Depletion2

Depletion2 - Optimal Depletion: Some Examples 1. Base Case...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Optimal Depletion: Some Examples
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1. Base Case Given q t = 10 p t t = 0,1 MC t = 2 q 0 + q 1 = 10 r = .1 p 10 2 0 8 10 q
Background image of page 2
Equilibrium Condition From demand equation p 0 MC 0 = p 1 MC 1 1 + r 10 q 0 MC 0 = 10 q 1 MC 1 1 + r
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Substituting for MC and r From stock constraint 10 q 0 2 = 10 q 1 2 1.1 8 q 0 = 8 q 1 1.1 ) 10 ( 8 1 . 1 8 . 8 0 0 q q = q 0 = 5.14
Background image of page 4
q 1 = 10 q 0 = 4.86 from stock constraint p 0 = 10 q 0 = 4.86 from demand equation p 1 = 10 q 1 = 5.14 from demand equation.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. Suppose we ignore the stock constraint. Then, But this is impossible since p 0 = MC 0 10 q 0 = 2 q 0 = 8 p 1 = MC 1 10 q 1 = 2 q 1 = 8. q 0 + q 1 = 16 > 10.
Background image of page 6
3. Suppose we ignore discounting. Then, and we get egalitarian allocation of the resource over time or, in other words, price and extraction time paths are flat. 10 q 0 2 = 10 q 1 2 8 q 0 = 8 q 1 8 q 0 = 8 10 q 0 ( ) 2 q 0 = 10 q 0 = 5 q 1 = 5
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4. Suppose 0 < r < .1, say, r = .02. Then, 10 q 0 2 = 10 q 1 2 1.02 8 q 0 = 8 10 q 0 ( ) 1.02 q 0 = 5.03 q 1 = 4.97 p 0 = 4.97 p 1 = 5.03.
Background image of page 8
So price and extraction paths are flatter than in the case where r = .1, but not perfectly flat, as in the case where r = 0. In general, for r > r’ , q r r r t t r p
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
5. Suppose we add a severance tax, = $1/unit extracted. p 0 MC 0 1 = p 1 MC 1 1 1 + r 10 q 0 MC 0 1 = 10 q 1 MC 1 1 1 + r 7 q 0 = 7 10 q 0 ( ) 1.1 q 0 = 5.10 q 1 = 4.90 p 0 = 4.90 p 1 = 5.10.
Background image of page 10
So price rises more slowly than without the tax (though the royalty continues to rise at rate r ), and production is reduced in the present, shifted to the future. In other words, the severance tax leads to conservation of the resource. Why?
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 33

Depletion2 - Optimal Depletion: Some Examples 1. Base Case...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online