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In the economy described above, set of efficient allocations is given by the red curve. Just do the slope of ICs comparisons at the boundaries and you will get that.


Any labor may be considered as a 'bad' (service) for which you are compensated by the firm by paying you salary/wages. In modeling labor market, this is generally described in the opposite sense, i.e., consuming leisure. When you work you let go of leisure, which is a good. So that, technically, makes supplying labor (which is a service) as an economic bad.


I will argue that social harm is the opposite of social services that deliver so-called economic goods. Further there are two kinds of social harm. One kind of harm gives rise to a cause of action (COA) at law. This is the type of harm for which the law stands ready to provide a social remedy. Another kind of harm does not give rise to a cause of action at ...


In order to have $x^*_j>0$, it is possible to impose either (i) a condition on the marginal utility: $\lim_{x_j\rightarrow0} \partial{U}/\partial{x_j}(x)=+\infty$ (ii) or an inequality $x_j \geq a_j>0$ where $a_j$ is interpreted as a subsistence level of $x_j$ Often the utility function is reparameterized and written $U(x-a)$ with the constraint $X:=x-...


Square root utility : $ U (x,y) = \sqrt{x+y} $


One that was not mentioned in question is the quadratic utility (aka preference for extremes): $$U(x,y) = x^2+ y^2$$ This one is less common but still used in micro courses.


Indifference curves represent preferences. Preferences are usually assumed to be stable, i.e. they do not change. So no, indifference curves don't shift.


Assuming the following: $ S > 0 $, $T > 0 $, $ c(S) = \left\{c\in\Bbb{R}^T_{+} : \sum_{t=1}^T{c_t} = S \right\} $, and $ U(\cdot) $ continuous. Let's start with convexity. To demonstrate convexity, we need to show that for any two points $c^1$ and $c^2$ in $c(S)$, any linear combination of the two is also an element of $c(S)$. Let $\lambda \in [0,1]$,...


The first thing to mention is that you cannot say who was the first to make the distinction. All can go back to Aristotele, Manzoni, the history of hedonimetry and utility measurement. It is more philosophy than utility theory (also here, on the name utility we could write books). But since you know the history and you just need references for the "...

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