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[answered] Microsoft Word - Econ 101 Fall 2016 Problem Set 11.docx Sup


Microsoft Word - Econ 101 Fall 2016 Problem Set 11.docx

Suppose that consumers? valuation of the marginal widget is given by the following function:

???????????? =200?2????.

Also, suppose that widget producers bear a constant (private) cost of $30 when producing the marginal widget:

???????? ???? = 40.

Finally, suppose that the marginal widget produced generates pollution damage given by the following marginal damage function:

???????????? =2????.

  1. (a) ?Draw a diagram showing the marginal valuation curve, the marginal (private) cost curve and the marginal damage curve.
  2. (b) ?What is the efficient quantity of widgets to be produced in this market? Show this quantity in your diagram. Be sure you can explain why your answer is correct.
  3. (c) ?If the economy produces the efficient quantity of widgets, what is the social cost of the marginal widget? How much pollution damage does the marginal widget generate? Identify both values in your diagram.
  4. (d) ?If the widget market is competitive, so that all producers and consumers are price-takers, what price do we expect to prevail in the widget market? Show this price in your diagram.
  5. (e) ?Do you expect the competitive widget market will produce the efficient quantity of widgets? If not, will it produce too many widgets or too few? Be sure to explain why. Calculate precisely how many widgets will be produced and mark this quantity on your diagram. If there is a deadweight loss in this market, show it on your diagram.
  6. (f) ?A sales tax of $t/widget imposed in this market would reduce equilibrium output if t > 0 and would increase equilibrium output if t < 0 (i.e. if t < 0, we really have a subsidy rather than a tax). If your goal is to encourage the market to produce the efficient quantity, what is the appropriate tax rate (t) to choose? Explain why


 


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