In economics, marginal cost is the change in the total cost that arises when the quantity produced is incremented by one unit; that is, it is the cost of producing one more unit of a good. Intuitively, marginal cost at each level of production includes the cost of any additional inputs required to produce the next unit. At each level of production and time period being considered, marginal costs include all costs that vary with the level of production, whereas other costs that do not vary with production are fixed and thus have no marginal cost. For example, the marginal cost of producing an automobile will generally include the costs of labor and parts needed for the additional automobile but not the fixed costs of the factory that have already been incurred. In practice, marginal analysis is segregated into short and long-run cases, so that, over the long run, all costs (including fixed costs) become marginal. Where there are economies of scale, prices set at marginal cost will fail to cover total costs, thus requiring a subsidy. Marginal cost pricing is not a matter of merely lowering the general level of prices with the aid of a subsidy; with or without subsidy it calls for a drastic restructuring of pricing practices, with opportunities for very substantial improvements in efficiency at critical points.If the cost function
C
{\displaystyle C}
is continuous and differentiable, the marginal cost
M
C
{\displaystyle MC}
is the first derivative of the cost function with respect to the output quantity
Q
{\displaystyle Q}
:
M
C
(
Q
)
=
d
C
d
Q
.
{\displaystyle MC(Q)={\frac {\ dC}{\ dQ}}.}
The marginal cost can be a function of quantity if the cost function is non-linear. If the cost function is not differentiable, the marginal cost can be expressed as follows:
M
C
=
Δ
C
Δ
Q
,
{\displaystyle MC={\frac {\Delta C}{\Delta Q}},}
where
Δ
{\displaystyle \Delta }
denotes an incremental change of one unit.
Hi,
I have question about finding marginal distributions from 2d marginal pdfs that lead to the probabilities being greater than 1.
Question:
If we have the joint probability distribution ## f(x, y) = k \text{ for} |x| \leq 0.5 , |y| \leq 0.5 ## and 0 otherwise. I have tried to define a square...
I am curently working on Forecast in cosmology and I didn't grasp very well different details.
Forecast allows, wiht Fisher's formalism, to compute constraints on cosmological parameters.
I have 2 issues of understanding :
1) Here below a table containing all errors estimated on these...
Homework Statement
Homework Equations
marginal revenue[/B] (R') is the additional revenue that will be generated by increasing product sales by one unit
The Attempt at a Solution
I don't know how to start. Q is the number of items sold at price x. y is the marginal cost, the cost of...
Homework Statement
f(xy)=49/8*e^(−3.5*y) 0 < y < inf and −y < x < y
0 otherwise
a. Find the marginal probability density function of X, fX(x). Enter a formula in the first box, and a number for the second and the third box corresponding to the range of x. Use * for multiplication, / for...
Homework Statement
Two components of a laptop computer have the following joint probability density function for their useful lifetimes X and Y (in years):
f(xy)=xe^(−x(1+y)) 0 <= x <= y
0 otherwise
Find the marginal probability density function of X, fX(x). Enter a formula below. Use * for...
Let $$X_1,\dots,X_n$$ be i.i.d $$N(\mu,\sigma^2)$$. What is the marginal pdf of $$\sum_{i=1}^n (X_i-\overline{X})^2$$.
I'm guessing it's some sort of chi square distribution but how to find this I am unsure. Thanks
Hello. Can you help me figure out how to pass, integrating, by the marginal cost: $MC_{i}(q)_{i}=q_{i}+10$ to the total cost: $TC=\frac{1} {2}q_i^2+10q_{i}$?
$i=1,2$, are the two companies. $q_{i}$ is the quantity. What are the calculations?
Speaking just of long straight wires, not loops, coils or solenoids.
Ideal wires have no resistance. Of course they would have no capacitance. And real wires have some very small amount of inductance, no?
Firstly, would an ideal wire have some ideal nonzero inductance? Why/why not? After all...
Homework Statement
Determine ##P(X<Y|x>0)##
Homework Equations
X and Y are random variables with the joint density function
$$
f_{XY}(x,y)=
\begin{cases}
4|xy|,-y<x<y,0<y<1\\
0,elsewhere
\end{cases}$$
The marginal densities are given by
$$
f_X(x)=2x\\
f_Y(y)=4y^3
$$
The Attempt at a Solution...
Homework Statement
Consider two random variables X and Y with joint PMF given by:
PXY(k,L) = 1/(2k+l), for k,l = 1,2,3,...
A) Show that X and Y are independent and find the marginal PMFs of X and Y
B) Find P(X2 + Y2 ≤ 10)
Homework Equations
P(A)∩P(B)/P(B) = P(A|B)
P(A|B) = P(A) if independent...
If there are X and Y two random variables. The pdf of Y is f(y), and conditional pdf of X is f(x|y). I want to find the marginal CDF of X, the F(x). Is this correct?
F(x)=\int^{F(x|y)}_{-\infty}f(y)dy
\dfrac{d}{dx}\int^{F(x|y)}_{-\infty}f(y)dy=\int^{\infty}_{-\infty}f(x|y)f(y)dy=f(x)?
A paper was published on today's ArXiv that questions the empirical basis of the acceleration of the expansion of the universe: Marginal evidence for cosmic acceleration from Type Ia supernovae . The authors are: Jeppe Trst Nielsen1, Alberto Guanti1, and Subir Sarkar1;2 (1Niels Bohr...
I'm trying to get a better understanding of marginal stability and the s domain in general. According to my textbook, a system that is marginally stable has poles that are conjugates of each other on the jω axis, and their magnitude are the resonant frequency for which if a sinusoid of that...
Find the marginal rate of technical substitution for the following production function:
Q=10(0.2L^{-0.5} +0.8K^{-0.5})^{-2}
Here is my attempt so far:
\frac{\delta Q}{\delta L}=[10(-2)][0.2K^{-0.5}+0.8L^{-0.5})^{(-2-1)}*[0.8*(-0.5)]L^{(\frac{-1}{2}-1)}=[(-20)*(-0.4)](0.2K^{-0.5}...
I have a set of two related queries relating to marginal pdfs:
i.How to proceed finding the marginal pdfs of two independent gamma distributions (X1 and X2) with parameters (α1,β) and (α2,β) respectively, given the transformation: Y1=X1/(X1+X2) and Y2=X1+X2.
I am using the following gamma...
Hello once again!
I've been doing this question and I was wondering if my workings are correct, if they are not correct, can you please correct them?
The question is as follows:
My workings are:
$\binom{y}{x} \frac{e^{-1}}{2^y y!}$We can rewrite this:
$\frac{y!}{x!(y-x)!} \times...
The cost function of a firm is given by C(x) = 300x - 10x^2 - 1/3x^3.
A) Find the Marginal Cost Function
B) Average cost function
C) The output at which marginal cost is equal to average cost.
Homework Statement
Your weekly cost to manufacture x bicycles and y tricycles is
C(x,y)=20,000+60x+20y+50√(xy)
a. What is marginal cost of manufacturing a bicycle.
b. What is the marginal cost of manufacturing a tricycle.
c. What is the marginal cost of manufacturing a bicycle at...
Given a plane with three points, (0,−1), (2,0), and (0,1) with x-axis and y-axis connecting three points to make a triangle. Suppose this triangle represents the support for a joint continuous probability density Pick one of the following:
The marginal density f(y), defined as ∫f(x,y)dx...
Given a plane with three points, (0, -5), (10,0), and (0, 5) with x-axis and y-axis connecting three points to make a triangle. Suppose this triangle represents the support for a joint continuous probability density
What can we say about the marginal density f_2(y)? Are they going to be...
Consider the function APL=\frac{\sqrt[4]{L}}{L}, where L is the number of workers. The company has just hired 8 workers. What is the marginal product of the labor?I know that if I had the total product I could differentiate it and get the marginal product, but it's the average product that is...
Let A be the set of possible states of the world, or possible preferences a person could have. Let G(A) be the set of "gambles" or "lotteries", i.e. the set of probability distributions over A. Then each person would have a preferred ordering of the states in A, as well as a preferred ordering...
Please see the attached image for my question. I don't understand how to compute the integral, is there some trick?
I do believe that
to find fx(x) I integrate the joint pdf, with respect to x with the bounds set as the range of Y. But this leaves me with a very complex integration
Similarly for...
Homework Statement
Homework Equations
My professor gives us the following formula: [ tex ] F_j(t) = \int\limits_0^t exp\Big\{-\sum\limits_{j=1}^J \int\limits_0^u \lambda_j^{\#}(v)dv \Big\} \lambda_j^{\#}(u)du[ / tex ] where [ tex ]\lambda_j^{\#}(t) [ / tex ] are the cause-specific...
Hi,
Homework Statement
I am having difficulties understand parts of the solution to the following problem in Statistics:
Let X and Y be two random, continuous variables, where X is distributed U(0,1) and Y|X=x is distributed U(x,x+1). I am asked to find the marginal density of Y.
Homework...
Homework Statement
Let the joint density of the material and labor cost of a project be modeled by
fx,y(u,v) = 2v*e-v*(2+u) u,v ≥ 0
= 0 otherwise
a) find marginal density of X and Y
b) find E(Y)...
Homework Statement
(X,Y) is uniformly distributed over the area
T = {(x,y): 0 < x < 2, -x < 2y < 0}
Find the marginal probability functions ie f_{x}(x) and f_{y}(y).
The Attempt at a Solution
The thing I'm having trouble with is that y depends on x. Am I supposed to rewrite the...
Hello,
i have the following conditional distribution
fXY(x,y)=2, of 0<x<1 and x<y<1
When i calculate the marginal distribution of y i don't know what interval of integration to choose.
I made the graph of x<y<1 and the points(x,y) for x<y are above x=y on that graph but i don't know how to...
The annual demand q for bottles of wine from a vineyard when the bottles are priced at p dollars each satisfies the equation
qe0.03p = 4000.
The price is currently \$12 per bottle. Find the rate at which demand changes (with respect to time) if the price increases at a rate of \$1.20 per year.
Here is the question:
Here is a link to the question:
CALC. HELP! Related Problems!?!? - Yahoo! Answers
I have posted a link there to this topic so the OP can find my response.
Homework Statement
Let X and Y be random variables of the continuous type having the join p.d.f.:
f(x,y) = 8xy, 0<=x<=y<=1
Find the marginal pdf's of X. Write your answer in terms of x.
Find the marginal pdf's of X. Write your answer in terms of x.
Homework Equations
The...
Homework Statement
Discrete random variables X and Y , whose values are positive integers, have the joint
probability mass function pXY(x,y) = 2-x-y. Determine the marginal probability mass
functions pX(x) and pY(y). Are X and Y independent? Determine E[X], E[Y], and E[XY].
Homework...
Homework Statement
A point is chosen randomly in the interior of an ellipse:
(x/a)^2 + (y/b)^2 = 1
Find the marginal densities of the X and Y coordinates of the points.
Homework Equations
NA
The Attempt at a Solution
So this ought to be uniformly distributed, thus the density function...
Homework Statement
The joint probability density function of ##X## and ##Y## is given by $$f(x,y) = \frac{1}{8}(y^2 - x^2)e^{-y},\,\,\,\, x \in\,[-y,y]\,\,,y \in\,(0, \infty)$$
Compute the marginal densities of ##X## and ##Y##.
The Attempt at a Solution
I know the defintions are $$...
Homework Statement
Hi, so I am having trouble understanding the steps to get to certain densities.
For example, suppose i have data y1,...,yJ ~ Binomial (nj,θj)
We also have that θj ~ Beta (α,β)
Now our joint posterior is:
p(β,α,θ|y) ~ p(α,β) ∏ (\Gamma(α+β) / \Gamma(α)\Gamma(β))...
Homework Statement
Hi all,
I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for -1<x<1 and -2<y<2
(A plot of it is here: https://www.wolframalpha.com/input/?i=%288%2Bxy%5E3%29%2F64+x+from+-1+to+1%2C+y+from+-2+to+2 ...sorry about the ugly url) and trying to find the marginal PDFs for X and...
Hi all,
I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for -1<x<1 and -2<y<2
(A plot of it is here: https://www.wolframalpha.com/input/?i=%288%2Bxy%5E3%29%2F64+x+from+-1+to+1%2C+y+from+-2+to+2 ...sorry about the ugly url) and trying to find the marginal PDFs for X and Y.
I know I want to...
Homework Statement
For a certain product, cost C and revenue R are implicitly given as follows, where x is the number of units sold (in hundreds)
a) Find and interpret the marginal cost dC/dx at x=5
b) Find and interpret the marginal revenue dR/dx at x=5Homework Equations
C2 = x2+100√x +50...
Homework Statement
Suppose that X1 and X2 have the joint pmf
f(x_{1},x_{2})=p^{2}q^{x_{2}},x_{1}=0,1,2,...,x_{2},x_{2}=0,1,2,...
with
0<p<1,q=1-p
Homework Equations
The Attempt at a Solution
I'm confused because the expression doesn't have x_1 in it. So usually, if I want to...
confused
Andrew, Beth, and Cathy live in Lindhville. Andrew’s demand for bike paths, a public
good, is given by Q = 12 – 2P. Beth’s demand is Q = 18 – P, and Cathy’s is Q = 8 – P/3.
The marginal cost of building a bike path is MC = 21. The town government decides to
use the following...
A biased coin lands heads with probability p and tails with probability q. An experiment
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tosses until the first head appears and let T2 denote the number of tosses (counted from
the start) until the second...
Homework Statement
The random variables X and Y have a joint probability distribution of f_{XY}(x,y)= \frac{1}{2\pi \sigma _X \sigma _Y \sqrt{1-\rho ^2}} \exp \{ \left [ -\frac{1}{2(1-\rho ^2)} \right ] \left [ \left ( \frac{x-\mu _X}{\sigma _X} \right )^2 + \left ( \frac{y-\mu...
In trying to work out what Fermat may have conceived of as his proof, using the mathematics available at the time I have the following suggestion:
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There are no natural numbers A, B, C, N >1 for which a non-trivial solution of the...
Homework Statement
Consider three random variables X, Y, and Z. Suppose that:
Y takes on k values y_{1}... y_{k}
X takes on l values x_{1}... x_{l}
Z takes on m values z_{1}... z_{m}
The joint probability distribution of X, Y, and Z is Pr(X=x, Y=y, Z=z), and the conditional probability...
Homework Statement
Problem 2
Assume that the number Y of customers entering a store is a Poisson random variable with rate λ
. Let X denote the number of these customers being a woman. The probability that a customer
is a woman is denoted by p. Also, assume that all customers enter the...
Homework Statement
Let f(x,y) = 24xy where x=[0,1], y=[0,1], x+y=[0,1]
Find E[X] and E[Y]
Homework Equations
E[X] = the integral from neg. infinity to positive infinity of x * f_X(x) dx where f_X is the marginal density function of X.
The Attempt at a Solution
f_X is found by...