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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If utility function is convex, what can be said about preference relation?

It is known that if a utility function is concave, then it is quasiconcave, and the preference relation is convex. What can be said if a utility function is convex? I've found on the Internet then in ...
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About infinite strategy sets and $\epsilon$-equilibrium from Game Theory: Analysis of Confilct by Roger Myerson

I am studying infinite strategy sets using Myerson's Game Theory: Analysis of Conflict. On Page 143, he defines an $\epsilon$-equilibrium as follows: Definition For any nonnegative number $\epsilon$, ...
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If utility function is homogenous of order 1, then partial derivatives of demand function are equal

Prove that if $U(\alpha x)=\alpha U(x)$, then $$\frac{\partial x_i(p,w)}{\partial p_j}=\frac{\partial x_j(p,w)}{\partial p_i}$$ for any $i$ and $j$. I've proved that $x(p,\alpha w)=\alpha x(p,w)$, but ...
Paul R's user avatar
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Second-degree price discrimination exercise

A monopolist produces output with constant marginal cost equal to 1. There are two of consumers that are potentially in the market for the good. Consumer A has inverse demand function $$p_A(x) = 7 βˆ’ x,...
Sofia Delacruz's user avatar
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Marginal and Average costs for constant returns to scale production function being constant

Suppose that we are dealing with a production function $q = f(k,l)$, of inputs capital and labor. If this function exhibits constant returns to scale then I know that both the marginal cost and ...
Nick's user avatar
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Showing UMP and EMP do not exhibit duality if the assumption of local non-satiation is absent

I have been trying to use the contradiction method to prove this, but it does not seem to be working. Suppose $x^*$ is optimal in both EMP and UMP. Then $u(x^*) \geq u(x')$ for all $x'$ in $B_pw$. And ...
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Is my understanding of Arrow's dictatorship correct? The dictator is free to update her preference and the social choice will always follow her taste

Suppose $R$ is a social ordering, $f$ is the social choice function, and $R_i$ is an individual preference. A profile of individual preference is $<R_i>$. $f(<R_i>)=R$ Suppose $i=1$ is ...
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Equilibrium asset prices of a risk-free bond and a stock

Setup: Two-period economy with two equally likely states of the world in the second period. Two consumers with Bernoulli utility and same discount factor
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FOCs for profit maximization using a transformation function

I'm (still) reading the microeconomics textbook of Mas-Colell et al. On p. 135, the profit maximization problem (PMP) for producers is introduced; characterizing the technology as $Y = \{ y \in \...
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Can anyone pls do the derivation of the cournot aggregation condition and make it explanatory

I'd like to know how the aggregation condition was derived.
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Understanding consumption units normalisation by $u^\prime (c) $

It is frequently noted that if utility is given by $u(c)$, then the object $$ \frac{u(c)}{u^\prime (c)} $$ puts the utility in consumption units via the normalisation by $u^\prime(c)$. What is the ...
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How could a market be designed to prevent hoarding?

Imagine that someone has been put in charge of creating a new market for some kind of commodity. They have ultimate regulatory power. What kind of market mechanisms could they put in place to ...
Crashworks's user avatar
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How to compare Preferences in Utility Functions?

When looking at utility functions, how do you compare preferences? I understand the economic concepts, but the math part is holding me down from understanding a lot in the textbook. (I am not typing ...
SelfTaughtEcon's user avatar
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Derive differen function of production

Find the optimal cost function, profit function, and input functions of the following supply functions: a. 𝑓(𝑙, π‘˜) = 4𝑙½kΒ½ b. 𝑓(a,b)= (a^Β½+3bΒ½)^2
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Microeconomics to show if indifference curve is convex to the original [closed]

) for the following utility functions and determine whether they have convex indifference curves i. π‘ˆ(π‘₯, 𝑦) = 3π‘₯ + 𝑦 5 marks ii. π‘ˆ(π‘₯, 𝑦) = √π‘₯ βˆ— 𝑦 5 marks iii. π‘ˆ(π‘₯, 𝑦) = π‘₯𝑦 π‘₯+οΏ½
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Can someone help me with constructing the strategic form and calculating the set of Nash equilibria in pure strategies? [closed]

I'm trying to solve it but my solution are different every time.
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Help Understanding AP Micro MCQ re: Monopolistically Competitive Firm's Demand Elasticity

Here is the question: A monopolistically competitive firm’s demand curve will be least elastic if A - the number of rival firms producing very similar products increases B - the number of rival firms ...
user27075's user avatar
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Why is the budget correspondence lower hemicontinuous?

Given income $y$ and a vector of commodity prices $p\in R_+^L$, the set of feasible consumption bundles is described by the budget correspondence, $B(p,y)=\{x\in R_+^L:px\leq y\}$. $B(p,y)$ is both ...
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Dynamic price competition with capacity constraints

I have a dynamic price (Bertrand) competition with 2 players with the same capacity constraints. Grim trigger strategy is to set monopoly price at t=0 or if the monopoly price was set by both players ...
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Explaining the relative share of the income & substitution effects of a price change

Let's say you have a Cobb-Douglas utility function, U = x^.1*y^.9 This will result in Marshallian demand functions x* = .1I / Px, and y* = .9I / Py. If you perform a Slutsky decomposition for x* as Px ...
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MCQ on income and substitution effects

Person A spends their income only on bread and cheese. Given a rise in the price of bread leaving income constant and the price of cheese constant, the consumer consumes less bread and less cheese. ...
secretrevaler's user avatar
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Exponential Income Consumption Curve

From the Engel's Law we know that as income increases the share of income spent of foods decreases and the share of income spent on luxury goods increases. I wanted to represent this using Consumer ...
João Maria's user avatar
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Equilibrium of Perturbed Dollar Auction Game - An Example from Game Theory: Analysis of Conflict by Roger Myerson

I am studying game theory using Myerson's textbook (Chapter 3 - Equilibria of Strategic-Form Games, Section 3.6 - The Decision-Analytic Approach to Games). I have difficulties understanding and ...
Beerus's user avatar
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non-ponzi condition

What Is The Differences Between R(T) And R(S) In No-Ponzi Condition In Ramsey Growth Model?
Huy Lê Thanh's user avatar
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Ramsey model problem

Explain the no-Ponzi game condition throughout the function. Does the constrain function: also reflect include the No-Ponzi condition?
Huy Lê Thanh's user avatar
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Debreu's ordinal representation theorem is unique up to a positive monotonic transformation, what is the source?

In Debreu's 1954 ordinal utility representation theorem, the utility is unique up to a positive monotonic transformation. While the uniqueness result is well-known, I fail to find a proper reference. ...
dodo's user avatar
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Deadweight loss and consumption externalities

here's the problem and my solution so far: In this case, the Marginal Private Benefit (MPB) is given by the equation MPB = 100 - 4q and the Marginal Social Cost (MSC) is given by the equation MSC = ...
Kedagi 16's user avatar
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why is the MRS same for everyone?

If the consumers are optimizing and at interior solutions and facing the same prices, then the MRS=p1/p2 will be the same for everyone no matter the preferences and income. but why? I don't understand ...
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Question About Stochastic Choice - MWG Exercise 1.D.5

I am studying microeconomic theory using MWG. I got stuck on Exercise 1.D.5, specifically part (c), but I would also like to have my part (a) and (b) checked by someone. Here is the exercise and my ...
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Deriving Unit cost function

Unit cost function is the minimum cost to produce one unit of output. The solution to the above problem is: where ai(w,r) is the amount of labour needed to produce 1 unit of good i at factor prices (...
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Cost Minimization

Guys in the following optimisation problem why are we not considering the partial derivate of K and L in the Lagrangian in the first two equations
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Calculating the value of this asset

calculate the cash value of a financed asset that is paid in the following way: an initial payment of 500,000, in month 2 a payment equal to half its value, in month 7 a payment equal to a third of ...
VOZ ESTOICA's user avatar
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Why is monotonic preference and monotonic utility function non-decreasing?

Obviously a monotonic function can be either nondecreasing or nonincreasing: However, in Economics, a quick google search gives: I am interested in the history or the motivation behind the econ ...
dodo's user avatar
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why is increasing price not more profitable when the demand is unitary elastic?

according to the theory (if p-p1=q-q1), the total revenue remains the same because the demand decreases by the same percentage price does. If this is the elasticity of a product, the company ...
wjkrkdfjkn's user avatar
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Price elasticity of demand when total expenditure is constant

I was recently given the following question: assuming that a consumer's total expenditure for a good does not change when the price of that good declines, what is the price elasticity of that consumer'...
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Increasing Returns to Scale and Perfect Competition

Increasing returns to scale due to internal economies are incompatible with perfect competition BUT increasing returns to scale due to external economies are compatible with perfect competition SOURCE:...
user205152's user avatar
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direction of causality between Increasing returns to scale and economies of scale

Does increasing returns to scale cause economies of scale OR is it the other way around?
user205152's user avatar
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the relationship between Returns to Scale and shape of Production Possibility Frontier (PPF)?

Guys any material that discusses the above in detail for a two commodity case?
user205152's user avatar
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Cutoff rule-mechanism question

I was checking on this paper where they define some rule-mechanism that is called cutoff rule-mechanism. I do not really understand why is this useful and how is this defined. Any help would be ...
Oliver Queen's user avatar
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Individual vs. Market Transformation Function

Let $F_j$ denote the transformation function of firm $j$, i.e., $j$'s production set $Y_j=\{y:F_j(y)\le0\}$. Also, let $F$ denote the transformation function of the market, i.e., $Y=\{\sum_j y_j: y_j\...
kenji's user avatar
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2 votes
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Marginal rate of technical substitution in a general setting

I am interested in the definition of the marginal rate of technical substitution (MRTS) under a general setting where the production set of firm $j$ is $Y_j=\{y: F_j(y) \le 0\}$. This formulation ...
kenji's user avatar
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For which number of firms in a Cournot oligopily a merger is profitable

Assume a Cournot oligopoly with N (equal to 2 or higher) symmetric firms. Firms face a demand function P=a-bQ and an average cost c. I need to find the number of firms N for which it will be ...
Ksenia's user avatar
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Stackelberg equilibrium with arbitrary number of firms

Consider a market, where N firms with average cost c compete in quantities. Assume linear demand P=a-bQ. Assume that N is arbitrary. a)Find the equilibrium of the game, where these N firms compete a ...
Super_Clown's user avatar
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Microeconomics question: Find consumer optimal choice after tax

Consider an economy with one farmer whose farm produces 100 units of food. The farmer can trade food for clothing from other countries, but he cannot produce clothing. The price of food in the market ...
Jackie's user avatar
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How do I show that the set of probability distributions that first/second-order stochastically dominate p is closed and convex?

I was trying to understand stochastic dominance when I came across this problem (Question 2). How do I show that the set of probability distributions that first/second-order stochastically dominate $p$...
Ludwig Gershwin's user avatar
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About Proof of Theorem 21.3 in Mathematics for Economists by Simon and Blume

Background Information I am studying concave and convex functions using Mathematics for Economists by Simon and Blume. I have difficulties understanding their proof of the following theorem: Theorem ...
Beerus's user avatar
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How to measure changes in consumer surplus empirically?

I am familiar with various ways of measuring consumer surplus "on the blackboard" (Compensating Variation, Equivalent Variation and simply measuring from the ordinary demand curve). Im ...
EconJohn's user avatar
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The sufficient condition for unique interior solution in utility maximization problem

Suppose the utility function is continuous, differentiable, strictly increasing and strictly quasiconcave. Whether the utility maximization problem has unique interior solution? If not, is there any ...
23134's user avatar
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Social Welfare Function (Pareto Efficiency)

What is the Pareto efficiency compensation criterion? Can you give me an example?
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Determine Whether A Preference Relation Satisfies The Continuity Axiom - from Exercise 1.1 in Game Theory: Analysis of Conflict by Roger Myerson

I am self-studying game theory using Game Theory: Analysis of Conflict by Roger Myerson. Here is an exercise from the textbook. I tried it myself, but I am not sure if it is correct. I would really ...
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