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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separability of a profit funtion in outputs and prices [closed]
I want to know how I can show that profit function is separable in factor prices and output prices. I know that the function is homogeneous of degree alpha. I started with the maximization problem ...
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1answer
25 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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1answer
42 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 ...
2
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0answers
36 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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1answer
41 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.
$$\frac{\delta}{\delta Y_t(i)} P_tY_t- \int_0^1 P_t(i)Y_t(i)di = \frac{\delta}{\...
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25 views
Example on profit function that contains the maximum of a decision and a random variable
I am looking for an example of a profit function that contains the maximum of a decision and a random variable in this form: $\max(d,X)$, where $d$ is a decision variable and $X$ is a random variable. ...
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1answer
36 views
Profit maximization, when $MC = P$, in a simple supply table and curve
Our economics school book states that the profits of a company are maximized when MC = P.
However, I am having some trouble wrapping my head around that.
For example, I have the following exercise:
...
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34 views
Given $f(x_1,x_2) = \min\{x_1,x_2\}^\alpha$ find the profit-maximizing factor demands, supply function and profit fuction
Given
$$f(x_1,x_2) = \min\{x_1,x_2\}^\alpha$$
I have to find the profit-maximizing demand functions, supply function and profit function but I am not sure how to when the function is given as it is.
...
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0answers
57 views
Optimization problem of a Cobb-Douglas function with 3 inputs
A perfectly competitive firm uses 3 inputs to manufacture a certain product according to the following Cobb-Douglas production function:
$$
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
102 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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vote
1answer
575 views
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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1answer
38 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
38 views
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, ...
0
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1answer
48 views
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
29 views
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
324 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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102 views
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
153 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
151 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 ...
1
vote
1answer
45 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. ...
0
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2answers
60 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
606 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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2answers
575 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:
...
0
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1answer
56 views
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 ...
1
vote
1answer
52 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
111 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 ...
1
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0answers
40 views
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: ...
0
votes
1answer
40 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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0answers
111 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 ...
2
votes
1answer
440 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
181 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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2answers
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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 ...
2
votes
0answers
1k views
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 ...
0
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0answers
277 views
Question about an economy with 3 components household, firm and government with functions given
I've spent considerable amount of time on this question, in vain. It is from one of the competitive exams for admission to a grad econ program. Help would be tremendously appreciated. Thanks.
An ...
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0answers
28 views
Question on Finding the Correct Emission Tax $t$
Let there be two companies $U_{1}$ and $U_{2}$ where, initially $U_{1}$ produces and sells $x$ units at $p=18$. Production costs are $C_{U_{1}}(x)=\frac{1}{6}x^3$ and in the process $a$ units of ...
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1answer
35 views
Effect of changing MC on monopolists' maximised profits
Let a monopolist have constant MC = c, with no fixed costs. If $p(c)$ and $q(c)$ are the profit maximising price and output as a function of MC and the market demand schedule is given by $q = D(p)$, ...
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0answers
173 views
Profit maximization problem using linear regression (pooled OLS)
I'm currently on a university assignment where I'm stuck more or less in the middle. I have to answer the following problem:
Suppose you are interested in estimating the production function for ...
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votes
1answer
282 views
Maximizing a Cobb-Douglas Function
Suppose that a competitive firm receives a price of $P$ for its output, and pays prices of w, r and v for its labor $(L)$, capital $(K)$ and natural resources $(R)$ inputs, respectively. The firm ...
2
votes
0answers
117 views
Convexity of profit function
The profit function is convex in prices. Are there any conditions under which it is linear in prices? (The property as written in most books doesn't mention strict convexity, so it seems to suggest ...
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1answer
3k views
Profit maximization and returns to scale relation
Suppose we have 2 inputs a and b , output is y=f(a,b).
In the long run, let us suppose profits are maximized at a* and b*.
Profit is py-wa-kb[p is price and w and k are constants]. Now for max profit, ...
2
votes
3answers
130 views
Is “$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$” always true?
For the productions $f(k,l) $ that are continuously differentiable, is the proposition that
"$f(k,l)$ is decreasing return to scale $\Leftrightarrow f_{ll}f_{kk}-f_{kl}^2>0$"
always true, I have ...
4
votes
1answer
239 views
Decision over “max” production function:
I've been presented with the following problem:
$$y=3(x_3)^{\frac13}(\max\{x_1,8x_2\})^{\frac13}$$
And the objective is to both maximize profit and minimize cost. First of all, if the problems are ...
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1answer
23 views
Understanding the use case of farming crickets in developed countries
Currently, farming crickets is quite labor intensive.
No wonder that if you compare prices, in developed countries you get crickets at say \$100/kg, while in Thailand they cost under \$2/pound, in an ...
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2answers
31 views
2 firms production decision for one agent
I'm trying to solve the optimal production $\{x,y\}$ for a risk neutral agent with weight $w$ in firm $X$ and weight $1-w$ in firm $Y$. Each firm has marginal cost $c^X$ and $c^Y$ respectively. The ...
0
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1answer
22 views
When to invest into additional products?
This is a very applied question so I hope it's the correct adress here for it:
I'm running a small entertaining business for virtual reality experiences. Investment was about 120 k. I now build it ...
4
votes
4answers
225 views
If house prices appreciate, why do developers sell them?
In many parts of the world, people buy a house expecting its value to increase over time.
But if is widely believed that the building's value will increase, what incentive is there for the developer ...
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1answer
441 views
Profit maximization and allocative efficiency result
I completely stuck to the last part of this exercise. I cannot understand how can I determine an allocative efficiency result.
Any help will be appreciated. Thank you.
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2answers
864 views
Question on profit maximization with government taxation
(I) A monopolist has a cost function $c(q)=q$. It faces the following demand function $ q(p)=100/p$ for $p\le 20$ and $q(p)=0$ for $p\ge 20$. What are the profit maximizing price and output.
(ii) a ...
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1answer
46 views
How to calculate the optimal wage and the optimal rent on capital in an economic model?
In Dhondt & Heylen (2009)*, they specify a certain production function.
Under some standard model assumptions such as perfect competition and so on, they calculate the optimal wage as
$$ w_t = \...
