Questions tagged [profit-maximization]
A modelling approach in which firms' plants are chosen via maximizing a profit function under a demand or resource limit restriction.
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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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How to properly annualize cost of initial investment
Let say you manage a supermarket chain and want to estimate profitability of a store over time, not only by using revenue and cost for a given unit of time - but also to include the initial investment ...
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How to prove that the profit function is increasing in p and decreasing in w? [closed]
How to prove that the profit function is increasing in output prices p and decreasing in input prices w?
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Why can bilateral negotiations reduce an upstream firms market power in the presence of downstream cournot competition?
In the article Market failures and public policy (2015), Tirole claims that when bilateral negotiations between the upstream supplier and individual downstream firms take place, downstream competition ...
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Source for maximising profit of a company
I was wondering if anyone could point me in the direction of a source, like a case study, where profit was maximised for a real (simple) company. I'm learning calculus for economics and a real life ...
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Monopoly problem: optimal quantity of production
I have this problem that I thought I could solve easily, but the solutions are different from the real ones...
Mediterchimica s.p.a. is the leader in the Mediterranean ethylene market and its demand ...
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Problem about production costs
I have this problem to solve:
The AOE (Association of Entrepreneurs) has decided to set up a tax and accounting assistance center for its members. Obviously, the volume (Q) of assistance that can be ...
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Show that the marginal cost of the total output equals the marginal cost of individual plant's outputs
Assume that the maxima/minima exists wherever referred (i.e., the necessary secondary conditions are satisfied). $p$ is the inverse-demand, $c_i(q_i)$ are the cost functions of the plants that a ...
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Does profit maximization imply cost minimization in both pure competition and monopoly?
How do I show that profit maximization implies cost minimization (in pure competition)?
Suppose we only consider inputs $l,k$ whose prices are $w,r$ and output price $p$. Profit is $\pi = pf(k,l) - wl ...
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Finding cost function
The production function is as follows
$$f(z)=(z_1+z_2)(z_3+z_4)$$
Find the cost function?
What I did is as follows. But I am not sure about my solution. How do you solve it?
*duplicated question
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Is P > AC under monopoly?
I would like to know why price is greater than average total cost under monopoly. In textbooks, average cost is drawn under monopoly price. However, if the fixed cost is so large, can monopoly get ...
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Why is a firm's profit maximized when MC=MR? Why not stop one unit before where it will still make a profit?
It seems that an equilibrium where MC<MR is preferred to one where MC=MR since in the case of the latter the firm still makes a profit.
Put differently, why would a firm produce a unit at all if it ...
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How can I choose how much to invest in each stock of my portfolio?
I'm trying to find a mathematical way to decide what percentage of my capital I should invest in each stock of my portfolio to maximize my profit.
Here's my attempt to the solution:
Let's say my ...
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Competitive equilibrium for an economy with a consumer and a producer
A representative agent’s preference over consumption $(c)$ and labour supply $(l)$ is given by the utility function $$ u(c_D, l_S)= c_D^a .(24-l_S)^{1-a}$$
Production of the consumption good $c$ is ...
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Complement in production and the slope of factor demand curves
Considering a firm taking prices for granted and maximizing profits
$$pf(x_1,...,x_K) - \sum_{i=1}^K q_i x_i,$$
where $f$ is strictly concave. Furthermore, let the factor demand curves be the ...
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On the profit maximization assumption: When it fails, does it fail gracefully?
This question was inspired by a comment on another question:
A basic cost-benefit analysis between two scenarios
My question is: Is profit maximization generally a good assumption for analyzing the ...
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Leisure and consumption maximization trouble
Not really sure how to to b). For a) I have (wh + Y – τwh) which I'm sure is fairly simple. I've never dealt with a utility function this complicated before and really confused by the notation in ...
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Bid-rent function in The Microgeography of Housing Supply
I came across the paper "The Microgeography of Housing Supply" (Baum-Snow, 2020)(https://luhan2.weebly.com/uploads/9/6/0/8/96080580/housing_supply_julyb2020.pdf) and I must admit that I do ...
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In the real world, do companies try to maximize return via maximizing profits or maximizing profits/costs (or neither)?
Suppose I buy $s$ shares of a stock at price $p_0$ and then later sell at price $p_t$. The initial and final values of my investment are then $I_0=sp_0$ and $I_t=sp_t$ respectively. The return is then
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Investigating the firm's supply function
Suppose the firm has a minimum cost function $C(\vec{w}, q)$ and sets up the following profit maximisation problem:
$max_{q} \text{ } pq - C(\vec{w}, q)$. The below FOC characterises the solution:
$p =...
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A profit max problem in a segmented market with a transfer fee
This must be a standard profit maximization problem, but I'm not seeing an example in my textbook. We have a monopolized market in two segments, each with its own demand function.
$$ {Q}_{1} = 35 - {P}...
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Maximization with a binding boundary constraint
I have following profit function -
$$ max_{x} ~ mx^{2a} - rx $$
$\text{Subject to,}$
$$ p \geq mx^{2a} - rx \geq q $$
Where, $ m>r, p>0, q>0$ and $a< \frac{1}{2}$
Since firm always want to ...
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Maximizing profit with a simple probabilistic production function (basic practice problem)
A restaurant finds that less orders for their soup of the day are placed on warmer days so they discount the usual 7USD price to 5USD on warmer days. The cost of making the soup is given by
$$
C = 0.1{...
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Isn't Laffer curve a special case of Profit Maximization curve if not the same? [closed]
I have discovered that Profit Maximization and Laffer curves convey similar ideas. Basically, down-side parabola.
Would it be correct to say that Laffer curve is nothing but application of the profit ...
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Is the pooling equilibrium profit maximising for the firm?
Is the pooling equilibrium profit maximising for the firm?
I understand that when there are no ways for the firm to distinguish among highly productive and low productive worker the best the firm can ...
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Effect of exogenous parameter on three player SPNE profits
Consider three agents $A_i$.
$A_1$ moves first and selects $0\leq q_1\in \mathbb{R}$. $A_2$ moves second and selects $0\leq q_2\in \mathbb{R}$. $A_3$ moves third and selects $0\leq p_1\in \mathbb{R}$ ...
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Interior Solution for profit maximisation problem
A function $c: \mathbb{R}^K_+ \xrightarrow{} \mathbb{R}_+$ is is said to be a cost function if
The value of function $c$ at $y = \textbf{0}$ is $0$: $c(\textbf{0}) = 0$
$c$ is continuous on the ...
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Short, Medium and Long-Run Profit Maximization
Suppose that, in a perfectly competitive industry, the firms' technology have the following cost function: $C(x) = 100 + 3x + 0.04x^2$. Assume the fixed costs are sunken.
a) If the demand for the ...
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When can one drop time subscripts? Example from Angrist and Kugler (2003)
Not the first time I am asking myself, but in this paper they actually start with a time dependent maximisation problem and then drop all time subscripts.
Background: They have profit maximisation ...
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When do the curves touch the axes and when don't they?
The Demand Curve
The Supply Curve
Monopoly: How to Graph It
In videos (1) and (2), we see that the supply and demand curves do not touch the axes.
In (3), we see that the demand curve touches the Y-...
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How would profit from labor exploitation be possible in a relatively competitive market?
Marxists often state that capitalists exploit workers by paying them less than than their labor is worth. The extraction of this surplus value results in profit.
I'm wondering why this would be ...
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Is my solution to finding the Hicksian demand correct? Maximize $x_1^{1/2} + x_2^{1/2}$ subejct to the budget constraint
Maximize $x_1^{\frac{1}{2}} + x_2^{\frac{1}{2}}$ subejct to the budget constraint $p_1x_1+p_2x_2=m$
Setting up the Lagrange and finding the first-order conditions:
$L(x_1, x_2, \lambda)=x_1^{\frac{1}{...
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Profit-maximization for a monopoly
Between two countries, Richland and Poorland, with a strict ban on cross-border sales agreed with the Poorlandian government. The respective demand functions for both countries are:
$Q_{poor} = 10 - ...
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Cost-optimal p2p-trade in a community of households
I’m trying to solve the following problem and I’ve been working on it for a long time already:
I want to optimize electricity-costs in a smart grid. There’s producer and consumer households in the ...
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Solving problem for optimal price (maximize profit) *attempt inside*
Let a demandfunction be defined as
$D(p)=B-bp$, where $b,B>0$. A firm has some production cost, $c$, and can set the price $p$ under the constrain given by the Demand.
What is the optimal price?
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Static Profit Maximization Short Run Shut Down Decision
In considering whether to stay open or shut down in the short run, a firm compares its revenues to its “avoidable costs”. We usually think of these avoidable costs as variable costs, but of course ...
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Solving for profit function $\pi (w,p)$ given the output of production function $f(z) = \sqrt{2z_1 + 3z_2}$
Solving for profit function $\pi (w,p)$ given the output production function $f(z) = \sqrt{2z_1 + 3z_2}$.
I approached this problem by trying to solve the $p\nabla f(z) = w$. This is derived from ...
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Show mathematically that in a competitive market, a price-taking firm has a zero profit. Also, justify the assumption that there is only one firm
Consider a firm that has a production function given by $F(x)$, where $x \in \mathbb{R}^n_+$. Assume that the function $F$ is strictly increasing in each argument, concave, twice continuously ...
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Max of a profit function: partial derivative of an integral function?
I am struggling with the maximization of the following profit function in a New-Keynesian model. Here there is the FOC.
$$\frac{\delta}{\delta Y_t(i)} P_tY_t- \int_0^1 P_t(i)Y_t(i)di = \frac{\delta}{\...
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Example on profit function that contains the maximum of a decision and a random variable
I am looking for an example of a profit function that contains the maximum of a decision and a random variable in this form: $\max(d,X)$, where $d$ is a decision variable and $X$ is a random variable. ...
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Profit maximization, when $MC = P$, in a simple supply table and curve
Our economics school book states that the profits of a company are maximized when MC = P.
However, I am having some trouble wrapping my head around that.
For example, I have the following exercise:
...
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Given $f(x_1,x_2) = \min\{x_1,x_2\}^\alpha$ find the profit-maximizing factor demands, supply function and profit fuction
Given
$$f(x_1,x_2) = \min\{x_1,x_2\}^\alpha$$
I have to find the profit-maximizing demand functions, supply function and profit function but I am not sure how to when the function is given as it is.
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Optimization problem of a Cobb-Douglas function with 3 inputs
A perfectly competitive firm uses 3 inputs to manufacture a certain product according to the following Cobb-Douglas production function:
$$
Q = A L_1^{\alpha_1} L_2^{\alpha_2} L_3^{\alpha_3}
$$
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Is optimizing revenue and expense objectives simultaneously better than optimizing profit as composite objective?
In the profit maximization problem, I am curious if co-optimizing revenue and expense objectives simultaneously are better than optimizing profit (revenue - expense) as a single composite objective? I ...
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How to determine price per unit and quantity sold of product from financial statement
Situation
I hope I'm asking in the right place. I'm writing a paper on the application of quadratic functions in economics and intend to use the Total Revenue function as well as the Profit function ...
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How to find the maximum profit in a graph?
We know the maximum profit will occur at the quantity where the gap of total revenue over total cost is largest. But how can we find such gap?
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How to find the profit-maximizing output level?
Table 11 In this post, step 5 states the profit-maximizing output level is quantity 5. But in this case, $p=28$, $MC=30$, $p\neq MC$. Why it is the profit-maximizing output level?
Step 4 states the ...
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When does the law of diminishing returns apply?
Law of diminishing returns does not always apply:
The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant, ...
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Does utility in economics also refer to producer's surplus ? How to balance the consumer surplus and producer surplus?
I am confused about the use of utility in economics and how it relates to allocative efficiency.
At 4:35 and 5:07 in this video (https://www.youtube.com/watch?v=9a3wXj1o91k) he talks about how at the ...
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Questions about profit function [duplicate]
I know that a profit function is defined by $\pi(p;w)=\max_{x\in\mathbb{R}}pf(x)-w\cdot x$ and $\pi$ is a convex function (i.e. $\pi$ is convex in $(p, w)$. My concern is how we can find the max value ...
