What is Cost function: Definition and 23 Discussions

In economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible level of production, and the result is a cost curve. Profit-maximizing firms use cost curves to decide output quantities. There are various types of cost curves, all related to each other, including total and average cost curves; marginal ("for each additional unit") cost curves, which are equal to the differential of the total cost curves; and variable cost curves. Some are applicable to the short run, others to the long run.

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  1. SaschaSIGI

    I Question about the Difference between Loss and Cost Functions in Quantum Computing

    Hello, Im currently hearing a module about quantum computing and Im wondering what is the difference of a loss and cost function for variational quantum algortihms? Both functions also can be presented into a loss/cost landscape? Are they the same ? Already a big thank you for all the upcoming...
  2. Z

    Derivative of Cost Function with Respect to Output Layer Weight

    This is an issue I've been stuck on for about two weeks. No matter how many times I take this derivative, I keep getting the same answer. However, this answer is inevitably wrong. Please help me to understand why it incorrect. To start, I will define an input matrix ##X##, where ##n## is the...
  3. W

    I Newton-Raphson in Least Squares: How is it used? Cost Function?

    I just went over analysis of a data set that was analzed using Linear Regression (OLS, I believe) and I saw Newton's method was used. Just curious, how is it used? I assume to minimize the cost function, but this function was not made explicit. Anyone know? Thanks.
  4. M

    MHB Negative minimum of the average variable cost function

    Hey! :o Can the minimum of the average variable cost function be negative? (Wondering) Suppose we have the cost function $K(x)=x^3-9x^2+11x+100$. The variable cost function is then $K_v(x)=x^3-9x^2+11x$. The average variable cost is $k_v(x)=\frac{K_v(x)}{x}=\frac{x^3-9x^2+11x}{x}=x^2-9x+11$...
  5. Dethrone

    MHB Optimizing Linear Regression Cost Function

    I'm trying to optimize the function below, but I'm not sure where I made a mistake. (This is an application in machine learning.)$$J(\theta)=\sum_{i=1}^n \left(\sum_{j=1}^{k}(\theta^Tx^{(i)}-y^{(i)})_j^2\right)$$ where $\theta$ is a $n$ by $k$ matrix and $x$ is a $n$ by 1 matrix...
  6. E

    Can CNNs Be Tuned to Enhance Specific Texture Parameters in Image Simulation?

    Hi I am using a convolution neural network (with inversion) to simulate images with the same "texture" as the input image, using a random image to start with. The activations of the CNN are first learned with an example or source image. A cost function then minimizes the difference between the...
  7. E

    A Understanding the Cost Function in Machine Learning: A Practical Guide

    Could someone please help me work through the differentiation in a paper (not homework), I am having trouble finding out how they came up with their cost function. The loss function is L=wE, where E=(G-Gest)^2 and G=F'F The derivative of the loss function wrt F is proportional to F'(G-Gest)...
  8. R

    How to interpret Cost Function?

    I am just starting a course about machine learning and I don't know how to interpret the cost function. When the teacher draws the straight line in the x and y coordinates, it looks like: I see that theta zero is the start of the straight line (in the left side) in the Y coordinate. The...
  9. 2

    Neural networks and the derivatives of the cost function

    Hello. I need some guidance on the derivation of the derivatives of the quadratic cost function (CF) in an artificial neural network. I can derive the equations for the forward propagation with no trouble but when it comes to finding the derivative of the CF with respect to the weight matrix...
  10. E

    What is the Appropriate Cost Function for a Start Up Business?

    Homework Statement Trying to determine appropriate cost function for my start up. Usually total cost= fixed costs + per unit cost* Q. However, it is usually assumed your fixed costs are monthly recurring costs, like rent, utilities, etc. Many of the costs we face are one time development costs...
  11. MarkFL

    MHB Marty's question at Yahoo Answers regarding minimizing a cost function

    Here is the question: I have posted a link there to this topic so the OP can see my work. edit: Unfortunately, the OP deleted the question before I had a chance to post my response there.
  12. B

    Reformulating a simple cost function - combining 2 variables

    Hi there, I have an equation below for the cost of energy for a house per hour. The house has an energy storage system (i.e.a very large battery) installed. You can charge the battery up and energy from the battery can be used to power the building. For example you can charge the battery...
  13. MarkFL

    MHB Jesus' question at Yahoo Answers regarding finding total cost function

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  14. 9

    Find long-run cost function, given production function

    I am completely lost... Production function: Q = L + K Given a hint that there are three answers, depending on the slope of the isocost line... ?
  15. T

    Simplex minimization problem reformation with modulus cost function

    Homework Statement If I said minimize the cost function |a-2b| + |-3a-b| subject to 2a + b <= 6 a,b >= 0 We can all see it's 0,0 but if I want to apply the simplex algorithm to it, how do I reformulate the problem into something I can use Homework Equations The Attempt at...
  16. J

    Logistic Regression Cost Function

    Hi, I am studying logistic regression and gradient ascent and have seen it used with a cost function and without one. Could anyone tell me why you would use a cost function? It seems just as effective without one. alpha = .05 h = data * weights error = labels - sigmoid(h)...
  17. A

    Minimize an cost function involving an integral

    Homework Statement The objective is to minimize J(x) = \int y^2 (x+y)^2 dy, where x is the design variable.The Attempt at a Solution I first integrate over y to get J(x) = \frac{x^2 y^3}{3} + \frac{y^5}{5} + \frac{2x y^4}{4} Now, I differentiate over x, and solve for the minimizer, the...
  18. W

    Model predictive control variable Cost function

    Hi all, I have a MIMO system which I have developed in Simulink and I have also work out the Model predictive control for it. Now I have a manipulated variable which I want to be used during night and remained turned off during day. I have tried but could not figure out how to do this in...
  19. K

    How to minimize the cost function

    Homework Statement The cost function: E(Cost)=E(F-LS)3 F is for Finished goods L is for Lambda S is for Sales After expanding the function, what assumption minimized this function with respect to F? The Attempt at a Solution F3-3F2LS+3F(LS)2-(LS)3 I know that I need to...
  20. I

    Microeconomics cost function question.

    q = 3K^0.5 L^0.5 where q is the number of engines per week, K is the number of machines, and L is the number of labor. Each assembly machine rents for r = $9000 per week, and each team costs w = $4000 per week. Engine costs are given by the cost of labor teams and machines. Suppose the...
  21. C

    Minimizing cost function Statistics

    Homework Statement Let X and Y be two unknown variables with E(Y)=\mu and EY2 < \infty.Homework Equations a. Show that the constant c that minimizes E(Y-c)2 is c=\mu. b. Deduce that the random variable f(X) that minimizes E[(Y-f(X))2|X] is f(X)= E[Y|X]. c. Deduce that the random variable f(X)...
  22. 4

    Given an average cost function, calculate output level

    A firm faces the following Average Cost function: AC=50q^-1 +30-1.5q+0.125q^2 Calculate the output level (q) which minimzies a) Average Variable cost How do i find this out if i don't know the amount of fixed cost? b) Marginal cost Total cost=50+30q-1.5q^2+0.125q^3...
  23. Z

    Optimizing Fuel Cost for a Truck on a 400 Mile Trip

    I was wondering if anyone can help me on this problem... A truck burns fuel at the rate of G(x) gallons per mile. Where G(x) = \frac {1} {32} \left(\frac {64}{x} + \frac {x}{50} \right) a. Find the cost function C(x) if the truck takes a 400 mile trip. Assume that the cost of fuel...
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