!Solve the following problems.

1. An exchange economy has two dates t = 0, 1 and two states of nature s = 1,2 which will be revealed at date 1. Unlike the model in class, agents in this economy do have endowments, consume and trade in goods at t = 0. Use s = 0 to denote the date-event pair corresponding to date 0. There is one physical commodity, and two consumers i = 1, 2 whose endowments wis are as follows: 10 = 2, wn1 = 4,w12 = 3, w/20 = 4, w21 = 2, w2 = 3. Both share the von-Neumann-Moregenstern utility log co + logo, where a denotes date t consumption. Consumer 1 believes s = 1 will occur with probability ?, while consumer 2 believes s = 1 will occur with probability 2. At date 0, there is a spot commodity (i.e., for delivery at s = 0) market, besides two assets k = 1,2 whose date-1 returns fox are given by ru = 1, m12 = 2, 121 = 0, raz = 1. So consumers divide their date 0 wealth between consumption at t = 0 and purchasing assets that yield returns at t = 1. At date 1, agents realize their asset returns and trade in spot commodity markets after the state is revealed. (a) Derive the entire set of er ante Pareto optimal allocations in this economy. Are these allocations ex post Pareto optimal as well?3. Consider an economg,r with A consumers and B rms. Each consumer is endowed with one unit of time and one piece of capital. A representative consumer's utility function is u(:.':, r) = 1111: + 2111 r, where :r is consumption of goods and r = 1 l is leisure time and l the time working. Each rm hires consumers to work and rents capital from consumers to produce goods according to technology: 3; = KGLI'\Question 1 Consider a production economy with two goods, X and Y, and two inputs, labour (L) and capital (K), with the following production functions: X = 2L355K5 Y = 4L55K35 This economy also has two consumers, A and B, with the following utility functions: UA = XgygA UB = Xg5Yg'5 while both consumers have endowments of labour, LA = L B = 10 and capital, KA = K3 = 5. We denote prices for all goods and factors as: 33;; = price of X 191; = price of Y 10 = price of labour or wage r = rental cost of capital Consumer A and B's demand for X and Y are given by: XA = 0.6(10w + 51") , YA = 0.4 (1011: + 57*) Pm Pg; X3 = 0.5(10w + 55") , YB = 0.5 (10w + 53") pm pt! (3.) Given the individual demands for the two consumers in the economy, derive the aggre- gate demand for X and Y. (Hint: this will he an aggregate demand for X and another for Y.) (4) The input demand equations for the two rms are given by: Lx = i (1)0.5'Kx = E (9)115 31005 YZ 1*\" 'r . w . \"7(5) J'F (b) Assume that these rms behave perfectly competitively. That is, supply is given by marginal cost. Given that the wage is w and the price of capital is 'r and that the demand for labour and capital by each rm (output) is given above, write an expression for the total cost of production for each good. Use these total cost expressions to derive the supply (marginal cost) equations for X and Y. (4) Sheridan Corporation is a privately owned company that uses ASPE. On January 1, 2020 Sheridan's financial records indicated the following information related to the company's defined benefit pension plan: Defined Benefit Obligation $1,370,000 Pension Plan Assets 1,520,000 Sheridan Corporation's actuary provided the following information on December 31, 2020: Current year service cost $86,000 Prior service cost, granted Jan 1, 2020 177,000 Employer contributions for the 91,000 year Benefits paid to retirees 27,000 Expected return on assets 5% Actual return on assets 6% Discount rate 5% Required: 1. Prepare a continuity schedule for defined benefit obligation for 2020 2. Prepare a continuity schedule for plan asset for 2020 3. Prepare pension related entries made by Sheridan Corporation for 2020. 4. Compare the plan's surplus or deficit at December 31,2020, with the amount reported on the December 31,2020 balance sheet