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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25 views

Can the indifference curve (set) not be a curve at all?

Does the indifference set have to be in the form of a curve, or of a form that is well-known? If it is not necessary to be a curve, how would the set look like? Can I get some examples? If we follow ...
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Why do we call certain linear (affine) demand curves “elastic” or “inelastic” even though PED varies along the slope of an affine function?

I get that PED varies along linear (strictly speaking, affine) demand curves in a way that for a demand function $Q(P)=\alpha - \beta P$: $$|\epsilon_D|=1 \iff \frac{\alpha}{2\beta}=P \land |\...
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How to calculate expected payment and revenue for a given bidder

I am studying for my exam in MicroEconomoics 2 which involves auctions. Consider the down below assignment: Then I have to say what a bidder $i$'s expected payment is given his valuation $v_i$ but ...
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GE with an intermediate good

intro I'm looking at a simple model with 1 consumer, 2 goods and 2 firms. I'm trying to get a price vector [p0, p1] that makes it work. By makes it work, I mean, ...
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58 views

Literature recommendation

Classic economic theory suggests people earn wages according to their productivity. Over time CEO's, directors, managers and the like seem to earn more relative to the 'normal worker'. Lets call this ...
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Understanding an article in the BMJ about the sugar tax

The research paper Changes in soft drinks purchased by British households associated with the UK soft drinks industry levy: controlled interrupted time series analysis was examining the impact of the ...
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18 views

Finding the pigou tax that supports a pareto efficient allocation as walrasian equilibrium

I have a two consumer economy with utility functions $u_1=x_{12}-x_{21}$ and $u_2=x_{21}x_{22}$. I am asked to find the Pigou tax $t>0$ on agent 2's consumption of good 1, such that the allocation $...
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3answers
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Finding the set of pareto efficient allocations with externalities

I have a two-agent exchange economy where utility functions are given by: $u_{1}=x_{12}-x_{21}$ and $u_2=x_{21}x_{22}$. I am looking to find the set of pareto efficient allocations. Since utility ...
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19 views

Static Bertrand duopoly with incomplete information [closed]

Does anyone know why in a static Bertrand duopoly with incomplete information in costs and heterogeneous goods the perfectly informed firm (i.e, knows its costs and the rivals') has always less ...
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0answers
18 views

Effect of change in endowments on prices in Walrasian equilibria

I have a two-good, two-consumer exchange economy. $(\omega_{i1}, \omega_{i2})\in \mathbb{R}_{+}^2$ denote consumer $i$'s endowments of commodities 1 and 2 for $i\in\{1,2\}$. Utility functions are ...
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2answers
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Proving local non-satiation in arbitrary metric space

I have a pure exchange economy where every consumption set $X_i$ is non-empty and convex and every preference relation $\succeq_{i}$ is strictly convex. I am asked to show that preferences are locally ...
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Optimal fee decisions in a Two-Part Tariff with resale and third-degree price discrimination

Say I have two customers - one is a low type and one is a high type (don't worry about their demand functions but assume they are linear). In the original case, we can differentiate consumers (i.e we ...
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1answer
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Finding the cost-minimising production allocation in a Cournot merger with symmetric costs

Suppose I have 3 firms in a market. They have an identical, convex cost function, $C(q) = 20q + q^2$ = $C_1 = C_2 = C_3$, and each firm produces in their own factory. Market demand is linear, $P=200-Q$...
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1answer
34 views

Marginal Productivity Theory - Clarks and Marshall-Hicks

I am referring to the HL Ahuja Microeconomics book and here is what I have understood - Clarks Version : Wage = Marginal Product of Labour ( w = MP(L) ) Marshall Hicks Version: Wage = Value of ...
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Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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How are weak preferences different to strict preferences/indifference?

Given a utility function $u(\cdot)$ and two bundles $x$ and $y$. Assuming $u(x)=u(y)$. I am to prove or disprove that $x \succcurlyeq y$. Now I'm confused by this. We say $x$ is strictly preferred to $...
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Is the pooling equilibrium profit maximising for the firm?

Is the pooling equilibrium profit maximising for the firm? I understand that when there are no ways for the firm to distinguish among highly productive and low productive worker the best the firm can ...
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Is the book by Nicholson and Snyder more rigorous when compared to Varian's Intermediate Microeconomics?

I am about to start learning college level Economics and the two books that are commonly used are Intermediate Microeconomics by Hal Varian and Microeconomic Theory: Basic Principles and Extensions by ...
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Information economics

We are in an Insurance Adverse Selection. Assume that consumers differ in their own risk $\pi_i$ distributed on the interval $[\underline \pi, \bar\pi ]=[0, 0.5] $. CDF is as follows $F(\pi)= 2\pi^2 + ...
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2answers
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Learning Economics in Three Dimensions

I am trying to teach myself microeconomics via video series. I have a fairly good mathematics foundation, currently studying Partial Differential Equations and having gone through all the prereqs you ...
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Demand function for substitutes

I have a problem where my answer does not seem to be right anywhere. For the following set up: Budget constraint: $400=40x+20y$ Utility function: $u(x,y)=3x+y$ the problems asks to derive the demand ...
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1answer
46 views

Offer curves for giffen good [closed]

I learnt that giffen good doesn't satisfy the law of demand, but can we draw an offer curve to represent giffen good?
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1answer
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Why is the Social Security tax split midway between employer and employee?

On page 99 of Hidden Order, David Friedman writes: Social Security taxes are paid half by the employer and half by the worker. How would the effect of the tax change if it were collected entirely ...
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1answer
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Comparative statics of a monopoly

Consider a profit maximising monopolist with linear demand Q(P*) and total production cost C(Q(P*)) who faces a per unit tax t. Suppose the slope of marginal cost is decreasing in some parameter, μ. ...
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0answers
37 views

Market efficiency given asymmetric characteristics of securities markets

In an ideal market buyers and sellers in aggregate incorporate all available information and, as a result, the market price of an asset reflects its fair value. But in real securities markets there is ...
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Linearization and the effect of a change

There is the following system of four equations and four endogenous variables $(K,L,w,q)$. Assume $F$ is a concave function. $\partial F(K,L)/\partial K = r + (1-p)$ $\partial F(K,L)/\partial L = w$ $...
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1answer
101 views

Why it is unit elasticity

If I always spend a total of exactly $\\\$10$ per week on coffee, then does my demand function have unit elasticity? According to me, the change in income doesn't affect my coffee consumption, so it ...
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2answers
108 views

Demand for minimum of $4$ different goods

The consumer has the utility function with $4$ goods $$U=\min\left \{ \sqrt{x+y},z+w \right \}$$ The prices are $p=(3,2,2,1)$ with wage $m=1$. Find the demand. So far I have observed that it is ...
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1answer
61 views

Derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1 + p_2\overline{x}_2)$ to derive Slutsky equation

Why is the partial derivative of $x_1^S(p_1, p_2, \overline{x}_1, \overline{x}_2) \equiv x_1(p_1,p_2,p_1\overline{x}_1+p_2\overline{x}_2)$ for $p_1$ $$ \frac{\partial x_1^S(p_1, p_2, \overline{x}_1, \...
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Unsolveable Demand/Utility Problem?

A consume has a preference relation on $\mathbb{R}^4_+$ with a utility function defined as $$ U(x_1,x_2,x_3)=(\ln(3x_1+2x_2+x_3))^3$$ Find the demand at prices $p=(1,1,1)$ and wage $4$. Attempt I ...
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Why are cost functions often assumed to be convex in microeconomics?

Why are cost functions typically assumed to be convex in producer theory of (introductory) microeconomics? For me this goes against the intuition of economies of scale. There are fixed costs (FC) ...
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31 views

Long run equilibrium price under perfect competition

I have a problem related to Ricardian rent. I have one firm, let's call it X firm, and all of the other firms in the market. All firms have to pay some transportation costs due to their land except ...
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1answer
47 views

Why does a higher risk aversion leads to a lower intertemporal elasticity of substitution?

Mathematically, a higher risk aversion leads to a lower intertemporal elasticity of substitution (there is an inverse relationship). But why? If I become more risk-averse, I would like to smooth my ...
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1answer
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Concept of Utility in demand systems

I have seen that researchers use different utility function in demand systems estimation such as Stone Geary. What is the role of these utility functions? What are utility function other than stone ...
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31 views

Pure Nash equilibrium in bidding game?

According to the answer key for a problem set, there is no pure strategy Nash equilibrium in the following problem. Yet I can't see why not. Could it be an error in the answer key? Here's the problem: ...
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1answer
68 views

Utility function and homogenous of degree zero

I've a utility function which is given by ($x_i$-$b_i$)$^{c_i}$ $\sqrt{x_2}$ . What values of b and c can I input to ensure Homogenous of degree zero in prices and wealth? I think c will be positive....
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Are the goods in additively separable utility functions normal goods?

Inspired by this answer. To make it a bit more precise, by normal good I mean demand is (not necessarily strictly) increasing in income, and by additively separable utility function I mean that a ...
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1answer
106 views

Expected utility theory (Lottery notation)

A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences $$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$ ...
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1answer
57 views

Cobb Douglas relation with uncompensated law of demand

Does a Cobb Douglas or homothetic function satisfy the uncompensated law of demand?
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1answer
76 views

Production Set: Not satisfying Free Disposal Assumption

I saw the figure which satisfies the free disposal assumption in Mas-Colell, Whinston and Green (1995), but wondering if there is a figure that DOES NOT satisfy the free disposal assumption? Any leads ...
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Perfect information game

Assume that there are two parents A and B who are tempted to pick up their children late. We denote the set of parents $N = {A, B}$. Each parent $i \in N$ chooses from the action set $A^i = {E, L}$ ...
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1answer
59 views

Trigonometric Cost Function [duplicate]

I've been reading on producer theory and came up with a ridiculous question. Has anyone tried to model costs with a trigonometric function? would it work with the assumptions we need? Thanks!
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1answer
56 views

Derive demand function from utility [closed]

Never encountered such a problem as I am new. $$U(x_1,x_2)=(a\ln(x_1)+b\ln(x_2))^n$$ and $a,b,n>0$ with income $w>0$ and prices $p_1,p_2>0$. Find the demand function. Attempt I am thinking ...
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Can an inferior good be necessary?

Usually the definition of necessary goods is the income elasticity between 0 and 1. But can a good with -0.5 income elasticity be considered necessary? There is this link that says that all the ...
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Better Model for Dynamic pricing - Stackelberg model or Bertrand model

Objective - I am building a dynamic pricing tool for airline tickets which will consider the competitor prices. Taking competitor price as reference, this tool will price the ticket. Also instead of ...
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2answers
129 views

Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

As we know that $Q*P=const.$ for Cobb-Douglas preferences, we can thus conclude that $\frac{dQ/Q}{dP/P}$ is always $-1$: $$ QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P} $$...
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1answer
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How do I determine PED from price consumption curve with slope of zero?

Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1. By ...
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1answer
59 views

Without knowing the Slutsky equation and income/substitution effect, how can I show a certain good is inferior or Giffen?

Say I've got a function $x_1(p_1,p_2,m)$ where $p_1, p_2$ are the prices for good 1, good 2 respectively and m is the income. Now, I haven't heard of the Slutsky equation yet nor the income/...
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2answers
213 views

Relation of Engel-curve to income elasticity of demand; is the slope of the Engel-curve equal to the elasticity of income?

I learnt that $\frac{\Delta x}{\Delta m} \gt 0$ for normal goods, $\frac{\Delta x}{\Delta m} \lt 0$ for inferior goods, $\frac{\Delta x}{\Delta m} \gt 1$ for luxury goods and $0 \lt \frac{\Delta x}{\...
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1answer
118 views

How to prove a generalised function is quasiconcave?

I have a question I have been asked to solve: Given that $(a_1, a_2,...,a_n)\in R_{++}^n$ and $(x_1, x_2,...,x_n)\in R_{++}^n$, and $A>0, \mu >0, p \neq 0$, if there is a function $f(x)=A(a_1x_1^...

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