q$ with ...


3

Here is the formulation of the problem : \begin{eqnarray*} \max_{c, h, l} \ & \ln (c - \gamma) + \beta l + \theta h \\ \text{s.t.} & l + h = 1, \\ & c \leq \omega h + \rho, \\ \text{and} & l, h \geq 0, c \geq \gamma \end{eqnarray*} Substituting $l = 1 - h$, we can rewrite the above problem as : \begin{eqnarray*} \max_{c, h} \ & \ln (c ...


2

Everything is explained here: http://en.wikipedia.org/wiki/Linear_programming#Another_example.


2

The shadow price is formally not the increase in the objective function for relaxing a constraint by a single unit, but by an infinitesimal relaxation. In the world of linear programming it can be valid for up to a unit but it doesn't have to be. In your example problem it is actually not. This becomes clearest when we use pictures. I am going to assume ...


1

The corner solution is not $c=a$ it cannot be because the marginal utility of even a tiny bit of consumption is unbounded there. However, you can have a corner solution where $h=0$. Since the agent has non-labor income $p$, the budget line has a kink. That is, if the agent receives a lot of income even without working, they may choose not to work, and fully ...


1

Your production function is basically a Cobb-Douglas function of the form $y=A(t_m-a)^\alpha(t_l-b)^\beta$. Therefore, the parameters $\alpha$ and $\beta$ measure the intensity with which inputs are needed for production. The smaller the value of such parameters, the smaller the marginal productivity of the inputs is. In your context, the company is more ...


1

I don't really understand your optimization problem as it stands. Just as a few examples, when you write out $$\min \sum_m \sum_v \left( \frac{\partial \vec f_v (\vec Q_v)}{\partial \vec f_m (\vec Q_m)} - \frac{\partial \vec f_m (\vec Q_m)}{\partial \vec f_m (\vec Q_m)} \right)$$ I have questions about why you are minimizing the difference between optimal ...


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