Solve these problems.as attached below.
4. A simple linear regression model relating a bank lending interest rate and investment in physical capital by companies is stated as: y = Bo + Bix+ 8 where & is the error term a. Which variable (lending interest rate or investment in physical capital) do you think should be the dependent variable in this regression model? Please justify your answer. [2 points ] b. What sign would you expect for the slope of this regression model for interest rate and investment in physical capita? Please justify your answer. [2 points] c. What is the role of the error term in the simple linear regression model like the one stated above? Please state at least three examples of the factors that you think belong in the error term of the simple linear regression model stated above briefly justifying each example. [3 points] d. Please explain how you would estimate the relationship between interest rate and investment specified above. [note: you do not need to write any formulas as an answer to this question. Just explain what you will need and the reasoning behind the method you would use to estimate the relationship]. [3 points] e. For what purpose could you use the estimated simple linear regression model for lending interest rate and investment in physical capital? Why could the simple linear regression model stated above be inadequate for the purpose? [2 points ] f. Using an example, please explain why a statistically significant relationship in a regression model for two variables does not necessarily imply "cause" and "effect" relationship between the two variables. [2 points]5. Consider a consumer who has preference towards specialization but that always prefers to consume positive of both goods rather than fully specialize in just one of them. Assume her preferences are represented by the following utility function: (POINTS: 18) u(x, y) = x +y', ifx>0 and y>0 jo, if x = 0 or y=0 Note that this consumer preferences is not continuous (do not worry if you do not see that, we will work through the problem). We will show that the UMP and EMP may not generate the same outcome. Fix Px = py = 1, 1 = $1, and u = 1 (a) Argue that this agent will never choose zero quantities for x or y, in either problem (UMP or EMP), as long as / > 0 and u > 0. (Points: 3/18) (b) Explain why neither (1,0) nor (0, 1) belong to /C(1). (Points: 3/18) (c) Explain why the agent's budget constraint do not have any point in common with IC( 1). (Points: 3/18) 10 (d) Argue why in the UMC the agent cannot choose a bundle with utility equal to or higher than 1. (Points: 3/18) (e) Argue why in the EMP the agent cannot choose a bundle with a cost equal to or smaller than $1. (Points: 3/18)Question 2 (A decrease in the rate of domestic money growth) (40 points) Consider the Canadian economy and suppose that the current growth rate of the money supply in Canada is arc-an. Suppose that at time to the Bank of Canada, unexpectedly, announces that from new on the growth rate of money supply in Canada will decrease to 11'0\(40pts) (Challenging) Let T : V > V be a selfadjoint linear operator on a n dimensional inner product space V over the eld F = (C. Let A1 5 A2 V is another selfadjoint linear operator with eigenvalues m S 11.2 S S on (counted with multiplicity). Assume the eigenvalues of T+U are given by '71 g 72 g 3 7n (counted with multiplicity). Let 1 S 2', j, k: 5 71. Hi +j = n+k, prove that 1% S A:- +uj
