Let X be a random variable representing the present value of the benefits of a whole of life assurance, and Y be a random variable representing the present value of the benefits of a temporary assurance with a term of a years. Both assurances have a sum assured of 1 payable at the end of the year of death and were issued to the same life aged x. (1) Describe the benefits provided by the contract which has a present value represented by the random variable X - Y. [1] (ii) Show that: cov(X, I) = ZAG - Ax And and hence or otherwise that: var(X - Y) = 'Ax -(m/4x)= _ 2Al where the functions A are determined using an interest rate of /, and functions 2 A are determined using an interest rate of i- + 2i. [7] [Total 8]Let X be a random variable representing the present value of the benefits of a whole of life assurance, and Y be a random variable representing the present value of the benefits of a temporary assurance with a term of a years. Both assurances have a sum assured of 1 payable at the end of the year of death and were issued to the same life aged x. (1) Describe the benefits provided by the contract which has a present value represented by the random variable X - Y. [1] (ii) Show that: cov(X, I) = ZAG - Ax And and hence or otherwise that: var(X - Y) = 'Ax -(m/4x)= _ 2Al where the functions A are determined using an interest rate of /, and functions 2 A are determined using an interest rate of i- + 2i. [7] [Total 8]Question 1 (total 15 points}. A rm has a production function: f (K . L} = EDLKD'E + LEE 2 LEKE a. What is its short-run production function if capital is xed at K=4'? b. What are the fum's marginal product of labour and average product of labour in the short run? c. Calculate the elasticity of output with respect to labour. Question 2 (total 16 points} . Do the following functions exhibit increasing, constant, or decreasing retiirns to scale? Explain you: answers. a. The production ftmction Q = Wigwam, where M is materials, K is capital and L is laboUr. b. q = L + 0.5K c. u = DELHI\" I d. if = M.3 + 4K Question 3 (12 points]. Find the Marginal Rate of Technical Substitution for the following production functions: 1 | a. 'FLEKE 11 q = L.5 + [(0.5 o. q = L + K Question 4 (Total It} points). Suppose a fum's cost uiction is C = 2q3 lql + Slq. average cost curve is described by the equation AC = 2432 lq + 94). At what output level does the marginal cost curve cross the average cost curve? Question 5. (16 points, 8 points each} For the following, please answer \"True" or "False" and explain why. a. When buying a piece of equipment, it is always bed for the rm to pay cash instead of borrowing the funds since this mnders the equipment less costly. b. University of Tomato is choosing a location for a new building. The university has campuses at Downtown1 Scarborough and Mississauga. A large parcel of land would have to be purchased at Scarborough or Mississauga if the building were to Jugs L be built there. So it is cost-effective to locate the new building at downtown because the university already owns the land. 1. The table on the right contains employment data for males and females between May 2020 and April 2021. The data is seasonally adjusted and comes from the Labour Force Survey for Canada as a whole. Employment a) What is the significance of the data being "seasonally Males Females adjusted"? How can we compare the data because of this May-20 8,800.50 7,643.40 Jun-20 9,277.00 8,108.70 trait? Jul-20 9,441.20 8,361.40 b) Create a time series graph using this data. Aug-20 9,519.40 8,496.90 c) Explain what the data shows in terms of trend for both Sep-20 9,688.70 8,699.90 Oct-20 9,742.90 8,740.10 males and females over the year. Nov-20 9,775.00 8,762.40 d) Does the relative size of employment change for one Dec-20 9,752.10 8,732.70 gender vs. the other? Jan-21 9,674.00 8,598.00 e) What other aspects of employment might be useful when Feb-21 9,797.60 8,733.60 Mar-21 9,951.60 8,882.70 comparing male and female employment? Apr-21 9,869.20 8,758.00II. Suppose the economy is in a recession, and the government is contemplating using expansionary fiscal policy (fiscal stimulus) to counteract the recession. (a) Define expansionary fiscal policy (fiscal stimulus) and give three examples. (b) Explain why crowding out in the credit market makes it more difficult for the government to eliminate a recession using fiscal stimulus. Use graphs to illustrate your answer. (c) Some economists have suggested that fiscal stimulus would be a more effective tool for fighting a recession if the Federal Reserve adopted an "accommodating monetary policy" by pursuing a loose monetary policy at the same time the government adopts expansionary fiscal policy. Draw a graph showing how the Fed can eliminate crowding out and maximize the impact of fiscal stimulus on output during a recession by adopting loose monetary policy at the same time the government adopts fiscal stimulus.II. Suppose the economy is in a recession, and the government is contemplating using expansionary fiscal policy (fiscal stimulus) to counteract the recession. (a) Define expansionary fiscal policy (fiscal stimulus) and give three examples. (b) Explain why crowding out in the credit market makes it more difficult for the government to eliminate a recession using fiscal stimulus. Use graphs to illustrate your answer. (c) Some economists have suggested that fiscal stimulus would be a more effective tool for fighting a recession if the Federal Reserve adopted an "accommodating monetary policy" by pursuing a loose monetary policy at the same time the government adopts expansionary fiscal policy. Draw a graph showing how the Fed can eliminate crowding out and maximize the impact of fiscal stimulus on output during a recession by adopting loose monetary policy at the same time the government adopts fiscal stimulus.05 Question (3 points) ' See page 38? A mail-marketing company combines two inputs, pre-stamped envelopes (input 1} and printed marketing campaign material (input 2). Every envelope can be stuffed with three pieces of paper. That is, the number of marketing mailers is determined by the following production function: y= minixl. '5'} where _y stands for the number of mal Iers. .u stands for the number of pre-stamped envelopes, and JEStBFIdS for the number of sheets of paper. v ist attempt Part 1 {1 point} 0 See Hint If the unit cost of Envelopes is an, and the unit cost of printing a sheet of mailing materials Is my. the conditional factor demands for envelopes and sheets are, respectively Choose one: Part2 {1 point} 0 See Hint Considering your ndings from Part 1, which of the following statements are correct? Choose one or more: Q AThe conditional input demand for envelopes {x1} is independent of the price the firm charges for producing each mailer [the price of . ' B.The conditional input demand for envelopes {x1} depends positively on the number of mailers iyi the firm wants to produce. E.The conditional input demand for envelopes {x11 depends negatively on the per-unit cost of printed sheets of mailer material (aid. ' ' D.The conditional input demand for envelopes {x1} depends negatively on the per-unit cost of envelopes (mi). E.The conditional input demand for envelopes {x1} depends positively on the per-unit cost of envelopes (on). F. The conditional input demand for envelopes {x1} depends positively on the per-unit cost of printed sheets of mailer material (033