Production function, MC, AVC, TC, lagrangian multipliers

(See attached file for full problem description)

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Consider the original following production function:

f(x) = x ^ 1/3

but now there is a fixed cost of F per year that the firm has already paid for this year.

a) assuming W = 1 and F = 2, draw the marginal cost function (MC), average variable cost (AVC) and the total cost function (TC). Be sure to find Y such that MC = AVC and Y such that MC = AC

b) What is the short run function? (This year in this case)

c) What is the long run supply function? (Next year in this case)

Consider the original following production function:

f(x) = x ^ 1/3

but now there is a fixed cost of F per year that the firm has already paid for this year.

a) assuming W = 1 and F = 2, draw the marginal cost function (MC), average variable cost (AVC) and the total cost function (TC). Be sure to find Y such that MC = AVC and Y such that MC = AC

b) What is the short run function? (This year in this case)

c) What is the long run supply function? (Next year in this case)

I assume here that 'x' is a production factor (such as labor) and that W is its cost per unit. In order to find the marginal cost function, we first need to find the total cost function.

Let's call Q to quantity produced. We have that:
(the production function)

By isolating x in this function, we can find how much labor we need in order to produce a given quantity Q:

So, if we want to produce, say, 3 units of the good, we would need units of labor. Therefore, the ...

Solution Summary

The supply curve is assessed. A production function for lagrangian multipliers is examined.

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Fixed capital and labor expenses are $1.2 million per year.
Variable expenses average $2,000 per van conversion.
Q=1,000 - 0.1P where Q is the number of van conversions (output) and P is price.
Calculate the profit maximizing output, price and profit levels.

1.
Fixed capital and labor expenses = 1.2million/year
Variable expenses = 2,000/unit of output
Demand: Q = 1000 - 0.1P
A. Calculate profit-maximizing output, price, and profit levels
B. Using the Lagrangian multiplier method, calculate profit maximizing output, price, and profit levels in light of a parts shortage that

Please assist with all parts. Thank you!!!
Palm Products Company has collected data on its average variable costs of production for the past 12 months. The costs have been adjusted for inflation by deflating with an appropriate price index. The AVC and associated output data are presented below:
obs Q AVC obs Q A

Consider the problems of maximizing u(x) subject to px = y and maximizing v(u(x)) subject to px = y, where v(u) is strictly increasing over the range of u. Prove that x* solves the first problem if and only if it also solves the second problem.
This is what I got, however i dont think its entirely correct.
To solve the

Suppose a firm faces a cost function of the form :
C (y) = 8 + 4y + y ^ 2
a) What is the firm's fixed cost, FC?
b) What is the firm's variable cost, VC?
c) What is the formula for the average cost, AC?
d) What is the formula for the average variable cost, AVC?
e) What is the formula for the marginal cost, MC?
f) On a

With reference to Figure 2, a small cylinder sits initially on top of a large cylinder of radius a, the latter being attached rigidly to a table. The smaller cylinder has mass m and radius b. A small perturbation sets the small cylinder in motion, causing it to roll down the side of the large cylinder. Assume that the coefficien

The text we are using is "A Second Course in Elementary Differential equations" by Paul Waltman. This section begins on page 77. Here is the link to the book
http://books.google.com/books?id=e1euiBF73yIC&dq=A+Second+Course+in+Differential+Equations+Paul+Waltman&printsec=frontcover&source=bl&ots=imup9X2PbZ&sig=g1__chkwNHxDDg-