\fPART A: PLEASE ATTEMPT BOTH QUESTION 1 AND QUESTION 2 Question 1 [15 marks in total, 3 marks for each part] Answer each of the following. In each case state whether the statement is True, False or Uncertain and explain your answer. (i) Good econometric results for a beer demand equation are more likely to be obtained in periods of industry stability where prices do not change much. (ii) Suppose the linear regression model y = Bo+ Bix+ Bzz+ u is assumed to hold. If the data to be used in estimation are cross-sectional at a point in time and z does not vary over the cross-sectional observations, then you should still include z anyway to avoid bias in your estimation of B1. (iii) The following estimated model is a problematic representation of housing prices because of the incorrect sign associated with the hsize coefficient: price = 151.5 -.26hsize + .0037hsizesq+ 14.51bdrms ( 85.4) (.18) (. 0017) (7.97) where price is sale price is $'000, hsize is the size of the house in square meters, hsizesq is size squared and bdrms is the number of bedrooms in the house. (iv) For the regression equation y = Bo + Bi*1 + 82x2 + u, the RESET test is a convenient diagnostic that is useful for investigating functional form mis- specification and is implemented by testing the joint significance of 8, and 62 in the auxiliary regression: y = Bot B1*1 + B2x2 + 615 + 6202 +vQuestion 1 [15 marks in total, 3 marks for each part] Answer each of the following. In each case state whether the statement is True, False or Uncertain and explain your answer. (i) Good econometric results for a beer demand equation are more likely to be obtained in periods of industry stability where prices do not change much. (ii) Suppose the linear regression model y = Bo + Bix + Bzz + u is assumed to hold. If the data to be used in estimation are cross-sectional at a point in time and z does not vary over the cross-sectional observations, then you should still include z anyway to avoid bias in your estimation of B1. (iii) The following estimated model is a problematic representation of housing prices because of the incorrect sign associated with the hsize coefficient: price= 151.5 -.26hsize + .0037hsizesq+ 14.51bdrms ( 85.4) (.18) (. 0017) (7.97) where price is sale price is $'000, hsize is the size of the house in square meters, hsizesq is size squared and bdrms is the number of bedrooms in the house. (iv) For the regression equation y = Bo + Bi*1 + 82*2 + u, the RESET test is a convenient diagnostic that is useful for investigating functional form mis- specification and is implemented by testing the joint significance of 6, and 62 in the auxiliary regression: y = Bot B1*1 + B2x2 + 619+ 6252+v where p are the predictions from the original regression. (v) A trending variable can't be used as the dependent variable in multiple regression analysis.1. Suppose an economy has two consumers, Evelyn and Kaitlyn, and two commodities X and Y. Evelyn's utility function and initial endowment are: Up = min{XE, YE} WE = (WEX, WEY) = (50, 100) Kaitlyn's utility function and initial endowment are: Uk = min{Xk, Yx} WK = (WKX, WRY) = (100, 50) (a) Please draw the Edgeworth box. (b) Please label Evelyn's and Kaitlyn's initial endowment points in the Edgeworth box. (c) Please draw at least three Evelyn's and Kaitlyn's indifference curves in the Edgeworth box. (d) Please draw the contract curve in the Edgeworth box.Amanda's utility function is Leontief and given by Wa(Xarya) = min(xa. yal while Brenda's utility is linear and given by us(xb. )b) = XD + VD Their endowments are wa = (2,3) and wo = (4, 1). Show this economy in an Edgeworth Box Show the Individually Rational allocations and show in Edgeworth Box Find the Pareto Efficient allocations for this economy and show in the Edgeworth Box. Show the core of the economy. Find the Walrasian Equilibrium of the economy and show in your Edgeworth box. Prove directly that the First Welfare Theorem holds Does the Second Welfare Theorem hold for allocation ((3,3)a, (3,1),}? If so how?Consider a pure exchange economy with two individuals (Adam and Bob) and two goods (x and y). Their utility functions are given by UA(TA, yA) = JAYA and UB(TB, yB) 0.5 0.5 = "ByB Initially, Adam has 100 units of good x and Bob has 100 units of good y (a) Find the general equilibrium price ratio px/py and the general equilibrium allocation (their demand bundles in the equilibrium). Illustrate this general equilibrium allocation using Edgeworth box. (b) Find all Pareto efficient allocations in this economy, and illustrate all these Pareto efficient allocations in the Edgeworth box. (c) The first theorem of welfare economics states that the general equilibrium allocation is Pareto efficient. Is the equilibrium allocation you found in (a) efficient and why? Show transcribed image text4. Consider a two person {1 and 2], two good {A and B] exchange economy. Social welfare forthe economy i5: W=U1+U2. a. Draw social indifference curves for the economy in question. What is the rate at which society is willing to trade one person's welfare for another? b. Suppose that person 1's utility function is U1=A+2El and person 2's utility function is U2=3A+EL Suppose that each person is endowed with 15 units of goods A and B {making a total of 3!] units in the economy]. Determine the optimal allocation in the economy, underthe condition that both individuals receive at least as much utility as their endowed consumption bundle. NOTE The marginal utitr'es for person I are: Muzl, MUB=2 The marginal utilities for person .2 are: MUAzi Muazl. c. Suppose social welfare is now characterized as: Wzmin[U1,U2], re-do part B. Describe how the optimal allocations change and why