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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How to find the price ratio $\frac{p_x}{p_y}$?

(Question) Suppose two individuals form an economy where each devotes $10$ hours of labour to produce goods $x$ and $y$. The utilities of the agents $S$ and $J$ are $U_S(x,y) = x^{0.3}y^{0.7}$ and $...
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Calculus in intermediate economics?

What are the best online resource on learning the Calculus used in college-level intermediate economics? Where can I find lots of problem sets and practice exams with solutions/explanations online for ...
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1 answer
108 views

Why does lump sum tax decrease budget line

I only need help with (f). A hint would be appreciated. Problem: Donald derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows: U(Qc,Qd) = (Qc)(Qd) The ...
1 vote
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Convergence of various forms of Prospect Theory?

I'm not a mathematician but it seems that my problem is a rather technical than an economic one, but i hope this is still the right audience. My problem is the following: I want to analyse the effects ...
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1 vote
1 answer
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How does macroeconomics change as state size of a country varies?

In my home country India, the states are sometimes of the size of countries. For example, Utter Pradesh, one of the larger states, is of population 200 million. For comparsion, a country like Germany ...
1 vote
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How does second-order utility affect supply-and-demand equilibria?

I'm trying to get a rough idea of how common microeconomics concepts such as supply and demand are affected by "meta-utility" or "second-order utility" (I'm not sure what to call ...
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Questions about Lagrangian and consumer's problem

Background: Suppose a consumer has the following utility function $u(x,y)=\sqrt{xy}$, then the Lagrangian equation is $\mathcal{L}(x,y)=\sqrt{xy}+\lambda(I-xp_x-yp_y)$. Then the optimal bundle is $(x,...
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3 votes
1 answer
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Differentiability of variables in Hotelling's lemma

Notation: Subscripts like $g_t$ denote partial derivatives $\frac{\partial g}{\partial t}$. If $\pi(p,v,w) = pf(k,l) - vk - wl$ where $\pi(p,v,w),k(p,v,w),l(p,v,w),p$ denote profit, capital, labour ...
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2 votes
1 answer
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How tax relates with utility function?

Suppose there are $n$ agents in an economy and the utility of person $i$ is given by $U_i(x_1, x_2, \cdots, x_n)$ where $x_j$ denotes the distance driven by each agent in the economy. One's utility ...
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Dynamic Information Provision model setup - It generalizes Dirk Bergemann and Stephen Morris

The following model setup is from the paper Dynamic Information Provision: Rewarding the Past and Guiding the Future by Ian Ball. It generalizes both the ideas of strategic information transmission of ...
2 votes
0 answers
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curiosity about some properties of Hicksian demand function

A curiousity arises from one of my homework problem: Given u(·) is strictly increasing, continuous, and quasi-concave, show that $\textbf{x}^h(\textbf{p}, u)$(Hicksian demand function) is a convex ...
1 vote
2 answers
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Why in some area businesses with similar premise place near each other?

I have noticed that in some areas I go to is filled with shops of the same type. For example , Restaurants which more or less have the same menu. Sometimes, people give such places names as "...
0 votes
1 answer
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Is marginal rate of substitution always positive

Concept question:Marginal rate of substitution(MRS)=$-\frac{dy}{dx}$ where dy is change in unit of y for one unit of x. Is it true that $\frac{dy}{dx}$ is always negative because of law of diminishing ...
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Why are small business open for continuous long hours?

I am trying to understand the economics of small local buisnesses like cafes, tea shops etc. I observe that they get 90% of their customer in certain rush hour/ time periods. Yet they keep the shop ...
1 vote
1 answer
132 views

Production economy general equilibrium

I encountered the following economic model. Consider the following general equilibrium model with only two households, two consumer goods ($x$ and $y$) and two inputs (capital $k$ and labor $l$). ...
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Every expected utility form represents a preference relation over lotteries

Suppose there are finite number of prizes or alternatives. L denotes the set of all lotteries over the prizes. Does every expected utility form defined on L represents a preference relation on ...
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1 answer
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Von Neumann-Morgenstern Utility Theory Question

There's a question in my ECON notes that I don't understand, any help would be greatly appreciated. Here are the definitions used about VNM Utility Theory. The question is posted after the definitions....
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What is an external price?

I am only given a demand curve and an "external price" for the good, but I can find no definition of external price in any book. I am supposed to find the price and quantity of equilibrium.
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How to draw indifference curve?

Question: George has a fixed income and can afford at most 7 units of X if he spends his entire income on X. Alternatively, if he spends all his income on Y, he can afford at most 6 units of Y. Draw ...
0 votes
2 answers
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Homogeneity of compensated demand for Leontief (perfect complements) function

In my assignment I have a Leontief (perfect complements) function u(x,y)=min(x,2y). Keeping utility fixed, we minimize the expenditure. Since we have a Leontief function, at a fixed level of utility u(...
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2 answers
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Strict preference relation implies weak preference relation

Condition A: Given x, y in X such that $yRx$ then it follows that $\lambda y +(1-\lambda)xRx$ for all $0< \lambda<1$ Condition B: Given x, y in X such that $yPx$ then it follows that $\lambda y +...
2 votes
0 answers
70 views

CES nested in a Cobb-Douglas Function

I have the following CES nested in a Cobb-Douglas production function: $$y(i)=[l(i)^{\frac{\epsilon - 1}{\epsilon}} +\alpha(i)(\tilde{\gamma}x(i))^{\frac{\epsilon - 1}{\epsilon}}]^{\frac{\epsilon \...
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Finding all symmetric mixed strategy equilibria in a finite game

There’s a pure strategy and one mixed strategy with probability distribution (0.5,0.5,0) and (0.5,0.5,0) for each player in this game. But I was wondering if this example fails the fact that there are ...
1 vote
0 answers
91 views

Find cost function for given production function

I have the following production function $$f(x_1,x_2,x_3,x_4)=max\{\min\{x_1, x_2), x_3+2x_4\}\}\ge q$$ And I want to find the cost function. What I think (1) $P_1+P_2 <P_3$ and $P_3/P_4<1/2$ ...
1 vote
1 answer
35 views

Backward bending supply curve

The following says that the point $(q_b,p_b)$ is an unstable equilibrium while $(q_a, p_a)$ is a stable equilibrium. May I know what that means and why that is the case? Here's the original paper, for ...
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1 vote
1 answer
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Question on the conditions for the existence of a Walrasian equilibrium

I have a production Economy with two consumers and one producer. Consumers have a consumption set in $R^2_+$ Y is production possibility set and $$Y= \{y | max (2y_1+ y_2, y_1+2y_2)\le 0\}$$. ...
0 votes
1 answer
137 views

Marginal Cost and lagrange multiplier

I'm studying basic micro, and I did not get how such a result is possible. According to what I studied, the marginal cost is simply the partial derivative of the cost function with respect to the ...
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1 vote
1 answer
161 views

Find the set of Pareto efficient allocations

There is an exchange economy with two people and two goods. Utility functions are $u_A(x_A, y_A)=\max\{x_A, y_A\}$ $u_B(x_B, y_B)=\max\{x_B, y_B\}$ Endowments are $w_A(1,\alpha)$ and $w_B(1,\alpha)$ ...
0 votes
1 answer
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Can we find the best combination of production by just using the PPF curve?

I have this doubt that when we have a concave PPF like the one below is it possible for us to determine the best allocation using just the PPF alone ? I understand that any point in the ppf curve is ...
3 votes
0 answers
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Unit cost function for CES

You do not need to make computations, you can just tell me how to make the following derivation: I'm studying a paper where the unique final good of the economy is produced according to the following ...
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1 answer
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Isoelastic demands and constant markup

Why if the monopolists face isoelastic demands, profit maximization(for monopolists) implies that each of them sets a constant markup over the marginal cost? ADD DETAILS: This is a common situation ...
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Can budget lines of two agents containing equilibrium allocations be different?

Consider a pure exchange economy that has two goods and two agents (people). Suppose the initial endowments of person $A$ and $B$ are $(e_x^{A}, e_y^{A})$ and $(e_x^{B}, e_y^{B})$ (resp.) such that $...
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Principal agent problem

The shareholders of PC (The Principal cooperation) are about to present a contract to a potential project manager. If she signs the contract, the manager has two choices: If she goofs off (exerts low ...
1 vote
0 answers
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Please check for payoffs which I calculated in the incomplete and imperfect game

Taxpayers may either have a high income or low income, and they may be either opportunistic or honest. The tax collector cannot observe any of these characteristics, but after receiving a report from ...
1 vote
0 answers
87 views

All-pay auction question

Two players take part in the following auction for a £1000 prize. The two players submit bids simultaneously, and the higher bid wins the prize (if bids are identical each gets £500). Both the winner ...
1 vote
1 answer
55 views

How to prove that preference relation is continuous if the utility function represent the preference relation is continuous

The reverse of Debreu Theorem, have no idea how to start the question.
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1 vote
1 answer
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MWG 8.B.7 - Any strictly dominant strategy must be a pure strategy

This question from MWG 8.B.7 Any strictly dominant strategy must be a pure strategy. How can I show this? My explanation is as follows: Suppose we have a strictly dominant strategy, $\sigma_i$ . ...
1 vote
1 answer
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Isoelastic Demands

I have a very simple question: I'm studying Acemoglu's book the horizontal innovation paradigm of endogenous growth. Here, the conditional demand function for the machine variety $\upsilon$, i.e., $x(\...
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0 answers
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Welfare economics and Equity

What would be the advantages of an equitable social security system in Australia? I am trying to explain this using Pareto efficiency and the efficiency/equity tradeoff.
3 votes
1 answer
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What does the idea of a price chosen as numeraire entail (both economically and mathematically)? A dumb down explanation would be appreciated

I would love to have a clear-cut explanation or reference about the usefulness of a price chosen as a "numeraire" in the general equilibrium framework.
1 vote
1 answer
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Quasicon... and quasilinearity

From the discussion under this question: Can utility function $U(x,y)$ that is both quasiconcave and quasiconvex always be transformed (via some positive monotonic function) into a quasilinear form $v(...
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2 votes
0 answers
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How to find the substitution and income effects?

The usual definition of Substitution Effect (pg. 30; also found in Varian) tells that the Slutsky SE is $x(p_x', I') - x(p_x,I) = x(2,15) - x(1,10) = \frac{15}{2 \cdot 2} - \frac{20}{2 \cdot 1} = -6....
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Selling a durable good by monopolist under price commitment

My Industrial Orgnization book by Church and Ware presents the following problem: A durable goods monopolist can produce at zero marginal cost. If $r_t$ is the rental or lease charge consumers pay ...
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0 answers
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Cobb-Douglas Aggregator

I'm working with the Rising product quality developed by Grossman & Helpman, based on Aghion and Howitt's job. I have a simple question, that is not only about macro but also about micro. Consider ...
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2 votes
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Uncompensated and compensated demand functions

I came across this lecture note online and some of the points below confuse me. I have added the part that confuses me as an image and here is the lecture note for further reference, if needed. ...
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1 vote
1 answer
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Please check those two production functions, they also seems to be quasiconvex?

Those two are generic production functions that we usually see, and I check the definition of quasiconvex and quasiconcave on wikipedia, and it seems those two graphs satisfy both definitions, and ...
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Find SPNE in the two stage game

Consider a firm in a two period world. The firm operates as a monopolist in the first period. In the second period, another firm will enter and the two firms will act as Cournot duopolists (i.e., in ...
1 vote
1 answer
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Finding the Pareto efficient allocations

Consider a 2 person 2 good economy where there is a private good $x$ and a public good $y$. Agent 1 has an endowment of 10 units of the private good and Agent 2 has an endowment of 20 units of the ...
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Using the 80:20 rule, what top 20% of economic concepts, theories, methods, tests, tools etc do you use to generate 80% of your results?

I'm curious to see what different economists use in their roles. Helpful if you could specify your area of work/interest too.
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im confused with the subsidy here and support price

The market demand and supply curve for an agricultural product are given by xd = 4500 - 250p Xs = 200p The government wishes to achieve a higher point on the supply curve than the initial equilibrium. ...

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