# 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 ...
1 vote
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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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1 vote
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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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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 ...
1 vote
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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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### 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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### 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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1 vote
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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? ... 43 views

### 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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### 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, ...
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 ...