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Question 2: Cost Estimation (10 marks) You have been asked to estimate the cost of manufacturing 100 extreme-weather tents that can be used by refugees after a natural disaster. Back in 2010 your company had a similar contact to produce 70 tents that provided 1,050 square metres of floor space each and were 2.5 metres high at the peak. This time the tents need to be a little bit larger, providing 1,200 square metres of floor space. The cost of materials in 2010 was $18.75 per square metre of floor space. The shop foreman's estimate of labour required to manufacture the first new tent is 98 hours. a) Using a cost capacity factor of 0.65 and cost index values of 175 in 2010 and 210 in 2021 estimate cost of materials for the new tents. b) Assuming a loaded labour rate of $120 per hour, a 91% learning curve what is the cost of the 50th tent? c) Calculate the average labour cost per tent. d) What will the total price of the contract be if you use a 20% profit markup?Problem 4 The current yield curve for default-free zero-coupon bonds is as follows: Maturity (years) YTM 10% WN N 11% 12% a. What are the implied one-year forward rates for years 2 and 3? b. What would be the shape of the yield curve according to the Expectations hypothesis? c. If you believe in the liquidity preference theory, what would be your guess as to the upper limit on the short-term interest rate expected for the third year?Question 2 It is intuitive to think that the presence of more agents in the economy "shrinks" its core, since there are more coalitions that can object a given allocation. You will understand in this question why this is indeed the case.' Fix a standard, two-person exchange economy & = ((u', w' ), (u', w?)). Define its replica as the four-person exchange economy 82 = ((u', w'), (ul, w ), (u', w'), (u', wa)). where (u', w3) = (u', wi ) and (u', wi ) = (uz, w? ). 1. Argue that if (p, x', x?) is a competitive equilibrium for &, then (p, x', x3, x3, x* ) with x' = x' and x* = x', is an equilibrium for &?. 2. Argue that if both utility functions are strictly quasi-concave, and (p, x', x', x3, x* ) is a competitive equilibrium for &', then, x' = x3 and x? = x*. 3. Argue that if both utility functions are strictly quasi-concave, and (x], x3, x3, x* ) is in the core of &', then, x' = x3 and x? = x*. 4. Argue that if both utility functions are monotone and strictly quasi-concave, and (p, x', x?) is a competitive equilibrium for &, then (x], x], x', x?) is in the core of &?. 5. Suppose that u'(x) = u'(x) =x'x. wi = (1,0) and w2 = (0, 1). Argue that allocation ((0, 0), (1, 1) ) is in the core of &, yet allocation ((0, 0), (1, 1), (0, 0), (1, 1)) is not in the core of &?. 6. Use these results to argue, informally, that the replication of agents does not affect the set of equilibrium allocations of the economy but shrinks its core.' We are using the term "shrink" loosely, since the presence of more agents changes the dimension of the allocation space, so comparing the sizes of the cores will require some refinement of the argument. In the limit, one can show that replication ad infinitum reduces the core to just the set of equilibrium allocations.3. To slow down transmissions of the viral disea 'lockdown" hence ordering business to shut and the citizens to adhere to limiting physical distancing, but leaving the timing of the lockdown to be decided by the two regional governments of Krona. Assume that both regions have roughly the same population size of 10 million citizens. Region 1 entered lockdown at the beginning of month 3, region 2 entered lockdown at the beginning of month 2. See Next Page The following table shows the cumulative infections and fatalities due to the viral disease over time and the time of the lockdown in each region at the end of each month. Month 1 Month 2 Month 3 Month 4 cases fatalities cases fatalities cases fatalities cases fatalities Region 1 100 3 5000 300 9000 540 15000 900 Region 2 100 5 2200 130 4500 270 5500 330 a) The minister for the economy argues that after both regions entered lockdown, in month 3 the number of cases in region 2 more than doubled, whereas the growth rate is lower in region 1 arguing that the lockdown was not effective in preventing the spread of the disease. Do you agree? Can you provide a better estimate using your knowledge of empirical methods introduced in the module? [word limit 250 words; 8 marks]. b) What kind of data would you prefer to have to estimate the full impact of the lockdowns on infections and fatalities? Explain how this would help to improve your estimate from the previous question. [word limit 200 words; 4 marks]. c) In response to the lockdown the economy in region 1 contracted by $1.1bn, and $1.114bn in region 2. What can we learn from these figures about the statistical value of life? [word limit 100 words; 3 marks]. d) Suppose a vaccine against the disease was available at the beginning of month 1 (and assume it works immediately by protecting the citizens from the disease). 60% of population require the vaccine to stop the disease from spreading. The vaccine is available for $20. Should the government introduce the vaccine? State any assumptions you implicitly make underlying your advice and briefly discuss the limitation of your advice. [word limit 250 words; 5 marks]