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2

From FOC, we know that: \begin{align} \nabla_x\pi(\mathbf{x},\mathbf{w})=p\nabla f(\mathbf{x})-\mathbf{w}=\mathbf{0} \tag{1} \end{align} This will be true at equilibrium, i.e. for any given $\mathbf{w}$, the input vector $\mathbf{x}$ will adjust so that the above holds. Now consider $d\pi(\mathbf{x},\mathbf{w})/d w_i$ (and using $(1)$): \begin{align} \frac{d\...

0

Suppose we have a function of income for a particular good, $f(x)$ for income $x$. Then its derivative is the income elasticity of the good (at a certain level of income, though for linear models it's all the same). The consumption of a normal good grows with income while the consumption of an inferior good decreases with income: we have $f'(x) > 0$ for a ...

1

The negativity of slope of the indifference curve depends on the monotonicity of utility function and non-satiation, not on whether the goods are inferior or normal goods. Inferior goods are goods which are consumed less when income increases but that is not the same as saying that the utility is not monotonically increasing in both goods or that non-...

1

Mortgage rate data: FRED page. The mortgage rate did move at various points in 2008, so the premise that they did not change appears incorrect. However, I can answer how they are priced. The easiest way to view mortgage rates is that they track the rates of mortgages traded in mortgage-backed securities. The fair value of their yields depend on the riskiness ...

3

Excellent question (I am assuming your intended question is "does positive returns to scale always leads to economies of scale"): The two concepts are related but Returns to scale (RS) is much restrictive than the Economies of scale (ES). The concept of RS is embedded in production function. If $Q=F(K,L)$ then it positive returns to scale simple ...

0

The given indifference curve formula can be written $Q_C=\frac{\alpha}{Q_B}$ where $Q_C$ is quantity of cheese and $Q_B$ is quantity of bread. Rearranging as $Q_CQ_B=\alpha$, this suggests that the indifference curve is derived from the utility function: $$U(Q_C,Q_B)= Q_CQ_B$$ Alpha appears to be just a particular value of $U$ defining the particular ...

3

I have quickly skimmed the chapter and there does not seem to be much about bargaining models so as the question says you have to solve this using supply and demand. We know that an equilibrium price on the market will occur when supply intersect demand. Given that the supply is fixed at $24$ and $25$ apartments respectively it will be just straight vertical ...

2

Because you are talking about constraints, it appears you do not consider the case of inserting such "access costs" (because this is what they are) in the utility function. It implies that they do not create disutility directly, only direct or indirect monetary costs. Let $d$ be the distance in some units. Let $C_d = c_dd$ be a linear (for ...

2

There are a bunch of examples for incomplete markets in the finance literature. The oldest (that I know of) is Hart (1975). In finance, the problem is that if you have two different assets they have different prices that make the market complete. But then equilibrium considerations make them have the same price, which forces the market to no longer be ...

3

I think you wanted to ask "Do returns of big scale always imply economies of scale?" The answer is no. Diseconomies of scale exist too. You can get big, get economies of scale, then get even bigger and get diseconomies of scale. It's a reason why even most profitable corporations don't grow like cancer, without bounds.

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There are "missing markets" such as in the case of pollution. We can try to create a price by charging fines against polluters, but no natural price exists.

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The minimization problem $$\min_{w(\cdot)} \int^{\pi_{max}}_{\pi_{min}}w(\pi)f(\pi|e)d\pi$$ s.t $$\int^{\pi_{max}}_{\pi_{min}}v(w(\pi))f(\pi|e)d\pi-g(e) = \bar{u},$$ is evidently an infinite dimensional optimization problem. The FOC, a la Lagrange, comes from standard consideration for such problems. To make this more explicit, define the objective and ...

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The answer by user Herr K. is very sensible and in fact is what MWG p. 481 footnote 6 suggest to do in order to obtain the f.o.c. But this approach begs the question: Then why on earth did we use the integrals in the first place, only to abandon them for the discrete formulation? If our problem is formulated in terms of continuous profits, then profits are a ...

7

For taking a derivative under the integral, I find it helpful to consider the discrete analog, i.e. taking a derivative under summation. Instead of having $\pi\in[\pi_{min},\pi_{max}]$, suppose $\pi$ takes value from a discrete set $\{\pi_1,\pi_2,\dots,\pi_n\}$. Then the problem becomes \min_{w(\pi_i)}\sum_{i=1}^nw(\pi_i)f(\pi_i|e)\quad\text{...

1

The way how they estimated elasticity is definitely not an accurate and unbiased way. You are correct that when you estimate elasticity it is important to control for income, but not only for that you should also have controls for prices of competing products and other relevant controls. Supply-Demand is an endogenous system and every observed price and ...

0

In a dual model, if one of than is a neutral, your utility function is variable only in terms of the good X. A preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption, i.e., a quasilinear relation only exists if the function has two terms (a numeraire and a second ...

2

...the controls in my IV model are correlated with my instrument? The controls should be in your model precisely because they are correlated with your instrument. In the exogeneity condition $cov(z, \epsilon) = 0$ for the instrument, $\epsilon$ is the error term after controlling for other variables. This condition may not hold without controls. Consider ...

2

This would not make instrument necessarily invalid. For some 2SLS instrument model of form: $$y_i = \beta_0 + \beta_1 \hat{x_i} + \beta_2 k_i +\epsilon_i$$ $$x_i = \pi_0 + \pi_1 z_i + \pi_2 k_i +e_i$$ where $y$ is dependent variable, $x_i$ is the endogenous regressor, $k$ some controls and $z$ instrument the main conditions for instrument validity are: $z$...

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The paper Optimum consumption and portfolio rules in a continuous-time model (Merton (1971)) presents (as far as I know, the initial presentation. [ Next we turn to a paper that discusses the importance of the HARA utility. The Fundamental Nature of HARA Utility (Perets and Yashiv (2013)) Many models in Economics assume a utility function belonging to the ...

3

A priori this is difficult to say without any empirical experiment but it is unlikely due to: Price floors do not necessarily lead to more competition on quality. Theoretical models do show that price floors can (depending on parameters) lead to an increase in quality (Bilotkach, 2012 and sources cited therein), but they can also just result in intensifying ...

2

Normally in order to full dollarization to occur there will be some conversion rate at which debt denominated in old currency is converted into new one. For example, according to the World Bank definition of full dollarization: All government and private debt under full dollarization is denominated in dollars, and both public and private accounts must be ...

1

I don't think it is appropriate to apply the such static visualization to dynamic problem. Let us for a second forget about the graph - the graph is just a visualization of the indifference curve. If two things are perfect complements which are consumed in 1:1 ratio their utility is given as: $$u(x, y) = \min \{x, y\}$$ In this case (before you break the arm)...

7

If in equilibrium, a player "chooses a mixed strategy" that plays $H$ and $T$ with positive probability, $H$, and $T$ must be both optimal choices. It is a standard result that for a (subjective or objective) expected utility maximizer, randomizing can only be optimal if it is over pure optimal choices. This is a direct consequence of expected ...

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The real-life question is "how do you persuade people to use mixed strategies"? To stick with your example, Consider a person that has to make a binary choice $(H, T)$, and, after contemplation, they conclude that the optimal strategy is the mixed strategy $(2/3, 1/3)$. I have never know of anyone putting two red and one blue ball in a vase and ...

2

If it is a lexicographic preference on $R^2$, the question sounds weird and I don't know if it can be represented by a utility function from $N^2$ to $R$. The domain of the utility should be the same as the domain of the preference relation, otherwise they cannot represent each other for sure. Now suppose that, you mean, we have a preference on $R^2$, but we ...

0

Here's a paper link where they picked up a $R^2$ of over .99 I don't think this is particularly unusual or strange of a result, either. In estimating costs for firms in public utilities, I recall doing numerous exercises with real data from various utilities. I typically got $R^2$'s in the 0.95's or higher, so I feel they are fairly accurate within sample. ...

1

Typically, we have concave, increasing utility functions. So that means, the more you consume of a good x the more utility you have. However, the marginal utility (the first derivative of the utility function) is decreasing in consumption. So each additional unit of consumption has less additional value than the one before. A simple example would be food. If ...

1

In micro-econometric work, prices may or may not be part of TFP. The literature recognizes two versions: TFPQ (Quantity-based) TFPR (Revenue-based) Clearly, TFPR must include prices (Revenue = quantity*prices). Many scholars argue that TFPQ is the purer and most correct measure of TFP. In the sense that higher productivity means producing more output (...

1

No actually by default when you use Cobb-Douglas function the output is not even measured in monetary units but rather as output per unit of time. This output per time can be still called income without assigning it any 'monetary' value. For example, in Robinson Crusoe economy if you catch 5 fish then those 5 fish are your income from economic perspective. ...

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Yes, a trivial example is the following utility: $$u(x,y) = x+ \sqrt{y}$$ which is both quasi linear and monotonic.

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Your intuition is correct. First, you're right that "marginal cost only depends on variable cost", since $$MC(q)=\frac{\mathrm dTC(q)}{\mathrm dq}=\frac{\mathrm d(FC+VC(q))}{\mathrm dq}=\frac{\mathrm dVC(q)}{\mathrm dq}.$$ Next, if marginal cost is some constant $k$, then variable cost must be $VC(q)=kq$, because we can ...

0

To understand inflation or deflation you need a financial model like this for each economic unit: NW = K + FA - L Net worth equals the valuation of non-financial assets K plus financial assets FA minus liabilities L. Next you need a model for direct lending by wealthy households to the working class households and/or a model for wealthy households lending to ...

0

The weak point of your logic is basing it on what happens to a \$20 bill. You can destroy such a bill, or the government can print such a bill, and it seems exceedingly likely that nothing measurable would happen to the aggregate economy. If we cannot measure the difference, we cannot say anything happened. (One can put forward theories about effects, but ... 7 If you start out with €0, then the certainty equivalent of losing €2.5 with probability 1 is -€2.5. Your exercise basically asks you to calculate what difference winning the lottery with a small probability makes. Given this utility function, not much. 4 You have to make distinction between short-run and long-run. Short-run: In short-run money is not neutral, meaning that in short-run money and other nominal variables can affect real output. A one example why this is true are sticky wages. In presence of sticky wages wages (for example due to nominal contracts that take time to renegotiate) a fall in money ... 0 Let's assume familiarity with the S&D model's components for now. Imagine a seller comes to the market anticipating price A. (Their anticipation is wrong, the real price is equilibrium, found by the vertical height where S&D meet.) They pay workers overtime, hire a few extra workers to produce F units, and this drives their costs up. When they ... 1 the practices of assigning salaries and bonuses, etc, would be difficult to adjust in the short term (i.e. more inelastic), so they'd tend to stay the same, This might be true empirically (I am not an expert on CEO compensation), but if you are doing a test you have to follow assumptions in exercise (which will not always be realistic - undergraduate ... 2 What is the proof of this formula? There is actually no proof for what the production function should be. There are infinite many possible production functions and to discover which one is the most appropriate we need to make some empirical observations. In different cases different production functions are appropriate. Cobb-Douglas is popular production ... 0 The advantage of having monopsony power is that producers can decrease the wage when they want to cut down their employment, due to some negative demand shocks or technological shocks. In the perfect-competitive market, the producers cannot cut wage as otherwise they would loose all their employment. The disadvantage of having monopsony power is, as you said,... 1 I haven't gone through all the papers so I just sampled 'The Firm as an Incentive System'. Browsing through it, it relies on Linear Algebra and Real Analysis. Again, I warn that I have not gone through the entire paper but seeing some of the terminology used there, I could guess that these two a clearly involved (maybe they use some bit of topology as well). ... 2 You can definitely do so! There are two versions of the income effect. The one that you are referring to is called the Equivalent variation. The two ways of looking at the problem were introduced by Sir John Richard Hicks. To see the impact of a price change in monetary terms, we ask how much money should have been taken before the price change to leave a ... 4 As is clear from the answer of VARulle, complete information is of no use. Every (finite) game in normal-form is the normal form of an extensive form game of complete information. The situation is different for games of perfect information, and one can prove a result to the effect that "Almost all finite games of perfect information have equilibria that ... 0 When the supply fully meets demand, there is no deficit of goods and price depicts Cost+General markup in the market. So the price is equal and fair for all participants of the market. When supply is greater than demand, there are too many goods, so the price has to go down for you to sell goods and as a supplier you need to sacrifice either cost(quality) or ... 5 This statement is wrong. Consider Alternating Matching Pennies with imperfect information (the follower doesn't observe the leader's move). The strategic form of this game is just the classical (simultaneous-move) Matching Pennies Game and the unique NE has both players mixing. 0 The area from$(0, 0)$to$(5, 5)$would be just like any other two-good indifference curve. Then since the area$\{(x, y): x \geq 5, y \geq 5\}$has the same utility, they're all on the same "indifference curve" (so that's more like an "indifference area"). Not sure what the indifference curves would look like, say, at$(80, 2)\$ though ...

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This is an example of a satiation point or bliss point. Basically you want a particular point and getting further away from this point decreases your utility. The indifference curves look like concentric circles around a specific point, in your case (5,5) is the bliss point.

0

This four page reference shows how producer surplus is defined and calculated using integral calculus: https://www.math.ubc.ca/~malabika/teaching/ubc/spring11/math105/surplus.pdf As quantity increases from q = 0 to q = qe (equilibrium quantity) the price rises at each point on the supply curve S(q). The equilibrium point (pe, qe) is taken independently by ...

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