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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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Why income elasticity of demand of luxury good in greater than 1?

According to textbook and wikipedia, "if income elasticity of demand of a commodity is less than 1, it is a necessity good. If the elasticity of demand is greater than 1, it is a luxury good or a ...
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How to prove that the walrasian demand function $x(p,w)$ is continuous in $p$ and $w$?

If the utility function $u$ is continuous and satisfies local nonsatiation, and walrasian demand function $x(p, w)$ is a function (i.e. always map to only single values), how to prove that $x(p,w)$ is ...
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What is meant by lump sum tax being non-decreasing in per unit tax?

While I have proven the first part of a question about showing that a consumer will be indifferent between a lump sum tax (T) and a per unit tax (t), I have to also show that T is non-decreasing in t? ...
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1answer
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Why does strictly Walrasian demand with quasi-concave utility function mean that the walrasian demand having only one single consumption bundle?

In the context of Walrasian demand: Suppose u is continuous, satisfies local nonsatiation, and is strictly quasi-concave, each $w(p, x)$ contains a single consumption bundle. The proof I got from a ...
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11 views

The centralized shift from barter to currency economy

Suppose some ancient king of small bronze age city-state wants to introduce universal currency instead of barter that is currently in overwhelming practice in his kingdom. In order to smooth the shift,...
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3answers
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Perfectly competitive firms. Economies of scale

My textbook says the following: "Perfectly competitive markets only achieve productive efficiency if you assume that there are no economies of scale in the industry." Why is this the case? And by "...
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2answers
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Algebraic approach towards convexity

I have a function: $ u(x) = x_{1} + x_{2} + \min\{x_{1}, x_{2}\}$. How do we algebraically show if it's convex or not? Also, what would be the general way to show if any given function is convex.
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Overlapping Generations Model Pension System Question

Part 1 Pension System OLG Model with pension system: Each individual lives up to two periods. The surviving probability at period 2 is p. At period 1, the young household consumes c1, saves s1, and ...
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Monotonicity of a function

Given a function $u(x_1, x_2) = x_1 +x_2 + \min(2x_1, x_2)$, how do we mathematically prove that it monotonic or not? Is there is a general algebraic technique to show monotonicity of suchlike ...
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Numerical Solution Using Excel about optimal consumption of households

I'm not sure how to solve this problem. I'm given the discount factor, interest rate, probability of high income shock, and various income shock sizes that I need to use to compute optimal consumption....
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1answer
21 views

Deriving demand function in case of multivariable utility functions with min and max structures

Suppose I have utility function like this: $u(x_1,x_2,x_3)=min\{x_1,a-x_1\}\times min\{x_2,b-x_2\}+x_3$ where a and b are real numbers and $x_1\in [0, a]$ and $x_2\in [0,b]$. What will be a procedure ...
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1answer
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Consumer Theory question

You plan to use the following specification for an empirical study: $$e_i = \alpha_i + \sum_{j=1}^{n} \beta_{ij}p_i + \gamma_iy +\delta_i, i=1,...,n$$ where $e_i$ is the consumer's expenditure on ...
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1answer
22 views

Does non-monotonicity imply non-satiation always? Why or why not?

I understand that monotonic preferences imply non-satiation. But I am not sure 100% if non-monotonic functions always have satiation. An intuitive and mathematical explanation would be very helpful.
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19 views

Local non-satiation in economics

I am having trouble completely understanding the mathematical definition of non-satiation. I have stated the definition from Wikipedia below. It would be great if someone can graphically explain.
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1answer
17 views

elasticity of income if price changes by 10 percent

Arista always spends 10 % of her income on whatzits. Assume that her income increases by some percentage while the price of whatzits remains constant (and that all whatzits cost the same). What is ...
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1answer
37 views

nash equilibrium public good - is this correct?

Two players, 1 and 2, simultaneously choose their consumption of a public good. Given the consumption choices, g1 and g2, player 1 derives a marginal benefit of MB1 = 10 - (g1 + g2), while player 2's ...
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1answer
36 views

Why does the profit function in standard neoclassical theory have exactly one maximum?

In neoclassical theory is said that the highest profit occurs when Marginal Cost equals Marginal Revenue, but this condition wouldn't be enough to determine the maximum if there were more than one. ...
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calculating socially optimal level of consumption

Assume the private marginal benefit from a good can be represented by the inverse demand equation, P=100−Q. Assume the private marginal cost of producing the good can be represented by the supply ...
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1answer
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A preference relation $\succ$ is defined as $(x_1,y_1)\succ (x_2,y_2)$ if $x_1>x_2$ and $y_1> y_2$

Does this satisfy completeness property? I need an intuitive explanation of this preference relation as well. I am confused about the way how this relation is defined. The commodity Y in the first ...
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2answers
102 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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Compensated demand function for perfect complement indifference curve

For example, the indifference curve for goods $A$ and $B$ is $min$. How should I express its compensated demand function if the quantity of A does not depend on its price because of the zero ...
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6answers
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Why does quantity supplied increase with price in economics?

The Law of Supply is my worst enemy in economics because I could never truly understand it, and as a result, the stuff I learned after that was built on a weak foundation. The Law of Demand is totally ...
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1answer
57 views

Log Utiliy Function Trick

I am watching Lecture 3 of Yale's Financial Theory Lecture (by John). At about minute 50 he explains something along this line (with reference to log utility functions). MUx/Px=MUy/Py And ...
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29 views

Why is the opportunity cost 0 in this case?

My book says that the opportunity cost of purchase of a specialized equipment that has no alternative use is zero and hence such an expenditure is a sunk cost. However, while calculating the user cost ...
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3answers
48 views

utility function always negative

In a problem set, I found a strange utility function: $U(c)=-1/2(c^* - c)^2$, where $c^* =$ positive constant level of consumption. Does this function have economic sense?
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Change of demand curve

I am supposed to solve the following problem: The price of coal oil is increasing more than 1%, due to the annoucment about decreasing the supply of coal oil on the market. How it will effect curve ...
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22 views

open economy, and reduced world market price [closed]

Can someone help ? :) Suppose that a small, open economy that exports labor-intensive goods experiences a reduced world market price for its export goods. Explain the effect this fall in prices ...
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How can I model the impacts of improved agriculture technologies and food aid in a multimarket model?

Given a multimarket model for staple agricultural commodities wheat, rice, maize and sorghum, in a low-income economy, Im trying to figure out how I can use the multimarket framework to look at the ...
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1answer
108 views

Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x1, x2\} + x3$

I know how to solve the two-good case with $u(x) = \min\{x1, x2\}$, but the addition of $x3$ confuses me. Problem Derive the demand function $x(p,w)$ from $u(x) = \min\{x1, x2\} + x3$ What I did ...
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1answer
58 views

Identifying utility function

I recently came across a utility function with min written at the start. I assumed that it was a case of a leontief utility function, and only after going ahead with the problem I found out that it is ...
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18 views

Is oil supply really inelastic in the short term

Is oil supply really inelastic in the short run? Though it remains evident that in the short run, the known capacities of oil can't be increased and hence we can assume that there remains a upper cap ...
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9 views

Perturbation Constraints for Excess Demand

It is my understanding that for regular economies, equilibrium indices and number are preserved under perturbations, typically conceived as some point-wise translation. Does this hold under any ...
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1answer
40 views

Most profitable conversion of stock into money

When Forbes-lists of top billionaires are published we are usually aghast of their riches and statements such as "the 8 richest people own as much as the poorer half" are disseminated. I was ...
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2answers
146 views

robinson economy with production

Facing a little bit of a problem with this questions, did a similar one BUT the utility function was not linear and got MRS dependent on goods (was not just a number) - here I am at a loss. The ...
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1answer
63 views

The law of supply and demand - How does it work?

I've learned what the principle of supply and demand says, and would paraphrase it like this: The price of a good is at equilibrium when supply and demand are equal. Or with other words: The ...
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1answer
31 views

Prove that $h(p,u) = \nabla_p e(p,u)$ is implied by Roy's identity

I am struggling a bit with the math in my first graduate microeconomics course. I'm not sure if this belongs here. If it doesn't, please direct me to a more appropriate place. Below is one question ...
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2answers
53 views

profit-maximization

I'm having trouble on my homework and I need some help. A company sells products in a perfectly competitive market, where the price is $p = 24.$ For each of the following cost functions, write down ...
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Elasticity of substitution

So, this is an economics question but the problem I have is a pure math problem I guess. So I have the following equation:f(x,y) this function have the elasticity of substitution(EOS): 1/(1-beta). a,...
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CPI Bias with consumers using computers extensively

I was studying Microeconomics from Microeconomics by Pindyck and Rubinfeld where it was written that CPI calculated on Laspeyres index has overstated the cost of living for consumers who use computers ...
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1answer
39 views

Trying to apply in practice the theory of finding the optimal price in a cournot competition

I recently received my bachelors degree in economics. For fun I wanted to try to apply some micro-economic theory of finding the optimal price in a cournot competition. I wanted to do this for a ...
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19 views

Has contest theory ever been used to design real-world contests?

Contest theory, very much like auction theory, studies how people act in a contest and the properties of such a competition. There is a large literature that investigates different aspects of the ...
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25 views

Is this utility function continuous?

$u(x_1,x_2)=|x_1 −2|+x_2$ Is this function continuous? PS: The continuity theorem I use is this: Whenever for any $x^n$, $n \in N$ with $x^n \to x$ (i.e. $\lim_{n \to \infty} x^n = x$) and for any $...
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23 views

What guarantees that endowed agents have non-zero prices in an Arrow-Debreu Economy

In my research I am trying to find minimal conditions to guarantee a quasi-equilibrium must always be a typical Arrow-Debreu equilibria in a rather specific production setting. This may be rather ...
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1answer
24 views

Returns to Scale

Consider a firm with the production function $y=CL^{a}K^{b}$, where $C>1$, $a>0$, $b>0$. Write down the conditions under which this production function exhibits: i) increasing returns to ...
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How to prove the connectedness of the Pareto Set? [closed]

How to prove that, in a 2-agent, 2-good economy, the Pareto set is a connected set given that agents have utility functions that are continuous, strictly monotonic, and strictly quasi-concave?
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Notation: is it correct to write $x \succsim y \succsim z$ before using transitivity?

Let $\succsim$ complete and $x, y, z \in X$. Suppose $x \succsim y$ and $y \succsim z$. Is it OK to write $x \succsim y \succsim z$ just knowing this? Or, on the contrary, such expression ...
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1answer
52 views

Decreasing and increasing returns to scale question

Hi, I have deduced that this function exhibit increasing returns to scale but I am not sure how to verify part d. My answer doesn't show that there is decreasing returns to scale but I can't be sure d ...
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1answer
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Given a rational $\succsim$ over a finite set $X$, show that there exists $x \in X$ such that $x \succsim y, \forall y \in X$

I have been able to show this constructively, but would like to prove it by induction. However, I am stuck with the induction step: Consider $\succsim$ defined over $X=\{x_1,...,x_n\}$ and where ...