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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Deriving FOC with non-substitable goods

I'm trying to derive the first-order condition of cost minimization when inputs are non-substitutable. The question is based on the problem raised by Rubens (AER 2021). Suppose firms $f$ produce $Q_{f}...
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Maximize profit with per unit profit of labor and capital (regulated firm)

Suppose a firm is regulated, such that it is permitted to recover the costs of its labor and capital inputs. Total revenue for the firm is therefore $R= \mu L + \sigma K$, where L=labor, K=capital, $\...
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From Cobb-Douglas Production Function to Profit Function

A firm's output is given by the Cobb-Douglas production function $$Y_t=X_tK_t^{\alpha_K} L_t^{\alpha_L}$$ where $\alpha_K\approx\frac{1}{3}$ is the capital share and $\alpha_L$ the labor share. ...
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Stackelberg model with 3 symmetric firms

Firm 1, the incumbent, sets quantity q1 first, then firm 2 enters the market and sets quantity q2, knowing q1. Lastly, firm 2 enters the market and sets quantity q3, knowing q1 and q2. Firms are ...
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Profit maximization; how to derive

Can someone expalin me the math process step by step behind this? I haven't been able to figure it out and I cannot find anything in google
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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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High Fixed Cost and Zero VC

Suppose a Monopoly has a High Fixed Cost= 0.5 and VC=0 . The Profit Max O/t : Q=1 But the Profit = -0.13 (which is < 0) which means -0.13 > -0.5 Should the Firm Produce produce Q=1 or Q=0 ? ...
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If wage is equal to P x MPL then where is the profit of the firm?

Excuse me if the question is too simple... Wage = Price x MPL (Marginal Productivity of Labor) I wonder how we can come to this conclusion as there is nothing left for Profit. I mean let's suppose ...
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How does Perfectly Competitive Output Level Compare to Cournot Output Level

So Let there be two firms with Output Level x1 and x2 .Inverse Demand Function $P=a-bX $ where $ X=x1+x2 $.Both firms have same MC denoted by $c$. Is the Perfectly Competitive O/t > Cournot O/t ...
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Problem with Optimizing Profit in Log-Linear Demand Model

I've trained a linear model to predict log(volume) to capture the elasticity of demand with respect to price difference between my product and a competitor's: $$log(volume)= constant+elasticityCoef×(...
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Are there any examples of companies prioritizing market dominance or intellectual property ownership over long-term profitability?

I want to know if market dominance (total share of a market's profits) is more important than long-term profitability because psychologists believe that humans and other animals have a social ...
Jude Zambarakji's user avatar
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Stability vs profit maximisation

I have a very general question to ask - if I am getting multiple equilibrium and I have to check which one will be picked ie. which Solution is stable, can I check it by comparing whichever produces ...
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Signalling a relation

I have a very basic, trivial question to ask. (I apologise if it is not a worthy problem) I have been trying to formulate an international Economics model where a larger country is trying to signal a ...
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Profit Functions are Homogeneous of Degree 1 in all prices

I'm struggling to understand the intuition behind why the profit function is homogenous of degree one jointly in all prices (i.e. input prices and output prices). the Intuition feels like it should be ...
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Profit Maximizing with a competitive fringe

I have this question: Your business is the dominant firm but there exists a competitive fringe. The competitive fringe produces with total cost: $\; c_𝑓(q_f) = 3𝑞_f$. There have also been some ...
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How to derive the input demand functions from a perfect substitutes production function

I am struggling to derive the input demand functions from a production function with inputs that are perfect substitutes. The production function is as follows: $f(x_1,x_2) = (x_1+x_2)^\frac{1}{2}$ I ...
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Mixed Partial Derivatives in Profit Function

$\pi(x,z) = p(a\ln(x) + b\ln(z)) - w_xx - w_zz$ Question 1: Using the first order conditions, we get: $x = \frac{pa}{w_x}$ $z = \frac{pb}{w_z}$ What do we call these Input demand functions as a ...
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Finding the constraints for a profit maximization program in Acemoglu et al, 2016

I have been reading the paper of Acemoglu et al., 2016 Networks and the macroeconomy : an empirical exploration, and I have been struggling with a maximization programm in the early pages of the ...
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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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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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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}{...
CorporateNationalism's user avatar
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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 ...
ElLl's user avatar
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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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