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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 ...


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 ...


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 ...


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 $\...


0

Probably just an issue with the phrasing of the problem you're tackling. I'd assume they just want you be using the Slutsky equation for own-price changes, so you should be good just differentiating what you derived with respect to px and then carrying on with the income effect.


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Let us assume all these functions exist and are differentiable. Furthermore let us denote the inverse of the function $\overline u^1(x_1)$ by $x_1\left(\overline u^1\right)$. Note that for any invertible function $f$ we have $$ \left.\frac{\text{d} f(x)}{\text{d} x}\right|_{x=x_0} = \frac{1}{\left.\frac{\text{d} f^{-1}(y)}{\text{d} y}\right|_{y=f(x_0)}}. $$...


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(...


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 ...


0

$$u(x, y) = 2$$ is a simple example of a continuous utility function with thick indifference curve. \begin{eqnarray*} u(x, y)= \begin{cases} x & x < 1 \\ 1 & 1 \leq x < 2 \\ x - 1 & x \geq 2 \end{cases} \end{eqnarray*} is another continuous utility function with thick indifference curve for $u=1$.


1

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


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I think what it’s referring to optimal $y$ (i.e. what would be normally in calculus denoted as $y^*$- but you already use that for the initial stock). It makes sense that to maximize the utility MRS should be equal to marginal productivity since MRS should be equal to ratio of prices and in case like this where the person produces goods for themselves the ...


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 ...


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 ...


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 $I_0$. ...


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This doesn’t make sense, because Free Cash Flow (in each period) already takes changes in assets and liabilities into consideration.


-1

Well, I'm not sure the claim "raise M by factor k and P will also rise by factor k" is valid unless one also stipulates that V and Y are held fixed. Indeed, interest rate policy relies on the assumption that movements in key interest rates will shift Y more than they do P, with some of that action arising from a shift in V. A two-good pure-exchange model (...


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 ...


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Why are we decomposing the effect of a change in price of one commodity into all these effects which are (as I have understood), all hypothetical. They're hypothetical, but they are nevertheless meaningful. We can easily imagine what it would be like if an agent had a larger budget while prices remain unchanged; we can also imagine what it would be like if,...


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 ...


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 ...


-1

The seller's idea is different from the buyer's. The seller wants to make money, so the seller can't ignore the cost. The buyer does not know the cost of shoes, so the evaluation may not be accurate, and the seller will use various means (such as advertising, preferential, packaging, etc.) to interfere with the buyer's judgment, making its evaluation higher ...


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, ...


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 ...


0

Each point is the summation of all individual demands of all consumers in the market at that price. Suppose you only have two consumers, A and B. At price $1, A demands 2 units and B demands 3 units. For the market demand curve at price $1 you would have quantity demanded 5 units. (2 + 3 as there are only two consumers in the market). So the market ...


0

Well this all boils down to the economic reason why cities exists at all. The economic reasons for cities to exist are: Division of labor - as was famously observed by Adam Smith “It is the great multiplication of the productions of all the different arts, in consequence of the division of labour, which occasions, in a well-governed society, that universal ...


0

The demand curve is: $$p = 60 - 0.002q$$ Marginal cost ($C'(q)$) is a constant 10 dollars and fixed costs ($k$) are 300,000 dollars. Hence, $$C(q) = \int_{0}^{q} 10 \ \mathrm{d}x + k = 10q + k$$ where $k = 300000$. Thus, $$C(q) = 10q + 300000$$ The monopolist’s problem is $$\max_{q} π = pq - C(q)$$ In this case, that is: $$\max_{q} q(60 - 0.002q) -...


1

Let demand elasticity be $\varepsilon$. Then $$\varepsilon = (\frac{p}{D(p)})\frac{\mathrm{d}D(p)}{\mathrm{d}p} \ \ \text{(1)}$$ For a perfectly elastic demand curve, $\frac{\mathrm{d}D(p)}{\mathrm{d}p} = - \infty$. Why? $$\frac{\mathrm{d}D(p)}{\mathrm{d}p} = \lim_{\Delta p \to 0} \frac{D(p + \Delta p) - D(p)}{\Delta p}$$ Now, $D(p + \Delta p) = 0 \ \...


1

Others have provided intuitive explanations; I thought I’d provide a short mathematical one. Suppose a firm faces a production function $q = f(K,L)$. Assume $f_K, f_L > 0$ and $f_{KK}, f_{LL} < 0$. (The former is entailed by the assumption that firms wouldn't invest in capital or labor if it wasn't increasing their gains, while the latter is the law ...


0

I'm just gonna try doing it. The problem is: $$\text{min } C = rK + wL \\ \text{s.t. } q = K + \ln(L) $$ The implied constraint, of course, is $L \in [1, \infty)$ (non-negativity constraint, as $q > 0$, and $K = 0$ is, of course, possible). We can try solving this using Lagrange multipliers. Define the Lagrangian: $$\mathcal{L} = (rK + wL) + \lambda(q ...


2

It seems to me that the topic is related to rational addiction: Individual preferences for consuming $x_t$ are conditioned by their past consumption $x_{t-1}$. See for instance: Becker, G., and Murphy, K. (1988). A Theory of Rational Addiction. Journal of Political Economy, 96(4), 675-700.


0

If it’s a “market demand curve,” that means the quantity demanded is that of the entire market. If it’s an “individual demand curve,” it’s the quantity demanded of an individual consumer. If you open an Econ 101 textbook and look at the supply–demand equilibrium diagram, they’re generally talking about market demand and supply curves.


0

I’m guessing what this means is that if $C$ is the cost function and $x$ represents the number of units of a good produced, marginal cost at production level $x_0$ is not the cost of producing the $(x_0)$th unit. And, importantly, if goods are not sold in discrete amounts, it’s not quite the cost of producing the next “unit” either. If the good is produced ...


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