Exercises for ECON31002 - Managerial Economics II Assignment 1
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Exercises for ECON31002 - Managerial Economics II
Assignment 1
• Information:
– The due date is Monday 14 March 2022 at 4pm.
– The maximum score is 100 points. Each of the 10 subquestions is worth 10 points.
– This assignment counts for 10% of your final mark.
• Instructions:
– Answer all questions.
– Provide every step of reasoning and calculation.
– All text must be typed up and the assignment must be handed in as one pdf.
– For anything that is not easy to type up (e.g., graphs, equations), you are allowed
to write by hand, scan, and insert in the document. Make sure to write neatly, anything that cannot be read will be counted as incorrect.
• Questions:
1. The game show Golden Balls aired on ITV from June 2007 to December 2009. In the last round, the two remaining contestants play for an amount of money W > 0.1 The last round works as follows: each candidate simultaneously chooses either Steal or Split, without knowing what the other has chosen. If both contestants choose Steal, neither wins anything. If both contestants choose Split, they split the jackpot equally. If one contestant chooses Steal and the other chooses Split, the former wins the entire jackpot and the latter does not win anything.
(a) Suppose that the contestants are gain maximisers.
i. Represent the “Steal or Split” game in its normal form.
ii. Calculate the players’ best responses.
iii. Do the players have any weakly or strictly dominant strategies?
iv. Find all (pure strategy) Nash equilibria.
v. What is the most likely outcome of the game?
(b) Over the time the game aired, contestants chose Split 52.8% of the time.2 Is
this consistent with your findings in (a)? If yes, provide intuition for why the prediction corresponds to the way people play. If not, explain what might cause the discrepancy. [Max 100 words]
(c) How would you expect the proportion of contestants who choose Split to change if, instead of being broadcast on National TV, the game was played behind closed doors and the contestants did not see each other? [Max 100 words]
2. The government wishes to purchase two submarines and is willing to pay up to 5 (million) for each of them. There are two profit-maximising firms i = 1, 2 that can produce these submarines and the government makes them compete for the contract by submitting a bid, i.e., a price they would charge per submarine. As ministers do not like complicated maths, the government has introduced two rules: (i) each firm’s bid must consist of a single price per submarine, i.e., firms cannot offer a discount if the government purchases two submarines; (ii) each bid must be a multiple of one million, i.e., a firm can set its price to 0, 1, 2, 3,... but not to, e.g., 2.5. Both firms face the same cost of production: 1.2 to produce one submarine and 1.6 to produce two. (This can be thought of as having a fixed cost of 0.8 to set up production, and then a variable cost of 0.4 for each submarine built.) Firm 2 has active lobbyists who have negotiated that firm 2 will be able to observe firm 1’s price before setting its own price. Therefore, the timing of events is as follows:
• Firm 1 sets its price p1 = 0, 1, 2, 3,....
• Firm 2 observes p1 and sets p2 = 0, 1, 2, 3,....
• If min{p1,p2} > 5, the government does not purchase any submarine. Otherwise, if p1 
p2 the government purchases two submarines from whichever firm has the lowest price and, if p1 = p2, the government purchases one submarine from each firm.
(a) Write the profit of firm i as a function of pi and pj (i,j = 1, 2, i 
j). (b) What is firm 2’s best response?
(c) What are the equilibrium prices?
(d) Suppose that the price increments are now half a million; that is, the firms can set their price to 0, 0.5, 1, 1.5, 2, 2.5, 3,.... What are the equilibrium prices?
(e) Looking at both scenarios: did firm 2’s lobbyists do a good job?
(f) Compare the government surplus and the social surplus in both scenarios. What
does this tell us about tender processes?
(g) Let again the price increment be one million (as in parts (a)-(c)) and suppose that
the firms reach the following agreement: if firm 2 makes a positive profit, 50% of that profit goes to firm 1. What are the equilibrium prices? Could firms actually do this in practice?
2022-05-13