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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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How to calculate quantity from a cubic cost function?

The problem goes: (Perfect competition) The current price of your product is 10. The cost function is: $$ C(Q)= 26Q - 5Q^2 + \frac{1}{3}Q^3 $$ Calculate the quantity to produce in the short run if ...
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0answers
33 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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0answers
14 views

Comparative Statics of Isoprofit line

So in Intermediate Microeconomics by HL varian, I was reading short run profit maximization( two goods with one good fixed and the other variable) They have given that "changing the price of factor ...
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1answer
36 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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30 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
313 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
34 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, ...
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1answer
63 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
20 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
28 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 ...
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0answers
28 views

Profit maximization under stochastically independence

Consider a risk-neutral profit-maximizing firm that produces output y from input x using the technology y = f(x), f’(x) > 0 and f’’(x) < 0. It is possible to ob-tain x from two sources: either ...
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1answer
20 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 ...
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4answers
124 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
187 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
196 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
19 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 = \...
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1answer
55 views

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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127 views

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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1answer
32 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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0answers
24 views

I'm having problems with determining price and profit maximization in Cournot example?

Hello, in the graph i provided we used 2 firms, Samsung and LG. LG produces 50 units. Then we have the residual demand curve which shifts left by 50 units because of that. However, as I understood, ...
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1answer
166 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 ...
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1answer
114 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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1answer
69 views

Profit maximization question

Two firms are in a market together. They produce a product. Total revenue from sales is $y=K+L$ K is the amount of capital L is the amount of labor These two firms each specialized in supplying ...
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2answers
890 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
44 views

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 ...
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1answer
55 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
56 views

How to prove that a point is a maximum point

I have the following function: $$ \Pi =\int_{0}^{z}[x_{1} + \alpha y + \alpha \frac{N-2}{2}y - \beta(z) - \gamma ( \beta(z) - \beta(y))](N-1)y^{N-2} dy $$ The first derivative with respect to $z$ is:...
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77 views

Maximizing utility function (auction theory)

There are two bidders (two individuals). Bidder 1 wants to maximize the following function (his utility function): $$ u_{1}(V,b_{1} | b^{w}) = \begin{cases} x_{1} + x_{2} - b_{1} & \quad ...
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0answers
36 views

How to find right MRP_L in this economic problem?

Economic problem from my textbook (here is my translation from Russian): There is a firm that is both monopoly and monopsony. It's monopoly on market of its product and it's monopsony on labor market ...
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1answer
376 views

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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1answer
54 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 ...
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1answer
463 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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2k views

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
757 views

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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2answers
31 views

How do calculate whether selling a product leads to profit?

To simplify things, imagine a company which sells two products, A, and B, and it has two types of revenues, two types of variable costs, and 1 type of fixed costs. I can calculate margins by taking ...
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1answer
108 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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1answer
154 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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637 views

Profit maximisation and cost minimization [closed]

Does profit maximisation always imply cost minimisation ? And Does cost minimization always imply profit maximisation ? Can we prove both the results ??
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963 views

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 ...
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1answer
39 views

What does this condition for a profit of a firm exist mean?

What is the intuition behind this? Let $Y=zF(K,N)$ be a production function. For a profit to exist Indana conditions must hold and : $$\frac{∂^2zF(K,N^d)}{\partial K \partial N} > 0$$ I ...
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0answers
156 views

How Would a Firm Which Produces a Giffen Good Maximize Profits?

I am curious as to how a firm which produces a giffen good would maximize profits? Having an upward sloping demand curve seems to imply that we cannot guarantee that there exists a quantity where ...
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1answer
219 views

Why do firms adjust their fixed costs in response to a change in price in a perfectly competitive market?

When firms make a profit in a perfectly competitive market, new firms enter the market and drive the price down. My textbook says that the existing firms will then adjust inputs that are fixed in the ...
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2answers
149 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
951 views

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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116 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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485 views

Monotonic Transformation

How does positive monotonic transformation of production function effect the resulting profit function? For example if we had production function $f(x) $ and that gave profit function $\pi(p,w)$. Now ...
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1answer
435 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 ...
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2answers
528 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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1answer
697 views

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
57 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 ...