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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14
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1answer
2k views

First Order Condition for Profit Maximization in Gambling Industry

I am working on a model of optimal payout percentages in the gambling industry. Because the nominal price of a \$1 ticket is always \$1, we use an effective price strategy where Q = \$1 in won ...
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2answers
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Monopolies are just a mathematical misunderstanding

A little head-scratcher (and a good example why we should be careful with notation). Consider a profit maximizing monopoly, that solves over price $$\max \pi = PQ(P) - C(Q(P)) \tag{1}$$ Following ...
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1answer
295 views

How does Google price the items on Google Play?

I am a fledgling computer science researcher working in intersection of economics and computation. Please excuse me if this question seems out of place to the administrator. I am currently studying ...
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Can destruction be profitable?

We often see news that some company destroys items they couldn't sell in time. Also we can see news of supermarkets destroying food just because it's not fresh although it's perfectly edible. If ...
7
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1answer
102 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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3answers
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Why are firms taken to be profit-maximizing? Shouldn't that make them risk-neutral?

Intro texts normally explain that insurance firms (casinos, etc.) "work" by diversifying risk from many clients. Unsaid, then, seems to be that risk is bad for both firm and client. But why should a ...
5
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1answer
77 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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2answers
858 views

Neoclassical economic profit and growth theory versus marxian

Marxists have a very specific "profit" and "economic growth" theory. According to marxists, profit doesn't come from technology, whose cost will be reflected in the price of whatever commodity the ...
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4answers
361 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 ...
4
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1answer
318 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
1k views

Could someone please explain the proof of Hotelling's lemma?

According to https://en.wikipedia.org/wiki/Hotelling%27s_lemma, the maximum of the firm's profit at some output is given by the minimum of the difference between the profit and the revenue. However,...
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2answers
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Optimize by MR = MC vs TR = TC

I know that I should optimize production by solving $MR = MC$ with respect to $Q$. But if $TR > TC$, I am making a profit. Why is not enough to just solve $TR = TC$ with respect to $Q$?
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139 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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1answer
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
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The relationship between gross profit and tax

I tried to do following question but I am not sure about my solution. Please tell me your opinions Since gross profit is strictly concave, I can say that $R’’(y)-C’’(y) <0$ Now I maximize the net ...
3
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1answer
72 views

Profit maximization under uncertainity

I have a seller say S and I have a buyer say B. Buyer’s willing to pay is equal to x which is private information. But Seller believe that it falls in the range [0,x1]. Seller’s belief distribution is ...
3
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1answer
758 views

Homothetic production function and Profit Function

I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as C(w,y)=h(y)C(w,1). Can some one help me derive ...
3
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1answer
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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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0answers
51 views

How do organisations diversify? Determinants of choosing new target industries

A very weird question I agree. I am interested in understanding the motives behind firm behaviours of diversification. Why would some firms choose new target sectors/activities? Is there any ...
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135 views

Appropriate economic/econometric tools to analyze segmented promotion optimization problem

I'm trying to determine which micro-economic/econometrics concepts, models, and/or tools are appropriate for an analysis of promotions. Below I Describe the problem in general terms Give ...
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3answers
829 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: ...
2
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1answer
404 views

Profit Function: Just revenue maximization subject to constraint? if so where is $\lambda$?

Disclaimer: I dont know i'm getting confused with basic microeconomic prodoucer theory (note: Ive been watching some Hak Choi Videos on youtube),but this is my overall thought process. We know that ...
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1answer
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Why is AC = MC in the monopoly?

Using the Microeconomic Theory Basic Principles and Extensions, Nicholson, W. and Snyder, C., I've reached to the point where Monopoly and Imperfect Competition is discussed (Chapter 14 and 15 to be ...
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2answers
3k views

Utility maximization question setting up.

Consider a consumer whose preferences can be represented by the following utility function: $$u(x_1,x_2)=\dfrac{x_2}{(1+x_1)^2}.$$ Assume the agent's income is $y=5$. The price of one unit ...
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1answer
574 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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1answer
177 views

Expectations in Gali's classical monetary model

In Gali chapter 2 we have the following constraint to the classical monetary model $P_t C_t + Q_t B_t \leq B_{t-1} + W_t N_t-T_t$. Then it seems that this is treated as an equality. Therefore my ...
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3answers
136 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 ...
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1answer
120 views

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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1answer
224 views

Help with this microeconomics exercise

The question: A price-taking farmer produces a crop with labor L as the only input. His production function is:$$F(L) = 10L^{1/2} − 2L$$ He has 4 units of labor in his family and he cannot hire ...
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2answers
190 views

How come websites such as Khan Academy and Anatomy Zone do not charge for their services?

I've noticed that most educational websites do not charge for their services, even if they are maintained by only one or very few people. Some of these websites are so comprehensive that they require ...
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2answers
9k views

Find the optimal demand functions for capital and labour for this firm

I'm trying to solve this question which states: Suppose that a profit maximizing producer has a production function described by Q = K^3/4 L^1/4 and faces the general isocost line (TC = rK + wL). ...
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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 ...
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1answer
296 views

Cournot equilibrium question

There are two firs in the market. They produce perfect substitutes at cost $c(y_i)=y_i/3$ for i=1,2. The demand function is $p=1-(y_1+y_2)$ Consider the Cournot competition where firms ...
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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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118 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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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 ...
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129 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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2answers
312 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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1answer
33 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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1answer
1k 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
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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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1answer
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Profit maximization with Cobb-Douglas function

I'm trying to maximize a firm's profit given the production function $F(L,K)=L^\alpha K^\beta$ (where $L$ is labor and $K$ is capital) and that $\alpha + \beta \neq 1$. So, I know that this ...
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1answer
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Duality of cost minimization and profit maximization

The firm tries to maximize profits $\Pi$ \begin{align} \max_{K,L}\{\Pi(K,L) = F(K,L) - RK - wL\} \end{align} where $F$ is the linear homogeneous production function, $R$ the rental rate of capital $K$...
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2answers
74 views

What is this economic theory? Cost of investment vs production accounting for time?

I know there has got to be a standard set of theories or formulas to chart this but I don't know how to search for it. Other than a great place like this. :) I'm a software developer and not an ...
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1answer
4k 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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1answer
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Cartel profit maximizing quantity question (Cournot game)

Find the Nash equilibrium of Cournot’s game when there are two firms, the inverse demand function is P(Q) = α – Q when α ≥ Q and 0 otherwise, and the cost function of each firm I is Ci(qi) = qi2. If ...
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2answers
176 views

Profit Maximisation if MC is still falling after intersecting MR

really basic one here, I am just in the process of re-covering old ground. I understand that for any profit maximising firm FOC: MC=MR SOC: MR'< MC' But suppose MC has a minimum beyond the ...
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1answer
157 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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1answer
905 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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1answer
54 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 ...