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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160 views

Assumptions for the existence of a Walrasian equilibrium

I have a problem set stating that a competitive equilibrium does exist under a series of assumptions on the economy. The question is "Show that the following six assumptions are needed for existence ...
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1answer
42 views

Sunk cost fallacy- is it a bug or a feature?

I was having a conversation with a colleague regarding sunk costs, and discussion came up that the appeal of falling for the sunk cost fallacy might be a feature rather than a flaw, as it is behavior ...
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2answers
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In perfect competition, why is there economic loss if marginal cost > marginal revenue?

Here's a graph for reference: In the left graph, I read from a book (CFA L1 notes) that At any output above the quantity where $MR = MC$, the firm will be generating losses on its marginal ...
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1answer
53 views

What is the monotone hazard rate assumption used for?

I was reading this article on advance purchase discounts and pricing in which the author uses the monotone hazard rate assumption. Why does the author use it? The article is Advance-purchase ...
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1answer
81 views

Is Marginal Revenue not always equal to the price?

Marginal Revenue is equal to the price in perfect competition, but MR is also defined as the revenue obtained by selling one extra unit of the good, so how is it not always the case that MR=P ? ...
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1answer
2k views

Income and substitution effect for perfect substitutes

I was recently asked about what the income and substitution effects are for perfect substitutes are. Given the rather peicewise nature of the demands for each good in a utility function considering ...
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1answer
80 views

Find a subgame perfect equilibrium and a Nash equilibrium

I want to know if my thinking is correct. Look at the following game. As the game has only one subgame (i.e., the game itself) then the Nash Equilibria will coincide with the subgame perfect ...
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1answer
49 views

How to show average cost is falling if we have IRTS

Using maths how could I show this, I am able to show that AC>MC By differentiating AC with respect to q and assuming AC is falling , but how do show its falling in the first place if we have ...
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1answer
155 views

Maximizing a Cobb-Douglas Function

Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm ...
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1answer
73 views

Is it right to derive social marginal benefit by adding individual prices instead of quantities?

I come across a lecture material on market functions and externalities that makes me quite confused. Here's the setup: Two stores are located next to each other. If one installs a camera system in ...
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1answer
264 views

How can perfectly competitive firms earn zero profits?

Consider a firm that chooses the quantity of labour $L$ to hire which maximises its profits. As usual, we suppose that output $Y$ is increasing in $L$ but at a strictly decreasing rate; and for ...
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1k 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
69 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
105 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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5answers
346 views

Convexity of indifference curve

The convexity of an indifference curve results from the fact that the absolute value of its (negative) derivative, which is the marginal rate of substitution is decreasing. But why do we say that it's ...
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1answer
102 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
127 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
74 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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48 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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0answers
41 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
51 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
29 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
114 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
85 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
426 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
91 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
1k 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
79 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
1k 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
2k 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
70 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
161 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
530 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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250 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
917 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
100 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
145 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
234 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
48 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
55 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
225 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
98 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
184 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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41 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
91 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
157 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
198 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
135 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
35 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
80 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 ...