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September 11th, 2009, 02:02 PM   #1
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Econometrics

A firmís cost function and the demand functions are
C ( x ) = 5x and p = 25 - 2x respectively, where x is the amount produced and/or demanded.

a) If a tax of t per unit is imposed, which the firm adds to its cost, find the output level that will maximize the firmís profits. What is the maximum profit? (Note that the optimal output and profits will both be functions of the tax rate t rather than some fixed values.)

b) Determine the tax t per unit that must be imposed to obtain the maximum tax revenue. (Hint: Use the solution of output as a function of t from a) to formulate the tax revenue function.)

c) Given the solution for t in (b), find the optimal output and profits using their optimal choice functions in (a). (This time, the solutions will be some fixed values.)
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September 11th, 2009, 06:29 PM   #2
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Re: Econometrics

What have you tried so far? Here's a list of questions that should get you going:

For part a:

1) What is the revenue function?
2) What is the cost function that accounts for tax?
3) What is the profit function, from 1) and 2)?
4) What is the maximum profit?

If you have P(x), the easiest way is to find maximal profit is to find where P'(x) = 0 for a positive x. This gives you optimal output. Then put this into the profit function for optimal profit. If you aren't using calculus, they have probably suggested some other way to find the maximum.

For part b: Do what they suggest.
For part c: Use the answer from part b as the 't' for part a and do what they suggest.
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