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Questions tagged [microeconomics]

Microeconomics is a branch of economics that studies the market behavior of individual actors (usually firms and consumers) and the aggregation of their actions in different institutional frameworks (usually the market).

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Some manipulations of the cost and factor demand functions

I am trying to understand a few manipulations of the conditional factor demand $z(w,q)$ and cost function $c(w,q)$, were $w$ are input prices and $q$ is a given quantity (the reference is Mas-Colell, ...
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1answer
185 views

Difference between Giffen and inferior goods. Why aren't all inferior goods Giffen goods?

What is the difference between an inferior good and a Giffen good? Are the two following definitions for an inferior good equivalent? Def 1: An inferior good is a good for which the demand decreases ...
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1answer
55 views

Does Preference have a Hierarchy? A Silly Question

I have what is probably a very silly question, but I have gone down the rabbit hole and can’t get back out..... Is there is a hierarchy of preference, and within each level of choice do we reset the ...
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1answer
73 views

Why does a homothetic function have constant ratio of marginal products along rays?

A homothetic ordering is defined as $x \succeq y \Rightarrow \lambda x \succeq \lambda y \qquad \forall \lambda >0$ where $x,y \in \mathbb{R}^n$ Then, any differentiable function representing ...
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4answers
83 views

Convexity of indifference curve

The convexity of an indifference curve results from the fact that the absolute value of its derivative, which is the marginal rate of substutution is decreasing. But why do we say that it's convext to ...
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2answers
76 views

Can $u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$ be solved by Kuhn–Tucker conditions?

Consider $\max_{x_1, x_2, x_3, x_4} u(x) = \sqrt{x_1 x_2} + \sqrt{x_3 x_4}$ s.t. $\; p_1x_1 + p_2x_2 + p_3x_3 + p_4x_4 \le w$ I know we can solve the max problem through separately considering ...
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1answer
109 views

Marshallian demand with Leontif preferences

Consider a utility function on the form $u(q_{1},q_{2},q_{3}) = min\{\alpha ln(q_{1}) + (1 - \alpha) ln(q_{2}), ln(q_{3})\}$ I know that optimal behaviour requires $\alpha ln (q_{1}) + (1 - \alpha) ...
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2answers
32 views

What happens in a bartering system when a resource is plentiful but cannot be paid for?

Here is a hypothetical scenario: Let's say there are two tribes which barter goods. Tribe A has an fairly large amount of fish, but no bricks. Tribe B has an extreme abundance of bricks, but no ...
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0answers
38 views

Lagrangian multiplier

Consumer's problem \begin{equation} \max \sum_{t}\beta^{t}[c_{t}-1/2(1-x_{t})^{2}], \end{equation} \begin{equation} \ s.t. c_{t}+q_{t}b_{t+1} \leq (1-\tau_{t})(1-x_{t})+b_{t}, \end{equation} where c=...
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25 views

Vertical Marginal Cost curves

When would a marginal cost curve be vertical? I understand this happens when the marginal cost jumps, from say 0 to 100, but in such a case, I think there should be a discontinuity rather than a ...
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1answer
35 views

Unrestricted domain vs complete

Arrow's impossibility theorem states that no social choice rule satisfies a certain list of desiderata. Amongst these are completeness and unrestricted domain. Could someone please explain the ...
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1answer
26 views

For a certain good, if there is a one-time fixed cost for a consumer to switch to a different firm, then this good is? [closed]

For a certain good, if there is a one-time fixed cost for a consumer to switch to a different firm in a later time, then we say this good is ____ (or has property ___). Examples include Consumer: ...
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1answer
58 views

How do I find optimal price or maximise profit in a monopolistic market?

How do I find the optimal price for a monopolist given the monopolist's cost function and market demand? I have $Profit(y) = p*y + C(y)$ where $p$ is price, $y$ is output, and $C(y)$ is total cost. ...
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1answer
55 views

Calculate optimal discount for product bundling

So recently I made some rules with my transaction data. Based on it I can determine which products are profitable to bundle it together. But even though I know e.g. product A→ product B, are there ...
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1answer
65 views

Cournot duopoly with differing costs

There are two firms in a Cournot duopoly that face inverse demand $P = \alpha - Q$, but one firm has total costs $c_1*q_1$ and the other has total costs $c_2*q_2$ with $c_1 < c_2$. I want to show ...
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1answer
72 views

Utility Function Implies Consumption of Not All Goods

Suppose we have a utility function with three inputs, $j, k,$ and $s$ described by $$u(j,k,s) = A\ln(k^\alpha + \beta j^\alpha) + B\ln(s).$$ The price of $j, k,s$ are $p_j, p_k, p_s$, respectively, ...
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1answer
422 views

Whats the difference between local non-satiation and monotonicity?

Is there a practical difference between local non-satiation and montonicity? Can one exist in a utility function without the other?
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1answer
73 views

need help from theorists: proof in Cole, Mailath, and Postlewaite (2001)

I have one question in the proof for section 4.1. in Cole, Mailath, and Postlewaite (2001). $$\lim_{\varepsilon \to 0}\frac{1}{2\varepsilon}\int_{\overline{l}-\varepsilon}^{\overline{l}+\varepsilon} ...
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1answer
384 views

Profit maximization and returns to scale relation

Suppose we have 2 inputs a and b , output is y=f(a,b). In the long run, let us suppose profits are maximized at a* and b*. Profit is py-wa-kb[p is price and w and k are constants]. Now for max profit, ...
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2answers
204 views

When demand increases why does the price decrease but equilibrium price increase?

On a demand curve when the demand increases the price will decrease. However on a demand and supply graph, when the demand shifts to the right, the price will increase. I understand why, but then what ...
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1answer
62 views

Market demand independent of distribution of income

If preferences are identical and homogeneous, then show that market demand for any good must be independent of the distribution of income. My workings are as follows: $$q^{d}(p)=\sum_{i=1}^{n}f(p_x,...
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1answer
105 views

Proof that EV = CV when there is no income effect

In every textbook it says that it is easy to see that with no income effect, the integral $\int_{p^0_1}^{p^1_1} \! h(p,u_0) \mathrm{d}p_1. = \int_{p^0_1}^{p^1_1} \! h(p,u_1) \, \mathrm{d}p_1$ Could ...
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1answer
105 views

Is there any formal definition of a relationship between resource availability and demand?

I do not have any background on economics. So my question might sound too simple and I hope it to be clear enough. I am curious about the following: Is there any formal definition of a relationship ...
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87 views

Quasi-linear Optimal Consumption Bundle

I have a question involving optimal consumption bundles for quasi-linear preferences. Utility is given by $$U(x_1,x_2) = 16\sqrt{x_1} + 2x_2$$ and $p_1 = 8, p_2 = 4, I = 30$. What I have so far ...
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1answer
158 views

Find optimal price from demand function?

I've been struggling with this for hours, trying to figure out how to solve this. "A perfectly competitive market has the marginal cost function, c (cost is C(y)=cy) and is facing the demand function:...
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1answer
84 views

Income effect $-\frac{\partial x_i}{\partial m} x_i$ or $\frac{\partial x_i}{\partial m}x_i$?

Recall that the slutsky equation is: $$\frac{\partial x_i}{\partial p_i}=\frac{\partial h_i}{\partial p_i}-\frac{\partial x_i}{\partial m}x_i$$ I know $\frac{\partial h_i}{\partial p_i}$ defined as ...
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1answer
94 views

The relationship between indirect utility and expenditure functions

I am trying to understand the fact that $e(p, v(p,y)) = y$. There is a proof in the text Advanced Microeconomic Theory (Jehle and Reny) that states the following: Because $u(·)$ is strictly ...
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1answer
127 views

Slutsky equation with marshallian demand

We have marshallian demands for goods 1 and 2: $x_1^* = \frac{I}{2p_1}$ and $x_2^* = \frac{I}{2p_2}$ where $I$ is income and $p_i$ is price. We need to solve the slutsky equation for income effect ...
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2answers
33 views

Utility function that generates a demand curve which will have an U shaped MR curve

This is based off an answer given by @Ubiquitous in here: Can marginal revenue be increasing? The solution he proposed involved a MR curve that sloped down, then up and then down. His equation for ...
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1answer
45 views

Existence of maximum utility with two bads

I am working with a consumption set $X = R_+^2$ and preferences that are complete, transitive, continuous and strongly monotonically decreasing. The economy is characterized by the presence of two ...
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1answer
69 views

Expenditure minimization with Leontief utility

I need to solve the expenditure minimization in a context where $u(x,y) = min\{x,y\}$, i.e. where utility is Leontief. The minimization problem is $$\text{min}_{x,y}\,\,p_xx+p_yy \\ \text{subject}\,...
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2answers
73 views

Does $U(x,y) = x^2 + y^2 + 2xy$ represent transitive, monotonic preferences?

I'm a monitor for a microeconomics course and a student came up with this question. That this utility function represents monotonic preferences I think it's clear. Both goods have positive and ...
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1answer
62 views

What is the concept of ordinal utility?

I have read in many books that since utility cannot be measured - so ordinal concept or comparison concept is used. If that is so, how can one define a mathematical function for utility which gives a ...
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0answers
30 views

Anscombe and Auman Expected Utility

I would like to hopefully get some insights on the Anscombe and Aumann Expected utility. I've read some proofs and understood the Expected Utility Theorem (VNM) which allows us to approach consumers ...
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2answers
76 views

Regarding the group formation in an oil-price experiment

I'd like to have your opinion on the following; Assuming that I'm doing a research on setting the optimal price for gasoline for a company and my client wants me to perform a study on​ customers' ...
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1answer
102 views

Completeness from an example

I have a set $X = \{1,2,3\}$ and a binary relation $B = \{(1,1),(1,2),(1,3),(2,3),(3,1)\}$. I am trying to understand if this relation is complete. The completeness definition I am using is if for ...
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1answer
122 views

Deriving average productivity from a CES production function

Following the work of Raurich et al. (2012) I got stuck trying to derive the average productivity starting from the following CES production function: $$Y=A\left [ \alpha K^{\frac{\sigma -1}{\sigma }}...
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2answers
59 views

Ruling out boundary solutions in Utility Maximization

Solving the basic Utility Maximization Problem, i.e. \begin{align} max_{x\geq 0} u(x) \\ s.t. \,\,\, p^Tx\leq w \end{align} we get the Kuhn-Tucker first order condition \begin{gather} \frac{\...
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0answers
32 views

Elasticity of Substitution between 2 factors, without knowing relative prices

I'm trying to figure out the elasticity of substitution between input $s$ and input $v$. I know that the marginal rate of substitution between these two inputs are $\frac{v^2}{s(v+k)}$, where $k$ is ...
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1answer
43 views

Monopsony diagram curves

Why is the marginal cost curve not the same as the supply curve? My personal explanation is that since the marginal cost curve is cost of producing each new product, the supply curve just represents ...
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0answers
17 views

Is WARP the same of consistent choice?

Is there any difference between WARP satisfaction and consistent choice? I'll explain my case better. Assume we have the consumer choosing $x_1=(2,1)$ at prices $p_1 = (1,2)$ and choosing $x_2=(1,2)$ ...
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2answers
137 views

Why can two functions represent the same preferences? [closed]

I wonder why two functions can represent the same preferences?
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1answer
44 views

Monopoly equilibrium with a completely inelastic demand [closed]

What is the impact of an inelastic demand function on a monopoly production and pricing strategy ? Theory states, that a monopoly will strive to maximize its profits, by arriving to a point where the ...
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1answer
156 views

Is this Cost function concave or convex?

Given the following cost function, where t is the quantity of some product. $$C(t) = 1/3t^3 - 7t^2 +11t + 50$$ here is a graph between $t= 0$ and $t = 25$ We are asked if this function is convex or ...
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2answers
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Solving a Cournot Equilibrium, the case of Q=q1+q2, Q(q1,q2)=q1+q2

I am struggling with the differentiating between when to use $ Q=q_1+q_2$ and $Q(q_1,q_2)=q_1+q_2$ For a 2 player cournot game, given $$ P=a-bQ, with \ MC's \ c_1 \neq c_2 $$ I find the ...
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1answer
196 views

Demand Curve Equation Explanation

I've been reading (trying to brush up on my economics knowledge) and came across the equation: $q_D = a + b(P)$. The variable $a$ is explained as "factors other than price affecting demand." I read ...
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2answers
112 views

Continuous function in microeconomics

In the following picture two preference relations are defined - Ist preference relation defines lexicographic relation. Though we know that lexicographic preferences doesn't have utility function. ...
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1answer
72 views

Slutsky Decomposition from Indirect Utility Function [closed]

Given the indirect utility function: V={M^2}/{4P1P2}, how do we establish the Slutsky Decomposition? I used Roy's Identity to get the Demand, but I'm stuck with the other components of the Slutsky ...
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2answers
89 views

Optimal basket and the maximum utility

Given two goods (where more is better), and I am consuming at a point that maximizes my utility (i.e on the budget line, with an indifference curve tangential to the budget line). When the prices of ...
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1answer
97 views

intertemporal utility maximisation

Adam's consumption period 1 and 2 are denoted by $c_1$ and $c_2$ respectively. His utility function is $U(c_1,c_2)=4c_1^{0.5} + c_2$ Ben earns an income of \$3 in period 1 and \$3 in period 2, ...