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 calculate the long-run equilibrium of firms in a Cournot competition?
I am trying to solve the following question:
'In a scenario in which there exist multiple identical firms with a large supply of products available, each firm must decide how much to provide to the ...
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Combined PPF (Equal quantities) & Combined PPF (Specialization)
I thank anyone who answers in advance.
I am taking a beginner microeconomics course and I am stuck on a question. I understand all the parts but the question they are asking is slightly different than ...
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Portfolio choice and risk aversion
Given utility function $U(w) = -e^{-w}$ of an investor (where $w$ denotes wealth) and two assets - risky and safe, will the investor's amount of investment into the risky asset be indifferent of his ...
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How does a lack of incentive to purchase new stuff affect economics?
How does a lack of incentive to purchase new stuff affect economics?
I've perceived as if a lot of economics is rooted in the idea of continued innovation and consumption, but then I've realized that ...
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Solve long run production function of a firm using technical rate of substitution
I don't understand the solution to a question which deals with the long run production function of a firm.
The question is:
Suppose a firm has a production function $f(x_1, x_1) = x_1^{0.5}x_2^{0.5}$, ...
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Understanding the Nash equilibrium for quadratic utilities
I need help to understand some steps of the article "Who's Who in Networks. Wanted: The Key Player" and I would greatly appreciate if someone can provide me with references or if they can ...
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Sellers and warranty
Suppose there are two sellers $\{H, L\}$ such that $H$ sells high quality products at $\\\$ 8000$ and $L$ sells low quality products at $\\\$ 5000$. The customers value the products at prices $\\\$...
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Screening models with multiple goods and interacting costs
I'm looking for a reference in the literature on monopolistic screening/mechanism design, where there are multiple allocative variables and these interact in the agent's utility function.
For example, ...
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Maximization of CD production function
I was reading the paper "Optimal Investment Under Uncertainty" (Abel, 1982). At one point the author addresses the following problem:
$$\max_{L_{t}}\left\{ p_{t}L_{t}^{\alpha}K_{t}^{1-\alpha}...
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Suppliers holding back production in expectation of better price in future
Anthony’s Ephemera Emporium sells signed photos of cryptids like Bigfoot, chupacabra, and other mythical creatures. These photos are substitutes in production.
If Anthony expects the price of signed ...
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Hardcore elasticity of substitution (bad results)
I have a following function and would like to find the elasticity of substitution between pairs:
$$U = \left( x_1^\delta + x_2^\delta + x_3^\gamma + x_4^\gamma \right)^{\frac{1}{\delta + \gamma}}$$
...
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How to derive a cost function when a firm takes over another firm to form a monopoly
Let's say firm 1 has a production function $\;=min(L1,K1)$
And firm 2 has a production function $\;= \sqrt{L}\times \sqrt{K}$
Total labour supply $\;=L1+L2\;$ Total capital $\; =K1+K2\;$
And firm 2 ...
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What is the difference among information acquisition, information providing and information design?
Taking a look at the literature of information economics I see three different terminologies about information that seem to have some intersection, though my understanding is not so good. These terms ...
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Looking for open learning material
in the next semester I am going to start studying some economics subjects at uni.
Since I have a little bit of time, I would like to start now already.
Does anyone know where I can find learning ...
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CES in Slutsky matrix (weird results)
We have a Slutsky matrix:
\begin{bmatrix}
\partial x_{1}^H/\partial P_1 & \partial x_{1}^H/\partial P_2 & \dots & \partial x_{1}^H/\partial P_n \\
\partial x_{2}^H/\partial P_1 &...
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How to solve the Bertrand model when marginal costs are different and not constant?
Find the equilibrium in the Bertrand model with two firms, with total costs given by:
$TC_1(q_1) = \alpha q_{1}^2$
$TC_2(q_2) = \beta q_{2}^2$
Inverse demand is given by
$P = A - Q$,
where $Q = q_1 + ...
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What is the economic intuition of prudence in the static case?
How can we interpret a "prudent" agent in the static case (i.e., someone with $u'''(\cdot)>0$)?
I understand that in a dynamic setting, someone exhibiting prudence would do precautionary ...
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The formula for expansion path
Is there a way how to precisely compute the expansion path?
I know a consumer's utility function $U(\boldsymbol{x})$, I know the budget constraint $\sum P_i x_i \leq M$, I am able to compute the ...
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Different elasticities of substitution
I have been reading into generalizations of the concept of elasticity of substitution for more goods/inputs and three main possibilities emerged:
Hicksian EOS
Allen-Uzawa EOS
Morishima EOS
HICKS
As ...
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Why is the supply function the first derivative of the profit function in the long run?
We have the profit function of the firm profit = $p^2 -2p -399$.
We take derivative of it we say that the output supply function is =$2p-2$
I understand that Profit = q*p - TC
But why do we say the ...
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Subgames in imperfect information games
I have not previously come across three player games and I am trying to solve for the subgame perfect NE/equilibria for the following game, where player 3's decision node is linked to the decisions of ...
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Supply function of a price-taking firm with a quadratic production function
For a firm with the production function
$$Q = 40L-L^2$$
where $L$ is labor and wage $w = 20$ find supply function of a price-taking firm under perfect competition. Fixed costs equal $10$.
Following ...
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Positional externalities - Are marketing and higher education examples of market failure?
As Mankiw explains in chapter 10 of the latest edition of Economics (chapter 9 in the previous few, I believe).
Positional externalities lead to "a professional squash player getting the extra ...
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What is the budget constraint when we assume a common utility function?
Let's consider an exchange economy with two identical consumers. The
common utility function is:
$$u^i (x_1, x_2) = x_1^α x_2^{1-α} \;\;\; \text{for} \;\;\; 0 < α < 1.$$
Society has 10 units of ...
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Finding Walrasian equilibria when Walrasian demands are not unique
I'm trying to solve the following excercise:
Find the Walrasian equilibria for a pure exchange economy where agents' ($A$ and $B$) preferences and endowments are given by:
$u_A = x_A + y_A$
$u_B = 2 ...
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Why is there a Walrasian Equilibrium if excess demand goes to infinity as price goes to 0?
In one exercise, we have to argue that a Walrasian Equilibrium exists and the solution says that if we can see that excess demand goes to infinity as price goes to 0, and as price goes to infinity, ...
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Marginal utility vs Total utility [closed]
If marginal utility is positive, consuming an additional unit of a product will cause total utility to decline. Is that statement true and why?
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reservation price
How do i use reservation price to determine when the car ride is the best option?
Assume we have utility function $$U(x_1,x_2)=4x_1^{0.5}+2x_2^{0.5}$$
and we have income $m=20$. If you stay in ...
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Does local non-satiation hold for this problem?
I am getting some confusing results solving this problem:
$max_{c_0\geq0, c_1\geq0} \bigg\{EU = R(1-c_0) [p t_1 + (1-p) c_1^{-2} t_2] \bigg\} ~ s.t. ~c_0+c_1 \leq 1$
where $p$ is the probability of $...
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Constructing Valuation As a Function of Condition
Suppose there is an item that deteriorates with use, its condition expressed as a number between $0$ (completely broken condition) and $1$ (perfect condition), for which I want to assign a monetary ...
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Determine for which prices and income the constraint is binding
Under what conditions constraints start to bind and how to find it
I was trying the following optimization problem:
$$ \mathscr{L} = x_1 x_2 + x_2 + \lambda(M-P_1 x_1-P_2 x_2) + \mu x_1$$
The thing is,...
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Conditions on turnover as a function of number of sales to be a concave function
Suppose I have a customer base of size 100. An arbitrary customer has a private valuation for my product, which shall be represented by the random variable $X$. (Suppose $X$ takes on values between $0$...
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What is the difference between preferences of the producer vs the consumer?
The book I am working with (Rubinstein) states that in the case of the profit-maximizing producer, preferences are linear and the constraint is a convex set. Meanwhile, in the consumer model, ...
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Truth behind Samuelson's statement against elasticities
I found the following statement by Paul Samuelson:
Through the influence of Alfred Marshall economists have developed a fondness for certain dimensionless expressions called elasticity coefficients. ...
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How to rationalize the following behaviors using preference relations?
The producer wishes to produce at least $y^*$ units. Once he has
achieved that goal, he maximizes profit.
The producer maximizes profit, but already employs $a^*_1$ workers
and will incur a cost c (...
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Universal Basic Income (UBI) policy proposals optimal hours worked and consumption
can someone please help me check my work for this question? I want to make sure I did it correctly.
Question:
Work:
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What are the conditions to determine whether demand function is rationalizable?
A consumer chooses a bundle (z, z, . . . , z) where z satisfies $z Σp_k = w$.
The book (Rubinstein's) states that the demand function x(p,w) can be rationalized if there exists a preference such that ...
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What does it mean if the derivative of the Utility function (at the optimal bundle) is 0?
It states in my book that under strict monotonocity, the derivative of U(x*)=0 can be possible although it's unlikely to happen.
What does this exactly mean?
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Deriving the constant relative risk aversion utility function
Here is the question I am trying to tackle:
Suppose that we are given a utility function $u$ with relative risk aversion $R_u$. Show that $R_u$ is constant and equal to $\rho$ iff there exist $\zeta\...
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What does differentiability of Utility function at an optimal solution x* mean?
I am working with Rubinstein's book. It states there that if preferences are differentiable, then value per dollar at a bundle of a commodity is as large as value per dollar of the bundle of any other ...
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Estimating Share Coefficients of Utility Function for a Calibrated CGE
Been reading The Textbook of Computable General Equilibrium (CGE) by Hosoe et al as a bit of side interest later in life.
Much of the book (and the CGE set-up generally) obviously follows naturally ...
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Help with checking work for preferences over consumption and leisure question
I was wondering if anyone could help me check my work for the following question, and if I am wrong, help me correct my mistakes?
Question:
Work:
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Can strict preference be represented by Utility function if not complete?
The definition states that a Utility function represents the preference relation because the relation on R satisfies transitivity and completeness. Yet, strict preferences (and indifference ...
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Incidence of cap and trade [closed]
Is there a way to show the incidence of cap and trade in a diagram? Similar to how in an indirect tax graph you can show consumer and producer incidence. I assume that the consumer incidence of cap ...
user43605
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Questions regarding Solving Melitz (2003) model
I am editing my question regarding solving the model in order to be more specific.
Regarding the demand side, In the beginning of the model, we have a CES utility function over a continuum of goods
...
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Trade and Opportunity Cost
This is a question on opportunity cost. I had problem in solving the last part. Please help me out.
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Composite good and preferences
Usually in economics, we could see some versions of multiplicative utility:
$$U(\boldsymbol{x}) = x*y$$
The thing is that most of the time an additional statement is given that $y$ is some composite ...
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How to determine elasticity of demand when equation has more than one variable
How should one go about determining the own price elasticity of demand of the following:
Assume that the market demand for barley is given by: Q=1,900−4PB+0.1M+2PW
, where Q
is the quantity of barley ...
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Can a preference relation not satisfy monotonicity and still be represented by an Utility function?
The book I am working with (Microeconomics Theory by A. Rubinstein) states that:
"In the case that preferences are represented by a utility function, preferences satisfying monotonicity (or ...
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Can the following statement be rationalized if it yields a choice function?
A person choose an alternative to maximize another person's suffering.
I thought we could define a sort of relation where the person suffers more from x than y. And if we can always do this, we can ...