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ECON 310: Problem Set #3 Please submit through Canvas Due Date: October 23, 2020 For all of the questions in this problem set, amume there is no tax at all. Stocks Consider stock A with a dividend yield equal to 2.5% (based on its dividend payments over the past year) The dividends are expected to grow at 8% per year. Stock A is currently traded at $52 per share. 1, According to Gordon's model, what would be the expected return on the stock? Answer: The Gordon's model states that P = DI TE - 9 Rearrange the terms we get Pi(1+g) +9= 2.5% . (1+8%) +8%=10.7%% 2. Suppose the total dividends paid over the next year is $1.4 per share, leading to a downward revision of the expected dividend growth rate to 7.5%%, Assume the expected rate of return remains the same for this stock, what would be the actual rate of return from holding this stock over the next year? Answer: The price of stock A a year from now, according to Gordon's model, is 1+9 -14- 1 +7.5% 10.7% -7.5% =$47.03/share The rate of return is Rut - Dent Ann -A_1.4+47.03-52 52 =-687% 3. Consider stock B which just paid $6 in dividends over the past year. The expected return on the stock is 12.5% and the stock is currently traded at $120 per share. At what rate are the dividends expected to grow for this stock according to Gordon's model? Answer: Again, starting with the Gordon's model 1+9 P = DITE - 9 and rearrange the terms we have Pi(TE - g) = D,(1+ 9)Consider the following IS-LM model: C = 400 + 0.25YD 1 = 300 + 0.25Y - 1500i G = 600 T = 400 (M/P)d = 2Y - 12 000i M/P = 3000 a. Derive the IS relation. (Hint: You want an equation with Y on the left side and everything else on the right.) b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with i on the left side and everything else on the right.) c. Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output.) d. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in part (c) into either the IS or LM equations and solve for i. If your algebra is correct, you should get the same answer from both equations.)Cost^ = C. Interpret the estimated slope coefficients ( 1 , B2 and B3 ). B1 : B2 : B3 : d. Using the p-value from the output, test at the 5% significance level that house size (X1) has a significantly positive effect on the heating cost. Ho: HA: Test statistic and its distribution: Decision rule: R-value: Conclusion:Answer the following questions, using the above information. a. Determine the dependent and independent variables of the model. Dependent variable: Independent variables: b. Based on the estimation results in the output, write down the estimated multiple regression model in the form Cost^ = Bo + Bi Size + 32 Windows + 3 Occupants, and the corresponding standard errors and p-values below the parameter estimates in parentheses.SUMMARY OUTPUT SUMMARY OUTPUT Regression Statistics Multiple R 0.9453 R Square 0. 8940 Adjusted R Square 0. 8350 Standard Error 34. 898 Ybar= $355.50 Observations 35 ANOVA SS MS F Significance F Regression 3 62588.8 15647.2 12.85 0.000 Residual 31 37754.0 1217.9 Total 34 100342.8 Coefficients Standard Error t Stat P-value Intercept 11.01 4.532 2.45 0.010 Size 5.632 1.489 3.78 0.000 Windows 3. 180 1.966 1.62 0. 048 Occupants 15.431 6.85 2.25 0. 016