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\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 4) Demand for Coffee (8 points/1 points each) Suppose you have the following estimated regressions for coffee consumption with 123 observations. Model1: C =2.43-1.22 P+ 2.35Y R= =0.48 (1.1) (0.18) (0.65) Model 2 : C =1.85-1.07 P+1.98Y +0.42 PT R= =0.59 (1.3) (0.13) (0.54) (0.16) Model 3:C =2.97-1.38P R= =0.39 (1.2) (0.13) Model 4:C =1.24-0.87 +1.48Y +0.32PT-0.18PM R' =0.60 (1.1) (0.20) (0.44) (0.13) 0.99 Where P is price index for coffee, Y represents the income index, PT is the price of tea, PM represents price of milk and C represents the cups of coffee consumed You are also given that C = 5, Y =1750, P = 8, PT =1.5, PM = 3.5. a) Consider Model 4, are these results consistent with economic theory? Explain your answer with statistical evidence. b) Can you test the overall significance for effects of price of coffee, income and price of tea on coffee demand? If YES, provide test result. If NO, explain your reasoning. c) Use an F-test approach to Test the following hypotheses. i) Price of milk and price of tea jointly affects the demand for coffee. ii) Income does not affect the demand for coffee. iii) Price of milk, income and price of tea jointly affects the demand for coffee. iv) Price of milk does not affect the demand for coffee. d) Do you agree with inclusion of price of milk in the regression estimations? Suggest other variables to be included in the demand line of coffee. Justify your answer. e) Is coffee an inferior good? Support your answer with statistical evidence. () Can you determine the price elasticity of demand for coffee? If YES, provide test result. If NO, explain your reasoning. g) Are coffee and tea substitutes? Support your answer with statistical evidence. h) Suppose that a researcher estimates Model I with a dependent variable of CT which is measured in 10 cups of coffee. Write down the results obtained by the researcher.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 + 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, Yk} WK = (WKX, WHY) = (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 two person [1 and 2], two good {A and B] exchange economy. Social welfare for the economy W=U1+U2. A} Draw social indifference curves for the economy in question. 1lullihat is the rate at which society is willing to trade one perso n'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+ Eli. Suppose that each person is endowed with 15 units of goods A and El [making a total of 3D units in the economy}. Determine the optimal allocation in the economy, underthe condition that both individuals receive at lea as much utility as their endowed consumption bundle. H*N0TE***: The marginal utiiities for person 1 as MUA=L Muff; The marginai utilities forperson 2 are: M [51:3, MUB=1 C] Suppose social welfare is now characterized as: W=minU1,U2]|, redo part El. Describe how the optima allocations change and why Consumer 2 has endowment w? = (4, 8) and utility function U2(x) = 23 +4V/x]. (a) Find all Pareto efficient allocations where both consumers consume strictly positive amounts of good 1 and good 2. (b) Argue that any feasible allocation r = (r), r?) where r? = 16 and 12