# 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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### 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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### 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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### 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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### Check if a utility function represents a monotone preference

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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### 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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### 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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### 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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### 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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### Consumer Theory question [closed]

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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### 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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### nash equilibrium public good - is this correct? [closed]

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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### Compensated demand function for perfect complement indifference curve [closed]

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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### 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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### 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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### 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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### 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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### Derive demand function $x(p,w)$ from utility function $u(x) = \min\{x_1, x_2\} + x_3$

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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### Returns to Scale [closed]

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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$u(x_1,x_2)=|x_1 −2|+x_2$ 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 $... 0answers 23 views ### Notation: is it correct to write$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$just knowing this? Or, on the contrary, such expression ... 1answer 24 views ### Given a rational$\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\}$and where ... 1answer 80 views ### Study whether$\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$.... 1answer 66 views ### Who took utimatum game and dictator game as the evidence against Homo Economicus assumption of individual utility maximization? Wikipedia and this McGill University page states that the two games "have been taken as both evidence for and against the Homo economicus assumptions of rational, utility-maximizing, individual ... 0answers 27 views ### Has contest theory ever been used to design real-world contests? Contest theory, very much like auction theory, studies how people act in a contest and the properties of such a competition. There is a large literature that investigates different aspects of the ... 1answer 60 views ### Prove that the set$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)$such as ... 1answer 56 views ### A preference relation$\succ$is defined as$(x_1,y_1)\succ (x_2,y_2)$if$x_1>x_2$and$y_1> y_2$Does this satisfy completeness property? I need an intuitive explanation of this preference relation as well. I am confused about the way how this relation is defined. The commodity Y in the first ... 1answer 47 views ### Constrained optimisation with transfer I have been stuck on this question for about two days and can find no way out (apologies if the question seems really simple as I haven't started university yet). I would strongly prefer it if this ... 0answers 42 views ### Quasilinear utility: if$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$, does ... 1answer 82 views ### Supporting Hyperplane Theorem and quasiconcave utility function My notes says that if$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$. I am ... 2answers 196 views ### What is an opportunity cost? Mankiw's definition and explanation of opportunity cost here is confusing. Since when have explicit costs become part of opportunity cost? Here is what the guide says: The concept of opportunity ... 2answers 36 views ### Why is Engel curve a straight ray through the origin if$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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### 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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### 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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### 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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### 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 ...
There are two identical firms, $1$ and $2$, with zero marginal costs. They produce homogenous product, which is demanded by a unit mass of identical consumers, each of which has inelastic unit demand ...