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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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Is the definition of Investment variable in Economics?

I studied that Investment is the expenditure incurred on the procurement of such goods that would help us in production of goods and services. And mainly consists of Fixed and Inventory Investment ...
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31 views

Finding individual utility

There are N agents living in an economy with two goods, $X$ and $Y$. Their preferences are described by the following utility function $u(X,Y) = 2 \sqrt{XY}$. Each agent is endowed with 1 unit of $X$ ...
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Pareto Optimality of Endowments

Consider a $2*2$ exchange economy where individual $1$ has an endowment $(4,5)$ and individual 2 has an endowment $(6,5)$. The utility functions of individuals are represented by $U({x}_i{y}_i)$=${x}...
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Blocking Coalitions

For $n$ individuals, can a blocking coalition only be formed by at least $n/2$ individuals? For example, if there are 6 individuals, can less than 3 individuals form blocking coalitions?
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Three consumers three goods competitive equilibrium

I have the economy described by the three consumers above with their respective preferences and endowments. I'm not so sure about how to proceed towards the competitive equilibrium...
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2answers
63 views

Linking top-down and bottom-up models for analyzing electricity price-based demand response: Expenditure constraint is violated?

I have a question about the contents of this paper*, which links a building energy model and a utility-maximization component. In it, the author tests several electricity prices using a Cobb-Douglas ...
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2answers
296 views

Strongly and strictly increasing utility functions

What's the difference between Strongly and strictly increasing utility functions? What I know is that if $x'>>x $ where $x'$ has all elements strictly greater than $x$ then $U(x')>U(x)$, I ...
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1answer
35 views

Necessary conditions for the existence of a competitive equilibirum

I got that in an exchange economy, conditions as preferences being continuous, strictly convex and strongly monotone and $\sum_i \omega_i\gg 0$ are sufficient conditions for the existence of a ...
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30 views

Competitive Market - Production & Number of Firms

The question is as follows: The inverse market demand for provision of gas services is given by p(y) = 1/(1+y), where p is the unit price and y measures output in appropriately scaled units. Suppose ...
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1answer
40 views

What is the difference between solving for utility maximization separately or aggregately?

I derived the Walrasian equilibrium for an economy of two consumers with their respective utility functions (u1, u2) and initial endowments but later on I am asked to maximize (u1+u2). Does anyone ...
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91 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
36 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
50 views

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
37 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
60 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
975 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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36 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
36 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
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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
61 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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2answers
148 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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1answer
534 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
56 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
78 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
140 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
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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
115 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
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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
41 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
32 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
39 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
27 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
74 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
71 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
167 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
77 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
796 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
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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
617 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
641 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
68 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
123 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
168 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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162 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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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
87 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
121 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
182 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
36 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
49 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 ...