8

Example. Each month, God gives Adam $60$ apples and Eve $40$ (for a total of $100$ apples). Let's write this allocation as $X=(60,40)$. The Devil now comes along and offers to increase their total monthly allotment of apples to $101$, but on the condition that the allocation must be $Y=(59,42)$. Observe: $X$ is Pareto efficient but not Kaldor-Hicks ...


3

Quoting from the question: $F(aK,aL)$ : simultaneous and proportional inputs increase $aF(K,L)$ : output increase But $F(aK,aL)$ is an output increase, that is why it starts with $F$. It is the output increase due to the simultaneous and proportional increase of inputs. At the same time, $aF(K,L)$ is a hypothetical output, the output were this if ...


3

In fact, the law is quite easy to prove (and holds under very general assumptions). Consider a firm that chooses which quantity $q \geq 0$ to supply taking the price $p > 0$ as given. Let $C(q)$ denote the firm's total cost from supplying $q$ units so that the firm's total profit can be written $pq - C(q)$. Assume that the firm chooses $q$ to maximise its ...


2

You have to look at this from the derivation of the profit equation. From the equation $\mathbb{E}(\pi_n) = e - c(e)$, you can see that the marginal benefit of increasing $e$ is equal to 1. That is, for each extra $e$ you put in, you get that exact amount back in terms of expected profits. The $e$ term is the benefits, and $\frac{de}{de} = 1$ is then the ...


2

The value is subjective. If the buyer values the shoes at 10 yuan and the seller values 10 yuan at 10 yuan then from economic perspective equal amount of value was exchanged (i.e 10 value of yuan embedded in paper notes for 10 value of yuan embedded in shoes) regardless of what were the costs of production costs. Also money just serves to solve double ...


2

You should quote directly from the book you're citing, because I think you might be mis-reading it. At the Econ101 level, there are two important frames for thinking about fixed costs: one is that in the long run, the contribution of fixed costs to average cost falls to zero. You can see this in the standard textbook graph, which will typically look ...


2

Objective function of Lagrangian can be set up either with $+\lambda$ or $-\lambda$, depending on how you solve the budget constraint. Actually, for the solution it does not matter if $\lambda$ has negative or positive sign in the equation. You can clearly see it from the formula if you expand the second term: $$ \mathcal{L}(x,y, \lambda) = U(x,y) + \lambda(...


2

In between eq. $(2.F.2)$ and $(2.F.3)$ we read ...Walras's law tells us that $w' = p'\cdot x(p',w')$ Assume now that homogeneity of degree zero does not hold. Then we have, $a>0$ $$x(ap,aw) \neq x(p,w)$$ see definition $2.E.1$ Then we can set $p'=ap,w'=aw$ to examine the case $x(p',w') \neq x(p,w)$. But then Walras' law would imply $$w' = p'\cdot ...


1

let $u \equiv xy^2$, then we have: $$U=lnx+2lny=ln(xy^2)=ln(u)$$ Since $U'(u)>0 \: \forall u>0$ it follows that the $(x,y)$ that maximizes $U$ also maximizes $u$; $\max \{U\}=\max\{ln(u)\}=ln(\max\{u\})$. $u$ represents the same preferences as $U$. Clearly, $u(x,y)=x^a y^b$ with $a=1$, $b=2$.


1

It is possible. Trivially if we have $Q^s=f(p)$ and $Q^d=g(p)$ and we plot this in a 3d-coordinate system with variables $p$, $Q$ and some other variable $x$ (which does not appear in our functions at all), then we can take a 'slice' for every $x$-value, and in fact every slice gives us the conventional 2d-depiction of this model. We could of course take ...


1

Returns to scale is directly related to homogeneous functions: For a homogeneous function $F(x,y)$ given $\theta>0$, for simplicity, $$F(\theta x,\theta y) = \theta^r F(x,y)$$ where would we refer to $F$ being a homogeneous function of degree $r$. Here it is much clearer to see that if $r>1$, we have increasing returns to scale because for a given $\...


1

You can estimate it in multiple ways. If you have panel data then you could first log linearize the expression giving you: $$ln(F_{it})=ln(A_{it}) + \alpha ln(K_{ti}) + (1-\alpha) ln(L_{it}) $$ Which could be estimated in multiple ways. You could estimate it as a pooled cross-section where the technology would be assumed constant across the time and same ...


1

It is not always necessarily 1/3rd. That just happens to be the outcome in the standard textbook example.


1

$W(4) = \max\left\{4+bW(4),\frac{1}{2}\left(4 - k + bW(4)\right) + \frac{1}{2}\left(16 - k + bW(16)\right)\right\}$ $W(16) = \max\left\{16+bW(16),\frac{1}{2}\left(4 - k + bW(4)\right) + \frac{1}{2}\left(16 - k + bW(16)\right)\right\} = 16+bW(16)$ First solve for $W(16)$ to get $W(16) = \frac{16}{1-b}$. Then substitute it in $W(4)$ to solve for $W(4)$ as a ...


1

This is some dynamic supply-demand model (I am not aware of it having some special name). The first equation gives you the evolution of prices. It says that there will be inflation if there is excess demand $d_t>s_t$ and deflation if there is excess supply (that’s why the first equation has ($d_t-s_t$). The second equation tells you how supply changes ...


1

It looks like a cash-accounting NPV that includes closing the position (selling the plant, the car, whatever) after the period of consideration. Asset values show up in the final term because cash accounting applies cash outlays to the period in which they actually occur. Typically, that asset value would be net of depreciation and therefore less than $I_0$. ...


1

Lots of people have good, comprehensive answers, but here’s a very short one: First, you’re assuming the firm is a price setter. In competitive markets, both producers and firms are price takers. When we draw the demand curve, we assume a consumer faces a given price; similarly, when we draw a supply curve, we assume the firm faces a given price. Second, ...


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