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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66 views

Equity-efficiency tradeoff examples

What could be an example of equity-efficiency tradeoff in healthcare, social protection or defense? For environment I did think of pollution permits that can cause geographical differences in ...
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How does definition of “price equilibrium with transfer” also include the case for the definition of “walrasian equilibrium”?

According to MWG and this answer, walrasian equilibrium is a special case of price equilibrium with transfers. However, since wealth distribution is predetermined in walrasian equilibrium, would it ...
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Special case for wealth allocation with quasilinear utility functions

Building on this question, regarding the answer from Bkay: Is it a general statement that when $m < \frac{p_y^2}{4 p_x}$, all income will be allocated to $x_M$? What about the case when the ...
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20 views

How to prove that the substitution effect is negative when price of another good is changed?

In Slutski equation, we have: $$\frac{\partial x_i(p,w)}{\partial p_j} = \frac{\partial h_i (p,u)}{\partial p_j} -\frac{\partial x_i(p,w)}{\partial w}x_j(p,w)$$ If $i \neq j$, the substitution effect ...
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38 views

Individual Firm and Market Demand Curve

In Section 10.2, Monopoly Power, in Pindyck's text on Microeconomics, an example says that suppose $N$ firms produce a particular product and the market demand curve is $P = -aQ + b$. An individual ...
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Software used for solving demands of different functions

I'm currently doing some research on demand systems and have been experimenting with different underlying utility functions which will generate different systems of demands. However I've been doing ...
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666 views

Is it possible to have a preference relation that is complete but not transitive?

I've been doing my own reading on non-rational preference relations. Im currently under the impression that transitivity follows as a direct result of completeness of preferences. However my (much ...
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32 views

Two different definitions for a Complete Relation

Many sources show this definition for completeness of a relation $$ \forall a, b \in A, a \neq b, (aRb) \text{ or } (bRa) \tag{1} $$ Others show only $$ \forall a, b \in A, (aRb) \text{ or } (bRa) \...
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Weakly monotone preferences with singleton indifference curves: do any of them admit a utility representation?

Inspired by this question. The original question was answered by Amit with some nice examples. I would like to know the generalized answer: Suppose we have a preference ordering $\succeq$, which is ...
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1answer
27 views

How is the utility function with constant relative risk-aversion obtained?

In this slide, it says that constant relative risk-Aversion utility function have this form. $u(x) = \frac{1}{1-b} x^{1-b}$ for $b≠1$ $u(x) = In(x)$ for $b=1$ When I tried to derive the utility ...
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32 views

Empirically checking efficiency and equity

I am aware that because of externalities or public goods (or for other reasons) there can be no allocative efficiency on the market. I am also aware that policy makers' subjective judgement of the ...
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22 views

Change in Consumer Surplus with two goods

Suppose we have two goods, price changes in the two are independent; having seen this question I am considering why the change in total Consumer Surplus is the sum of the change in Consumer Surplus ...
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61 views

A question about the property of quasi-linear preference

In case of quasi-linear preference, why would one unit more of the numeraire good (good 1) give the same additional utility as spending an additional amount of wealth equal to the cost of one unit of ...
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A question about MWG Exercise 3.D.4

I'm doing exercises of Chapter3 of MWG, there's a problem that I don't understand (I didn't figure out the solution manual either...). It is about exercise 3.D.4, the full statement of the exercise ...
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1answer
36 views

What would be the shape of the Indifference curve with slope 1/xy? [closed]

Let the utility function be: $U(x,y) = \log x +y^2$. In this case, the MRS is coming out to be $\frac{1}{2xy}$. Thus, how will the shape look like?
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Optimal Production Input in Relation to Cost Minimization Problem

I was doing my homework and got really confused about how to approach the optimal levels of inputs when there are three variables. My current understanding is that the problem is to solve the ...
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47 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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How to go from demand elasticities to a demand function? (merger simulation)

I am reading this paper: https://econpapers.repec.org/article/oupjleorg/v_3a10_3ay_3a1994_3ai_3a2_3ap_3a407-26.htm (Werden and Froeb 1994) about merger simulation. The paper is above my level, so I'...
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Why hipothesis of perfect competition market implies fixed price of a product in every transaction?

My book says that from the axioms of perfect competition follows that the price is fixed in every transaction but it doesn't specify in which way it is possible to prove it. Besides, are all the ...
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1answer
2k views

convexity of the profit function for profit maximization

the profit function is convex in prices and wages (output and input prices respectively). How does this interact with profit maximization since convexity implies tangents always lie below the curve I ...
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3answers
103 views

Why would microeconomics be considered more “objective” than macroeconomics?

I can imagine the following reasons for this: conflation of positive vs normative economics in macro micro phenomenon is less complex (or smaller): thus easier to create reliable models for Thanks
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2answers
91 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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1answer
65 views

How to prove that profit function is convex in price (with smaller price)?

According to this site, if output price increases from $p*$ to $p'$ and factor prices remain constant, then a new production bundle chosen must yield at least the same amount of profits as the old ...
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1answer
48 views

Short cuts to solve Cobb Douglas Utility function (minimization)

Say a Cobb Douglas like: $$\max_{X,Y\: s.t. X \cdot P_x+ Y \cdot P_y=I} U=X^\alpha Y^\beta$$ When it comes to maximization I would do the following way (for the fastest result): x: $\alpha/(\alpha +...
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Pricing Cross-Side Platform Mediated Markets

I have a question regarding the optimal pricing strategy for cross-side Platform Mediated Markets. Suppose we have two categories A and B, 100 potential customers each. How do I derive the optimal ...
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35 views

Does quasilinear preference contain rationality, monotonicity or other assumptions?

I have a question when I'm doing exercise 3.C.5(b) of MWG. The exercise asks to prove that a continuous preference on $(-\infty,\infty)\times R^{L-1}_+$ is quasilinear with respect to the first ...
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3answers
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Optimal decision for perfect substitutes utility function ?

Given $u(x_1,x_2)=4x_1+14x_2$ and $m=\frac{1}{2}x_1+\frac{3}{2}x_2$, I shall choose the optimal decision among: $a)(2m,\frac{2m}{3})$ $b)(2m,0)$ $c)(\frac{m}{2},0)$ $d)(0,\frac{2m}{...
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1answer
4k views

Quasi-linear utility functions

I have the following quasi-linear utility function given: $u_0 = f(x_1) + x_2$ (with $f'>0$,$f''<0$). I know that the indifference curves are vertically parallel, which means that the slope is ...
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1answer
50 views

How to prove that a concave production imply that the input requirement sets are convex?

According to page 7 of this slide, "A convex production set Y implies that the associated input requirement set V(y) is convex". How can one go about proving it?
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2answers
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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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113 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 it's convex or not? Also, what would be the general way to show if any given function is convex.
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Purchasing Power Parity and Baskets of Goods

On the exact definition and understanding of "purchasing power parity" it depends what it means when the World Bank defines the “extremely poor” people of the world as those who are currently ...
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1answer
38 views

How to find change in the optimal choice with a utility function in general form?

Suppose the utility function is represented as $U(x_1,x_2;I)$, where $I$ is the level of information the consumer possesses. How to find the change in the optimal choice of $x_1$ as price of $x_1$ ...
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How to show that a homothetic utility function has demand functions which are linear in income

A homothetic utility function is one which is a monotonic transformation of a homogeneous utility function. I am asked to show that if a utility function is homothetic then the associated demand ...
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26 views

Homothetic preferences linear in income [duplicate]

How to prove that $x(p,I)=I \cdot x(p,1)$? I would favor an argument based on showing that these are the $argmax$ to different problems and they coincide rather than using the fact that the MRS are ...
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1answer
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Why is a monotone increasing but nonlinear transformation of a utility function not represent the same preferences if the preference is complete?

According to a textbook, in the context of uncertainty (e.g. in lottery), if the preference is complete, a monotone increasing but nonlinear transformation of a utility function would not represent ...
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1answer
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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
38 views

Why might a monotone increasing but nonlinear transformation of a utility function not represent the same preferences?

According to a textbook, a monotone increasing but nonlinear transformation of a utility function might not represent the same preferences. Why is it so? An example of such preference would be ...
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2answers
254 views

Finding demand functions for an unusual utility function

I have a utility function: $U = x + \min\{x,y\}$ I want to draw the indifference curve and find the demand functions. Will it be the case of the usual perfect complements? Also, what preferences ...
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Would households rather live in a world with or without the unemployment insurance?

Would households rather live in a world with or without the unemployment insurance? What is a good example of world in which unemployment insurance is seen as a benefit, and not a hindrance?
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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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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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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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1answer
39 views

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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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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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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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
26 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 [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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1answer
52 views

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 ...