5

If the utility is continuous and locally insatiable then the Hicksian demand equals the Walrasian demand. So you'll need to look for a utility function which violates atleast one of these. Lets try a simple violation of non-satiation $$ u(x,y) = \left\{ \begin{array}{ll} x+y & \quad x+y \leq 1 \\ 1 & \quad \text{ ...


5

Convexity can be a very important assumption as much of economic analysis is built on working with convex sets, which makes things easier. Very importantly, convexity of sets allows us to work with the Separating Hyperplane and Supporting Hyperplane theorems, which have applications to many results in economics, as partially discussed here and here. Here ...


4

That statement is not generally true. It is true of rivalrous goods (e.g. when I take a slice of a pizza, there's that much less left of the pizza for you). It is false of non-rivalrous goods (e.g. when I step into the sunshine, there is usually* no less of the sunshine for you). *Unless of course I somehow also block the sunshine for you.


4

Without convexity, we'd lose the convenience of using the first order condition (or the tangency condition) to identify the optimal consumption bundle. As shown in the following figure, where the red-shaded region is a non-convex budget set, the tangency at point $E$ is not the optimal consumption point; rather, the optimum is a corner solution, where only $...


3

As we have discussed in the comments, the utility function used in the book is Cobb-Douglas: $U = CM^{\mu}A^{1 - \mu}$. The well known fact mentioned in equation (3.3) on page 57 - the one that you highlighted - is that the Cobb-Douglas utility function is homothetic - the share of total income spent on any of the goods is constant over all possible incomes. ...


2

The following is a slight rewording of an example in Richard Thaler's Misbehaving (1): Positive framing of certain outcome Imagine you are $300 richer than you are today. You are given a choice between: A. A certain gain of \$100. B. A 50% chance to gain \$200 and a 50% chance of losing \$0. Negative ...


2

Why are averages preferred to extremes on the same indifference curve? That is false. Whoever told you this is mistaken. Or it could also be that you misheard/misread and are confusing this with the idea that the bundle of 100 apples + 100 oranges is (usually) preferred to the bundle of 200 apples or the bundle of 200 oranges. Doesn't everything along ...


2

The MRS represents the rate of exchange between goods x and y that would leave the agent indifferent to trading the two. It is the slope of the indifference curve for a given value of utility U. To derive the indifference map (the set of indifference curves), take U constant in the utility function, and solve for y in terms of x. You can check if your MRS ...


2

I believe this comes from a very beginning of the book, which tries to emphasize the concept of scarcity... a very important idea in economics. Later on, you'll see that there are certain types of goods that, when one person "consumes" it, it doesn't mean that other people cannot consume it as well. In economics, this is called a non-rivalry good. Some ...


1

From the Oxford dictionary: (emphasis added by me) externality (noun) A consequence of an industrial or commercial activity which affects other parties without this being reflected in market prices... Another way to put this is that externalities are not the results of market rivalry. So if you and I are bidding on the same item on e-Bay, and you ...


1

The problem formulation admits the following Normal Form representation. We can reject any strategy involving price greater than 2, as demand falls to zero and such strategies are strictly dominated by those for which prices are either 1 or 2. 0 1 2 0 [0,0] [0,0] [0,0] 1 [0,0] [0.5,0.5] [1,0] 2 [0,0] [0,1] [1,1]...


1

As mentioned by Mas-Colell, Whinston and Green, the equality is true "for all $p$ and $w$". It is a consequence of the budget constraint, which is satisfied for any prices and income values: $$ \Sigma_{k=1}^{L} p_k x_k (p,w) = w. $$ As you mention, the equality $$ \Sigma_{k=1}^{L} \frac{\partial x_l (p,w)}{\partial p_k} p_k + \frac{\partial x_l (p,w)}{\...


1

You may find this article useful Licensing and Rent Dissipation. In simple terms you might think of it as the devaluation of an 'asset' of some sort.


1

At the level of individuals (and in the differentiable case), the first order derivatives of the demand system are related to the second order derivatives of the utility function. This implies that the second order derivatives of the demand system are related to the third order derivatives of the utility function. \ Indeed, from the first order condition ...


1

Let $q$ denote the output of the firm, and let $\varepsilon_p(q)$ denote the elasticity of price w.r.t. quantity sold. We know that when profit is maximized $$ |\varepsilon_p(q)| = \frac{p(q)-MC(q)}{p(q)}. $$ We also know that in the long-run equilibrium firms have zero economic profit, i.e. $$ AC(q) = p(q). $$ Productive efficiency is achieved when $AC(q)$ ...


1

Common pool resources can be depleted by overuse. For example, an area of communal grazing land would be a common pool resource because grazing too many animals decreases the amount of grass available to each animal. Wikipedia is a common good but are not a common pool resource - reading a lot of articles on Wikipedia does not reduce the number of ...


1

To start with, plot the line for which \begin{equation} x + 3y = U \end{equation} The red line in the graph above is this line. For simplicity, I've assumed U = 9 in this case but the solution would work for any U > 0. The region to the right of this line would satisfy your constraint but since we are interested in minimising our cost, we would want our ...


1

Expenditure minimization problem in the question is as follows : \begin{eqnarray*} \min_{x\geq 0, y\geq 0} & \ \ p_Xx + p_Yy \\ \text{s.t.}& \ \ x + 3y \geq U \end{eqnarray*} where $p_X > 0$, $p_Y > 0$ and $U \geq 0$ are given. Since prices are positive, the cost minimizing choice will satisfy the condition that $x + 3y = U$. So, we can rewrite ...


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