UNIVERSITY OF TORONTO DEPARTMENT OF MANAGEMENT INDUSTRIAL ORGANIZATION MGEC41H3 Y (LEC01) MID-TERM TEST DURATION: 90 MINUTES JUNE 14, 2013 IMPORTANT: (i)
This test should be answered in BALLPOINT PEN (except diagrams) and students who attempt the test in pencil would surrender their rights to request for re-assessment. (ii) Answer all questions in POINT FORM and only in the DESIGNATED PAGES. Answer every part of all the questions and CLEARLY LABEL EACH PART of your answer. (iii) Please ensure your HANDWRITING is LEGIBLE. (iv) A 10-MARK PENALTY will be imposed if any PAGE is SEPARATED from this test. (v) Only NON-PROGRAMMABLE calculators are allowed.
Student Name:
Student ID#:
Question
1
2
3
Total
Marks
45
30
25
100
Diagram(s)
8
(a)
10
8
12
(b)
15
4
5
(c)
12
6
8
(d)
2
(e)
6
(f)
4
Score
45
30
100
25 Page 1 of 4
1.
(a)
Suppose a monopolist’s total cost function is and faces a market demand where is the output of the monopolist. Demonstrate how to derive the profit-maximization condition of a typical single-price monopolist and show the profit-maximization condition implies the relationship between Lerner Index and demand elasticity. Derivation and Explanation: 10 marks
1.
(b)
Use two properly labeled diagrams side-by-side to help you explain in details (according to lecture discussion) the economic intuition (including the setup of the model) under what conditions a dominant firm may co-exist with other fringe firms and when will this dominant firm become a monopolist in an industry with the assumption of no new entry. Use another two properly labeled diagrams side-by-side to help you explain in details (according to lecture discussion) the economic intuition (no need to repeat any explanation that you already put in part (a)) under what conditions a dominant firm may co-exist with other fringe firms and when will this dominant firm become a monopolist in an industry with the assumption of free entry. Explain why results are different or same as those in part (a). Diagrams: 8 marks Explanation: (b) 15 marks and (c) 12 marks
(c)
Page 2 of 4
2.
Suppose there are two firms selling differentiated products and under the Bertrand model. The demand equation for Firm ’s product and the demand equation for Firm ’s product . Both firms have same costs . (a) Derive the best response functions for these firms and . (b) Solve for the Bertrand-Nash equilibrium price for each firm and . (c) Plot , , , and in a properly labeled diagram. Assume Firm initially believes , use the best response functions for these firms to demonstrate there is a tendency that these firms will converge to the Bertrand-Nash equilibrium. (Hint: Use four points on these best response functions just like the example for Cournot-Nash equilibrium shown in lecture discussion and review class) (d) Calculate equilibrium quantities and . (e) Calculate profits ( and ), consumer surplus ( and ), and producer surplus ( and ) in each market. (Hint: Figure out the demand curves for and at the BertrandNash equilibrium). (f) Suppose these firms are now regulated by the government such that they must behave like perfectly competitive firms. How much output would these firms produce? Compare the consumer surplus to the results in part (e) and explain the reason for the difference. (a) 8 marks; (b) 4 marks; (c) 6 marks; (d) 2 marks; (e) 6 marks; and (f) 4 marks
(a)
(b)
(c)
The zigzag pattern from point to point indicates there is a tendency that these firms will converge to the Bertrand-Nash equilibrium.
(d)
(e) ,
When symmetry
(f)
,
and due to
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and
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. Page 3 of 4
3.
Suppose a pharmaceutical company sells a patented flu medication and it separates its customers into two different groups by using different labels. Let be the price and be the quantity for each group of customers. The first group is served with the label “safe for pregnant females” on the package and the demand in this market segment is represented by . The second group is served with the label “pregnant females please consult your physician for advice” on the package and the demand in this market segment is represented by . The cost of manufacturing the drug is assumed to be constant regardless of which market segment the drug is sold to. (a) Show the step-by-step derivations of the profit-maximizing quantity ( and ) and price ( and ) in each market segment, and the total profits ( ). Use your results to determine the demand elasticity ( and ) in each market segment at and . Explain the economic intuition why these two groups of customers are charged different prices? (b) Suppose a professor at University of Toronto confirms the drug in the two packages are identical except the labels. Now the company can no longer segment the market (the company becomes the least powerful monopolist) and the combined demand of all females becomes . Show the step-by-step derivations of the profit-maximizing quantity ( ) and price ( ), profits ( ), and consumer surplus ( ). (c) Suppose the same professor at University of Toronto also invents a brain scanner to reveal the maximum willingness-to-pay for this drug, which would turn the pharmaceutical company into the most powerful monopolist when facing the combined demand in part (b). Show the step-by-step derivations on how to determine the maximum price that the pharmaceutical company is willing to pay for this brain scanner. Comment on the statement made by a consumer advocate that “the government should buy the brain scanner and give it to the pharmaceutical company for free because everyone knows the most powerful monopolist produces the same output as the perfectly competitive industry in which the consumers in the society will benefit from larger total surplus.” Explanation: (a) 12 marks; (b) 5 marks; and (c) 8 marks
(a)
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(b)
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(c)
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. The maximum price the pharmaceutical company is willing to pay for .