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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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 ...
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How to prove that profit function is convex in price (with smaller price)?

According to this site, if output price increases from $p*$ to $p'$ and factor prices remain constant, then a new production bundle chosen must yield at least the same amount of profits as the old ...
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Revenue maximization problem

There are $N>0$ Households in an economy. The government has aim to maximize a weighted average of income by imposing tax on the rich people and redistribute the tax revenue to the labor ones. ...
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A profit maximization problem (whole problem has been solved, I just have question about interpretation)

I would like to discuss with you about the following production function. $$y=f(t_m, t_l)=\rho t_m^m(n+t_l)$$ where $0<m<1 $ and $n>0$ are fixed parameters. $t_m$ is manager time. $t_l$ ...
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Utility function_maximazation [closed]

A consumer is deciding about her hours ($h$) and consumption ($c$), her preference over bundles of work and consumption are as follows: $U(c,h)= c + \sqrt{24-h}$ The consumer would get an hourly wage ...
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Why does the profit function in standard neoclassical theory have exactly one maximum?

In neoclassical theory is said that the highest profit occurs when Marginal Cost equals Marginal Revenue, but this condition wouldn't be enough to determine the maximum if there were more than one. ...
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profit-maximization

I'm having trouble on my homework and I need some help. A company sells products in a perfectly competitive market, where the price is $p = 24.$ For each of the following cost functions, write down ...
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Can I get a more detailed explanation of the Weak Axiom of Profit Maximization?

In Hal Varian's Book "Microeconomic analysis" on page 35 he gives the following description of a profit maximising firm. "...If the firm is maximising profits, then the observed net output choice at ...
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Opportunity profits vs. opportunity costs

Having learned that Opportunity costs = the costs for avoided profits are a well established and quite useful economic concept, I wonder how its counterpart is officially called and investigated: ...
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Maximizing units under a budget constraint and increasing costs

Consider two columns. Column A has total cost per day, Column B has units bought that day. The marginal cost of each unit is increasing because of limited supply. My goal is to estimate total ...
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Value Function For Durable-Good Monopolist with General Distribution

It is known that with a unit mass of consumers, each of whom has a value distributed between 0 and 1, one can think of the monopolist solving \begin{equation} \max_{p} \ p[1-F(p)] \end{equation} when ...
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Why are there not more competitive nonprofits?

For example, when I go to the grocery, and peruse the various goods for sale on the shelves, there is at least a 99.9% chance that any given product is produced for-profit. Even "Newman's Own", which ...
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