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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)

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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)

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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