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Analysis of Decentralization in Gas Market: WX3.21

This presentation explores the material covered in the WorkedExamples.pdf file, with added graphics and comments. It discusses marginal cost, fixed cost, utility, and the feasibility of decentralizing the gas market.

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Analysis of Decentralization in Gas Market: WX3.21

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  1. EC212: Worked Example #3.21 Frank Cowell April 2004 • This presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments • To start the presentation select Slideshow\View Show or click on icon below left. • Mouse click or [Enter] to advance through slide show

  2. WX3.21: part 1 Marginal cost Fixed cost • x1 units of good 1 must cost F + mx1 of good 2 • There are X2 units of good 2 available in the economy • So the maximum possible amount of good 1 is:

  3. WX3.21: part 1 x2 X2 Fixed cost F marginal cost m gas x1

  4. WX3.21: part 2 • We can easily check the MRS • Clearly MRS goes to 0 as x1 goes to  • For a given x1 MRS is the same for all x2 • MRS is high for high a and vice versa

  5. x2 gas x1 WX3.21: part 2 U=x2 when x1 = 0 high a low a

  6. WX3.21: Part 3

  7. x2 X2 Utility increases gas x1 WX3.21: part 3 - high a • B At A MRS=m • A

  8. WX3.21: part 3 - high a • MRS is: • So at A we have: • This implies: • Utility at A is a[1 - exp (x1*)]+x2* : • Utility at B is X2 • So UA > UB if

  9. x2 X2 Utility increases gas x1 WX3.21: part 3, low a • B • A

  10. WX3.21: Part 3, implementation • Budget constraint must pass through B • It must be such as to make A utility-maximising • This can be achieved if a non-linear budget constraint can be introduced • A public corporation could do this • Make a fixed charge F and then sell gas at marginal cost m.

  11. WX3.21: Part 4 • Idea here is simple • (formal analysis can get a bit tiresome) • Obviously a private corporation might market the gas in the same manner as the public corporation • But can gas market be decentralised? • Obviously if p > m (case of simple monopoly) this would be inefficient. But what about a market solution with p = m ?

  12. x2 X2 • B • A price = MC gas x1 WX3.21: part 4 Profit maximisation at price p=m will take economy to B, not A!

  13. WX3.21: Points to note • Draw a simple picture of each part of the problem • Use the diagram to determine location of PE allocations • Interpret diagram in terms of a budget constraint. • Rest of problem can be understood in similar way. Feasible set is obviously non-convex, so decentralisation may not be possible.

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