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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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10 views

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
18 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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2answers
30 views

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 its convex or not? Also, what would be the general way to show if any given function is convex.
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1answer
21 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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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
15 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
39 views

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
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
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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15 views

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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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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23 views

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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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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open economy, and reduced world market price [on hold]

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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Under what conditions should I use a Social Accounting Matrix Model vs. Multimarket Model vs Computable General Equilibrium Models?

What are the differences between the SAM, multimarket and CGE models. When should I use one over the others?
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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
107 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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0answers
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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15 views

Derive the combined demand function for the market [closed]

QT(P) = 1500−P QL(P) = 4000−4P Derive the combined demand function for the market.
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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
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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36 views

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
57 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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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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22 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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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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How to prove the connectedness of the Pareto Set? [on hold]

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
15 views

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 ...
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1answer
29 views

Study whether $\succsim$ represented by $u(x)=\lfloor x \rfloor$ is continuous

Using the following definition of continuity: $\succsim$ is continuous if for any bundles $x,y,z$ such that x$\succ$y$\succ$z, there exists $\alpha \in (0,1)$ such that $\alpha x + (1-\alpha)z \sim y$....
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1answer
55 views

Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization?

Wikipedia and this McGill University page states that the two games "have been taken as both evidence for and against the Homo economicus assumptions of rational, utility-maximizing, individual ...
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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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1answer
44 views

Prove that the set $X = \{x \in R^L_+| u(x) \geq \bar u\}$ is closed

Prove that the set $X = \{x \in R^L_+| u(x) \geq \bar u\}$ is closed. Saw this statement in the textbook but I'm not sure how this is the case when we don't have any restrictions on $u(x)$ such as ...
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1answer
53 views

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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1answer
44 views

Constrained optimisation with transfer

I have been stuck on this question for about two days and can find no way out (apologies if the question seems really simple as I haven't started university yet). I would strongly prefer it if this ...
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0answers
38 views

Quasilinear utility: if $x \succeq y - ae_1$, does it mean $x + ae_1 \succeq y$?

Quasilinear preference is defined to be: $x \sim y \Rightarrow x+ae_1 \sim y+ae_1$ and $x + ae_1 \succ x$ with $e_1 = (1,0,0,...)$, Given a quasilinear preference, if f $x \succeq y - ae_1$, does ...
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0answers
29 views

Supporting Hyperplane Theorem and quasiconcave utility function

My notes says that if $u(.)$ is strictly quasiconcave and differentiable, by the supporting hyperplane theorem, there exists $p >>0$ and $w \geq 0$ such that $ x = x(p,w)$ $\forall x$. I am ...
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1answer
39 views

What is an opportunity cost?

Mankiw's definition and explanation of opportunity cost here is confusing. Since when have explicit costs become part of opportunity cost? Here is what the guide says: The concept of opportunity ...
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2answers
27 views

Why is Engel curve a straight ray through the origin if $D_wx$ = x(p, 1)$?

I see in the textbook that the Engel curve will be straight if $D_wx(p,w) = x(p,1)$ but it's not immediately clear to me why this is the case. Could someone kindly explain to me?
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1answer
34 views

Two firms competing ala Cournot

So I´m a bit stuck on this one. There are two firms in the country that sell cars. Both sell Toyotas and they buy their cars directly from the manufacturer, which is Toyota. We can assume that ...
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On the beliefs on the nature of Economy, Money and Profit

I have been taught in Money and Banking that money is any entity that has the following properties. 1 It is generally accepted as a means of transactions. Nonetheless how much is "generally" is a ...
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2answers
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Can i check monotonicity with the marginal utility?

For example I have a Cobb-Douglas utility function $U(x,y)$ and I want to check the monotonicity property. Can I use the marginal utility functions to see that they are always positive to conclude ...
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2answers
58 views

Utility function is given as U(x1, x2) = 10x 0.5 1 + 5x2

Given a utility function $U= {10x^{0.5}} + 5y$, calculate the MRS and explain its economic meaning. The MRS I calculated is $\frac{1}{\sqrt{x_1}}$, but I can't really understand it's economic meaning ...
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3answers
67 views

Why is that when one person or group gets a good or service, someone else will have to live without it?

! There's this statement in my Applied Economics book that I don't understand. Why is that when one person or group gets a good or service, someone else will have to live without it? I hope you ...
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2answers
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Is there an externality if someone buys all stock of some merchandise?

Is there an externality if someone buys all stock of some merchandise? On one hand, if they buy all of everything and there's still demand then they've taken it away from other people. On the other ...