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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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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273 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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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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139 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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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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58 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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479 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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472 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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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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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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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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109 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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389 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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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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972 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 ...
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275 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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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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34 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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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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273 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 ...
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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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2k 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, ...
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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 ...
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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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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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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 ...
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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 ...
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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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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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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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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 = \...
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When do firms pursue the cost minimization objective instead of profit maximization? Are there any intuitive/practical examples/reasons?

I understand that profit maximization implies cost minimization, that is, if a firm is maximizing profits, it will definitely minimize costs. However, under what conditions does cost minimization ...
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Firm's profit max problem, in present value terms

So I am kinda stuck on this question. The question goes as follows: Consider a multiperiod firm, selling q1 units of a product in period t=1 at spot price P1 and q2 units in period t=2 at spot price ...
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How to work out Price with only the Derivative of Profit Function?

Best response functions are obtained by differentiating a profit function and solving for q. In equilibrium, the firms produce 30. But, there's no inverse demand function, so how would equilibrium ...
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398 views

Revenue maximization

We have two firms with identical cost structure compete in a market Demand function = $p=a-bq$ And $q=q_1+q_2$ They are identical in every way. However, firm 1 maximizes profit and firm 2 ...