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Assume there is perfect competition with a tax of $2 per unit of x. What is the deadweight loss of this tax?

Provide a formula for J and K. Note that these are values on the graph’s axis. Hint: The solution must be in terms of the problem’s parameters. To solve this problem, you will use the production level (y), scalars (a, b ,c, d, and e), and input prices (p1 and p2). You may use one or a combination of such parameters. The final formulas must not show x1 nor x2.

How does the production level y1 compare to y2? Is it great, smaller, or equal?  How about y4 and y3? Justify your answer based on the isoquant graphs.

The following description will be used in questions 1a to 1d and for bonus question I. Consider two distinct production functions (f1 and f2) that use two inputs (x1 and x2) to produce one output (y). Such functions have the form f1 = min (a*x1 , b*x2) and f2= c*x1+d*x2, where a,b,c and d are positive scalars, p1 is the cost of one unit of input x1, p2 is the cost of one unit of input x2, and y represents the production level.     

How does the production level y1 compare to y2? Is it great, smaller, or equal?  How about y4 and y3? Justify your answer based on the isoquant graphs.

After solving 2d, you can find that the market will offer 40 units of x at a price of 20. As expected, the competitive market can offer x at a lower price than the monopoly. Calculate the dead weight loss from the monopoly.

Write down the first-order conditions.

Write the profit maximization problem for a monopolist producing x. (Write down the problem, you do not have to solve it).

Write the profit maximization problem for a monopolist producing x. (Write down the problem, you do not have to solve it).

Your typed answer is the driver of your grade: show your solution and justify using written English. You must show work to get full credit on each question. As well as for partial credit when your final answer is wrong.    In addition to typing, you can email your handwriting work within 30 minutes of finishing this exam.  Instructions to email supporting handwriting notes: after completing and submitting the exam on Canvas, scan your notes and email them to ppimentelfur@umass.edu with the title “MIE 654 Final Exam Notes for STUDENT_NAME”. Use a scanner or scanning app for better quality; if the instructor cannot understand your notes, they will not be considered. You can only use your phone after submitting the exam; otherwise, Honorlock will flag you for dishonesty.   Please indicate your choice below: