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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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.
$$ {Q}_{1} = 35 - {P}...
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58 views
Maximization with a binding boundary constraint
I have following profit function -
$$ 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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1answer
53 views
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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55 views
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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57 views
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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1answer
184 views
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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60 views
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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83 views
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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707 views
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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1answer
74 views
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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53 views
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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39 views
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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53 views
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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1answer
81 views
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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1answer
38 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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2answers
216 views
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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42 views
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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57 views
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.
$$\frac{\delta}{\delta Y_t(i)} P_tY_t- \int_0^1 P_t(i)Y_t(i)di = \frac{\delta}{\...
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Example on profit function that contains the maximum of a decision and a random variable
I am looking for an example of a profit function that contains the maximum of a decision and a random variable in this form: $\max(d,X)$, where $d$ is a decision variable and $X$ is a random variable. ...
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1answer
40 views
Profit maximization, when $MC = P$, in a simple supply table and curve
Our economics school book states that the profits of a company are maximized when MC = P.
However, I am having some trouble wrapping my head around that.
For example, I have the following exercise:
...
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46 views
Given $f(x_1,x_2) = \min\{x_1,x_2\}^\alpha$ find the profit-maximizing factor demands, supply function and profit fuction
Given
$$f(x_1,x_2) = \min\{x_1,x_2\}^\alpha$$
I have to find the profit-maximizing demand functions, supply function and profit function but I am not sure how to when the function is given as it is.
...
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196 views
Optimization problem of a Cobb-Douglas function with 3 inputs
A perfectly competitive firm uses 3 inputs to manufacture a certain product according to the following Cobb-Douglas production function:
$$
Q = A L_1^{\alpha_1} L_2^{\alpha_2} L_3^{\alpha_3}
$$
...
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0answers
30 views
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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1answer
518 views
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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1answer
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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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54 views
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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2answers
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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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1answer
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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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1answer
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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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1answer
1k views
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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1answer
158 views
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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2answers
189 views
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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1answer
51 views
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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2answers
65 views
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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1answer
1k views
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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3answers
957 views
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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1answer
58 views
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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3answers
118 views
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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Why equilibrium efficiency wage maximizes worker effort per dollar wage
In the Keynesian model,
to make as much profit as possible, firms will choose the level of the
real wage that gets the most effort from workers for each dollar of
real wages paid
Source: ...
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1answer
44 views
Production function involving profit maximisation
Hi, I don't get how the answer of d is deduced in this question because I don't think I made any mistakes in my calculation and have also used all the information given. After knowing L is 800, I ...
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119 views
Derivation of demand function
Hello.
I'm graduate student in Japan.
This time, what I want to ask is how to solve the profit maximization problem using the image production function and derive the demand function.
This ...
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1answer
705 views
CES production function profit and supply function
I need to derive the profit function for the following CES function: $$ f(z) = (\sqrt{z_{1}^{\rho} + z_{2}^{\rho}})^{1/ \rho}$$ where $\rho \leq 1$. This is the answer that I am supposed to be getting:...
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2answers
368 views
In the real world, how does a firm know their marginal costs and revenue? How do they mathematically calculate MC=MR?
I understand the theory behind it but in practice how is this done?
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Stackelberg with 3 firms
I'm currently trying to solve the following problem:
Stackelberg with 3 firms Imagine there are three firms on a monopolistically competitive
market. The marginal cost of produc- tion in each ...
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0answers
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Finding long run equilibrium price, quantity and number of firms with a linear average cost function
I've been been brushing up on my micoreocnomics lately and I came across a question in Perloff that looked really simple, but for some reason I am struggling to answer:
Assume we are in the long run ...
