Explain your answers for the questions below.
For each of the payoff tables:
1. Identify all strictly and weakly dominated strategies.
2. Check whether each player has a dominant strategy and if so specify whether it is a weakly dominant strategy or a strictly dominant strategy.
3. Use the process of iterated elimination of dominated strategies to check whether there exist(s) some dominant strategy equilibrium/equilibria. Be careful that if you eliminate weakly dominated strategies, the order of elimination matters (in that case you need to analyze all possible sequences of elimination of strategies so that you obtain all the possible profiles of strategies that survive this process)....
I wo bonds paying annual coupons of 5% in arrear and redeemable at par have terms to maturity of exactly one year and two years, respectively. The gross redemption yield from the 1-year bond is 4.5% per annum effective; the gross redemption yield from the 2-year bond is 5.3% per annum effective. You are infonned that the 3-year par yield is 5.6% per annum. Calculate all zero-coupon yields and all one-year forward rates implied by the yields given above. [12] A loan pays coupons of 11% per annum quarterly on 1 January, 1 April, 1 July and 1 October each year. The loan will be redeemed at 115% on any 1 January from 1 January 2015 to 1 January 2020 inclusive, at the option of the borrower. In addition to the redemption proceeds, the coupon then due is also paid. An investor purchased a holding of the loan on 1 January 2005. immediately after the payment of the coupon then duc, at a price which gave him a net redemption yield of at least 8% per annum effective. The investor pays tax at 30% on income and 25 on capital gains. On 1 January 2008 the investor sold the holding, immediately after the payment of the coupon then due, to a fund which pays no tax. The sale price gave the fund a gross redemption yield of at least 9% per annum effective. Calculate the following: (i) The price per $100 nominal at which the investor bought the loan. [6] (ii) The price per $100 nominal at which the investor sold the loan. 141 (iii) The net yield per annum convertible quarterly that was actually obtained by the investor during the period of ownership of the loan. [5] [Total 15]3. (8 pts. each) One question that economists are interested in when studying the produc- tion possibilities of a country is the following: If the amount of both capital (K) and labor (L) in a country doubles, will its output double as well? The intuition behind this is simple. If a company can build 1,000 vehicles with one fully staffed factory, it should be able to produce 2,000 vehicles with two fully staffed factories. To that end, we will say that a production function exhibits -Constant Returns to Scale (CRS) if F(2K, 2L) = 2F(K, L). That is, if a country is producing output F(K, L), doubling the amount of capital and labor will in fact double the output. - Decreasing Returns to Scale (DRS) if F(2K, 21) 2F(K, L). That is, if a country is producing output F(K, L), doubling the amount of capital and labor will result in more than double the output. It is easy to see that with our normal Cobb-Douglas function, given by F(K, L) = K3L.T does in fact exhibit constant returns to scale. To see this, notice that F(2K, 2L) = (2K) (21)1 = 23 . 27K-317 = 2347K-3L.7 = 2K-3L.7 = 2F(K, L) For each production function function below, determine if it exhibits constant, increas ing, or decreasing returns to scale: ! (a) F(K, L) = 2K L.7 (b) F ( K, [) = (1+ + [t)? (c) F(K, L) = Kb + LIU5. Use successive elimination of dominated strategies to solve the following game. Explain the steps you followed. Show that your solution is a Nash equilibrium. U6. Find all of the pure-strategy Nash equilibria for the following game. De- scribe the process that you used to find the equilibria. Use this game to explain why it is important to describe an equilibrium by using the strategies employed by the players, not merely by the payoffs received in equilibrium. COLIN Left Center Right Up 1, 2 2, 1 1,0 ROWENA Level 0, 5 1,2 7,4 Down -1, 1 3,0 5,2
