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6. (20 points) The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep. The estimated model is: sleep = 3638.25 - 0.148 x totwrk - 11.13 x educ + 2.20 x age (112.28) (0.017) (5.88) (1.45) n= 706, R2= 0.113 where sleep and totwrk (total work) are measured in minutes per week and educ (education) and age are measured in years. a. Interpret the coefficient on totwrk. Is there a interpretation for the intercept term? (Hint: There is!) b. Is either educor age individually significant at the 5% level against a two-sided alternative? Report the p-values in both cases. Show your work.1. Consider a pure exchange economy.r with two goods. 1urine {I} and cheese (1;) and two con- sunierst A. and B. Let chemo he the numeraire good with price of 51. Consumer A's utilit:,r function is U'Aht', y} = I'yl while B's utility function is Winn} = Ilf'l'yaf'l'. as initial allocation is 31!] units of a: and 31.] units of y. B's initial allocation is it'll units of e and 20 units of y. {a} Put wine a: on the horizontal axis and cheese 1; on the vertical axis. Measure goods for consumer A from the lower left and goods for consumer B from the upper right. Marl: the initial allocation 1with the letter W. Draw the indifference curves for each person through this point. Calculate utility at this allocation for both consumers. Is the initial resource allocation consistent with Pareto efficiency? Explain. {h} Identify the contract curve of Pareto efcient allocations in this econo'lrljr and show this on your graph. {cl Find the competitive equilibrium prices and consumption for each type of consumer. Derive A's and B's demand functions (grossfhiarshallian). Calculate the equilibrium price of wine assuming price of cheese is 51, using 1illi'stlras" Law. {d} Verify that the First Fundamental Theorem of WEHEIE Economics holds, 2. In the simulation exercise we will compare the relative performance of the two Wald statis- tics. Consider the following DGPs in Ho with X, and X2 obtained using Xli 0.6 0.3 X1i-1 Eli + (61i, (2i, U.) IID ~ MVN (0, Is) (3) X 2i 0.3 0.6 X2i-1 X 10 and ~ MVN (0, 12) ; (4) X 20 Furthermore, consider the following sample sizes n = 20, 30, 50, 100, 500 and the values of regression parameters (Bo, B1, B2) : (1,10,0.1),(1,5,0.2). Report the empirical rejection