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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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Optimization with a Cobb-Douglas and demand function

I have a Cobb-Douglas-like function for a product consisting only of material a and material b (for example $a^{0.2}b^{0.8}$) and I know the unit prices of both a and b. I also have a demand function (...
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23 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
56 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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1answer
40 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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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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87 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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220 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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21 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
24 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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65 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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1answer
136 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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53 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
993 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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3answers
107 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
71 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
22 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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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
140 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
253 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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498 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
23 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
73 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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177 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
77 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
191 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
187 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
103 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
2k 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
56 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
75 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
57 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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39 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
874 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
58 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
520 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
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
1k 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
124 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
165 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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809 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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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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193 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
257 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
160 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
1k 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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136 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 ...