# Tag Info

32

Is it simply for saving warehouse costs? Probably yes, holding onto inventory is very expensive. You have to pay for warehousing of the good, it takes the spot of some other inventory that might be in high demand. Food is also perishable so it cannot be stored indefinitely. Stores have to always guess what demand for their products will be, sometimes they ...

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It's not about saving warehousing cost. They can't sell 12 months old Christmas chocolate next year, so they have to sell it in the next few months. Their options are to either sell it to customers, sell it to a business, or pay to throw it away. The price indicates that they think selling it very cheaply to customers is the most profitable option, all ...

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Since the exponents add to one the production function has constant returns to scale, which means that, given factor prices, total cost is linear, which means that it's derivative (= marginal cost) is contant. If you change the exponent 1-alpha to beta where alpha+beta < 1, there will be decreasing returns to scale (but still homotheticity) and you will ...

7

Let $z_1$ and $z_2$ be $\geq 0$ and solution to $$\min_z \{w^\top z\lvert f(z)\geq q\}$$ then clearly $f(z_1)\geq q$ and $f(z_2)\geq q$ and since $\{z\geq 0\lvert f(z)\geq z \}$ is convex it then follows that $z_3 := \lambda z_1 + (1-\lambda)z_2$ must satisfy the constraint $f(z_3)\geq q$. Since $z_1$ and $z_2$ are both minimizers it cannot be the case that $... 7 Imagine that you are a dictator in Sausageland. Your legitimicay depends on you delevering sausages to the inhabitants. Each inhabitant must be given 1 sausage and there are$y$inhabitants. To produce sausages you command two factories: One factory produces$x_1$vegan sausages using$x_1$cabbage heads the other factory produces$x_2$pork sausages using$...

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One usually rules this out by assumption, as Mas-Colell, Whinston, and Green do in their textbook (). The goal is often to try to characterize preferences that guarantee (at least for finite choice sets) the existence of choices from a revealed preference point of view. There is also the methodological point that if you confront a decision-maker with a ...

6

The utility function under consideration is $v(c,q)$ and then $$MRS(c,q) = \frac{\partial v/\partial q}{\partial v/\partial c} = v_2/v_1$$ make the functional denpendency of on $u$ explicit then you have $$\frac{\partial}{\partial u}MRS(c(u),q(u)) = \frac{\partial MRS(c(u),q(u))}{\partial c} \frac{\partial c(u)}{\partial u} + \frac{\partial MRS(c(u),q(u))}{\... 5 If you are interested in the case where \rho \geq 1 then look at the post CES \ \ \rho \geq 1. For the standard case where 0 < \rho < 1 you should get a result like this$$C(w_1,w_2,y) = \left(w_1^{\frac{\rho}{\rho -1}} +w_2^{\frac{\rho}{\rho -1}}\right)^{\frac{\rho - 1}{\rho}} y.$$To see this you should start by setting up the cost ... 4 Pareto optimality requires that, after the agents trade once to a new allocation on the contract curve (set of Pareto optimal points), they each maintain at least the same utility they had prior to the trade, there are no potential "next" trades that make either agent better off, and there is no wastage in the economy (all goods are consumed). None ... 4 It's a matter of choice how one writes the Lagrangian in the context of Lagrange/KKT. Depending on how it's written, the gradients of the objective and constraint functions are either parallel or anti-parallel at a (suitable) optimum, and the Lagrange multiplier is neither negative or positive. At the end of the day, it is the same (subset of) optima that ... 3 There is indeed and it is called a bid function. Consider a standard set up where preferences of the agent are given by the utility function$$u(c,h) = \bar u$$with c being a composite good and where the budget constraint is given as$$c + ph = I.$$In this case the price p must satisfy$$p = \frac{I-c}{h}$$and the maximal price \phi(\bar u,I) that ... 3 This problem is most easily solved using iso-cost lines and production level curves. Consider the (x_1,x_2)-plane and the line defined by$$y = x_1 + x_2 \Leftrightarrow x_2 = y - x_1$$which is a line cutting x_2-axis in y and having a slope of -1 as shown here Consider now isocost-lines given by w_1x_1 + w_2x_2 = c such that x_2 = \frac{c}{w_2} ... 3 So we have$$S^A = I^A + NX^A S^B = I^B + NX^B $$where S^A and S^B are exogenous constants. And since there are only two countries we have$$NX^A = -NX^B $$which leads to$$S^A - I^A = -( S^B - I^B ) $$Use that last equation to solve for r (after plugging in the I formulas). Then solve the first equation and require that NX^A be positive. 3 There can't be an equilibrium in which no one tells the police. In that case, it is a profitable deviation to tell since v-c>0. There can't be an equilibrium in which more than one player tells the police. In that case, it is a profitable deviation for one of them to remain silent since v>v-c. There are five pure strategy Nash equilibria in which ... 3 As I said in the comment, Nash's theorem shows the existence of a Nash equilibrium (possibly but not necessarily in mixed strategies). If you are interested in Nash equilibria is proper mixed strategies, i.e., NE in which all players play at least two actions with positive probability, you can easily show the following impossibility result: No such NE can ... 3 When integrals look different than what pops into your head, often the reason is integration by parts. For your example note that$$\int_R^1 (\theta -R) g(\theta) d \theta + \int_R^1 G(\theta) d \theta = (1-R) - 0,$$where the right-hand side is equivalent to \int^1_R 1 d\theta. Hence, the two expressions you consider are equivalent. It's of the form$$\...

2

There are two goods and two consumers, no production. The aggregate endowment is strictly positive. Consumer 1 cares only about the amount of good 1 they consume, with more being better. Similarly for consumer 2 and good 2. Preferences here are continuous and monotone but not strictly monotone. The allocation in which consumer 1 consumes the entire aggregate ...

2

Set of Pareto efficient allocations is given by the dashed line in the Edgeworth Box. It is the set of feasible allocations satisfying $y_1 = x_1$ and $x_1y_1 \geq 9$ .

2

For starters, elasticity is the percentage change in quantity (demanded or supplied, depending on what we're looking at) due to a one percent change in price. Or more vaguely: elasticity measures the sensitivity to price of behavior. From this definition it is clear that stating that a 'price is elastic' is nonsense. Trivially, the elasticity of price with ...

2

While it's not explicitly mentioned in the question, it seems safe to assume that the manager gets to observe separately the outcome of each worker, i.e. the value of $v_i$ for $i=1,2$. If this is the case, the IR and IC conditions depend on the exact terms of the contract. For example, suppose the manager conditions each worker $i$'s wage on both $v_i$ and $... 2 First of all good question. I tried myself on that one, but if any other member of this wonderful site has additional input please also answer :) In a monopol we know there exists a consumer who would be willing to pay a price for an additional unit of the good that is higher than the additional cost to produce that unit. Possibility of Pareto improvement: ... 2 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. 2 Consider the utility function$u(x, y)= -|x-5|-|y-5|$. Indifference map for$u$is as follows : 2 To solve for competitive equilibrium, we can first find the demand : Demand for commodity$X$by A is$x_A = \frac{5}{p_x}$if$p_x < 1$,$x_A \in [0,5]$if$p_x = 1$,$x_A = 0$otherwise. Demand for commodity$X$by B is$x_B = \frac{(30p_x+5)}{2p_x}$. Now we can equate demand and supply and solve for$p_x$.$x_A + x_B = 30$yields$p_x = \frac{1}{2}$. 1 Expenditures on good$2$are, indeed, included and can vary. We know from Shephard's lemma that whenever the marginal change in expenditure for good$1$with respect to its price varies with the price of good$1$, the Hicksian demand for good$1$must vary too. But since utility is fixed, changes in the Hicksian demand for good$1$require changes in the ... 1 Core Allocations are Pareto efficient allocations that must satisfy individual rationality i.e. these allocations must yield at least as much satisfaction to the individuals as their respective endowments. In the given question, core allocations are represented by line connecting$(e/2, e/2)$to$(e,e)$. Dashed line on the left graph is representing the set ... 1 These are some good introductory resources that I have found helpful: https://mru.org/principles-economics-microeconomics https://app.senecalearning.com/dashboard/courses/add?text=economics I really encourage you to attempt the questions as it will help you understand and apply the theories 1 In a perfectly competitive markets for factors of production the marginal productivity of factors is equal to price of factor, which in turn decides the cost of production. For example, consider two factor production function$Y=F(K,L)$. At equilibrium, under assumption of perfect competition in market for both factors,$F_K = r$and$F_L = w$, where$F_K, ...

1

Assume the following profit function: $\pi = pY - wL -rK$ and a two factor economy $Y(L,K)$. Optimal labour and capital inputs for the firm can be found by taking the respective derivatives and setting them to zero: $\frac{\delta \pi}{\delta L} = p \frac{\delta Y}{\delta L} -w = 0 \iff \; \frac{\delta Y}{\delta L} = \frac{w}{p}$ \$\frac{\delta \pi}{\delta K}...

1

But my question is, will the slope of the demand curve change as it moves leftward? The slope does not change because one assumes that relative prices and consumer preferences do not change. This is a ceteris paribus interpreation you want to see what happens when new competitiors enter the market (keeping everything else as it is). There are the same ...

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