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.
134
questions
0
votes
1
answer
21
views
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 \...
- 283
0
votes
0
answers
15
views
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 ?
...
- 3
0
votes
2
answers
49
views
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 ...
0
votes
0
answers
15
views
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 ...
- 3
1
vote
1
answer
55
views
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×(...
- 11
0
votes
1
answer
59
views
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 ...
1
vote
1
answer
112
views
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 ...
- 499
1
vote
0
answers
36
views
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 ...
- 499
0
votes
1
answer
219
views
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 ...
- 897
1
vote
1
answer
107
views
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 ...
- 21
1
vote
1
answer
391
views
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 ...
- 25
1
vote
1
answer
98
views
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 ...
- 897
0
votes
1
answer
61
views
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][1], and I have been struggling with a maximization ...
- 1
3
votes
2
answers
161
views
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.$$
Society has 10 units of ...
1
vote
1
answer
50
views
How to properly annualize cost of initial investment
Let say you manage a supermarket chain and want to estimate profitability of a store over time, not only by using revenue and cost for a given unit of time - but also to include the initial investment ...
- 111
1
vote
0
answers
28
views
Source for maximising profit of a company
I was wondering if anyone could point me in the direction of a source, like a case study, where profit was maximised for a real (simple) company. I'm learning calculus for economics and a real life ...
- 11
0
votes
0
answers
22
views
Monopoly problem: optimal quantity of production
I have this problem that I thought I could solve easily, but the solutions are different from the real ones...
Mediterchimica s.p.a. is the leader in the Mediterranean ethylene market and its demand ...
0
votes
0
answers
27
views
Problem about production costs
I have this problem to solve:
The AOE (Association of Entrepreneurs) has decided to set up a tax and accounting assistance center for its members. Obviously, the volume (Q) of assistance that can be ...
1
vote
1
answer
43
views
Show that the marginal cost of the total output equals the marginal cost of individual plant's outputs
Assume that the maxima/minima exists wherever referred (i.e., the necessary secondary conditions are satisfied). $p$ is the inverse-demand, $c_i(q_i)$ are the cost functions of the plants that a ...
- 13
3
votes
1
answer
270
views
Does profit maximization imply cost minimization in both pure competition and monopoly?
How do I show that profit maximization implies cost minimization (in pure competition)?
Suppose we only consider inputs $l,k$ whose prices are $w,r$ and output price $p$. Profit is $\pi = pf(k,l) - wl ...
- 366
0
votes
0
answers
59
views
Finding cost function
The production function is as follows
$$f(z)=(z_1+z_2)(z_3+z_4)$$
Find the cost function?
What I did is as follows. But I am not sure about my solution. How do you solve it?
*duplicated question
- 120
1
vote
2
answers
283
views
Is P > AC under monopoly?
I would like to know why price is greater than average total cost under monopoly. In textbooks, average cost is drawn under monopoly price. However, if the fixed cost is so large, can monopoly get ...
- 35
0
votes
3
answers
432
views
Why is a firm's profit maximized when MC=MR? Why not stop one unit before where it will still make a profit?
It seems that an equilibrium where MC<MR is preferred to one where MC=MR since in the case of the latter the firm still makes a profit.
Put differently, why would a firm produce a unit at all if it ...
- 573
1
vote
1
answer
58
views
How can I choose how much to invest in each stock of my portfolio?
I'm trying to find a mathematical way to decide what percentage of my capital I should invest in each stock of my portfolio to maximize my profit.
Here's my attempt to the solution:
Let's say my ...
- 11
2
votes
1
answer
309
views
Competitive equilibrium for an economy with a consumer and a producer
A representative agent’s preference over consumption $(c)$ and labour supply $(l)$ is given by the utility function $$ u(c_D, l_S)= c_D^a .(24-l_S)^{1-a}$$
Production of the consumption good $c$ is ...
- 23
7
votes
1
answer
93
views
Complement in production and the slope of factor demand curves
Considering a firm taking prices for granted and maximizing profits
$$pf(x_1,...,x_K) - \sum_{i=1}^K q_i x_i,$$
where $f$ is strictly concave. Furthermore, let the factor demand curves be the ...
- 3,286
1
vote
1
answer
102
views
On the profit maximization assumption: When it fails, does it fail gracefully?
This question was inspired by a comment on another question:
A basic cost-benefit analysis between two scenarios
My question is: Is profit maximization generally a good assumption for analyzing the ...
- 391
1
vote
1
answer
65
views
Leisure and consumption maximization trouble
Not really sure how to to b). For a) I have (wh + Y – τwh) which I'm sure is fairly simple. I've never dealt with a utility function this complicated before and really confused by the notation in ...
- 11
4
votes
1
answer
41
views
Bid-rent function in The Microgeography of Housing Supply
I came across the paper "The Microgeography of Housing Supply" (Baum-Snow, 2020)(https://luhan2.weebly.com/uploads/9/6/0/8/96080580/housing_supply_julyb2020.pdf) and I must admit that I do ...
1
vote
0
answers
23
views
In the real world, do companies try to maximize return via maximizing profits or maximizing profits/costs (or neither)?
Suppose I buy $s$ shares of a stock at price $p_0$ and then later sell at price $p_t$. The initial and final values of my investment are then $I_0=sp_0$ and $I_t=sp_t$ respectively. The return is then
...
- 3,454
1
vote
1
answer
26
views
Investigating the firm's supply function
Suppose the firm has a minimum cost function $C(\vec{w}, q)$ and sets up the following profit maximisation problem:
$max_{q} \text{ } pq - C(\vec{w}, q)$. The below FOC characterises the solution:
$p =...
- 57
1
vote
0
answers
17
views
A profit max problem in a segmented market with a transfer fee
This must be a standard profit maximization problem, but I'm not seeing an example in my textbook. We have a monopolized market in two segments, each with its own demand function.
$$ {Q}_{1} = 35 - {P}...
- 309
0
votes
1
answer
98
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 ...
- 499
1
vote
1
answer
60
views
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{...
- 309
0
votes
1
answer
58
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 ...
- 103
0
votes
1
answer
84
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 ...
- 45
3
votes
1
answer
58
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}$ ...
- 95
7
votes
1
answer
789
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 ...
- 155
0
votes
0
answers
109
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 ...
- 400
5
votes
1
answer
95
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 ...
- 1,781
0
votes
2
answers
2k
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-...
- 145
3
votes
1
answer
111
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 ...
- 165
1
vote
2
answers
147
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}{...
1
vote
1
answer
51
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 - ...
- 123
0
votes
0
answers
54
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 ...
- 1
1
vote
1
answer
123
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?
...
user31331
0
votes
1
answer
45
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 ...
- 57
3
votes
2
answers
403
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 ...
- 145
2
votes
0
answers
47
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 ...
- 485
0
votes
1
answer
79
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}{\...
- 5