Help in answering all the questions below. Kindly include explanations in your answers.

1. Calculate GDP loss if equilibrium level of GDP is $6,000, unemployment rate 8.5%, and the MPC is 0.90.

a) How much money should the government spend to eliminate this GDP loss?

b) Calculate the tax cut needed to eliminate this GDP loss.

2. Calculate MPC, MPS and the Multiplier if consumption expenditure increases by $6,000 as a result of increase in income from $40,000 to $48,000.

3. Assume that initially G (Government Expenditure) is $200 and equilibrium real GDP is $5000. If MPC is .9, what would be the new equilibrium level of GDP if G (Government Expenditures) increases to $300.

Agriculture extension officers would like test the effective of 4 different fertilizers on the yields of tomatoes. They prepare samples of 5 plots for each and applied the fertilizers accordingly. The yields per plot for each of the fertilizers are given below. A 5% level of significance, test whether the fertilizers are equally effective. A B C D 6 4 7 3 5 3 4 0 2 10 Total 10 15 20 35 Means 2 3 4 7 Variance 0.8 2.8 1.6 4A credit manager for American express has found that 10% of their card users do not pay the full amount of indebtedness during any given month. She wants to determine the probability that if 20 accounts are randomly selected, 5 of them are not paid.A life assurance company is examining the force of mortality, / , of a particular group of policyholders. It is thought that it is related to the age, x, of the policyholders by the formula: Ux = Be* It is decided to analyse this assumption by using the linear regression model: Y = a + Bx; + &; where &; ~ N(0,of) are independently distributed The summary results for eight ages were as follows: Age, X 30 32 34 36 38 40 42 44 Force of mortality, 5.84 6.10 Ux (x10*) 6.48 7.05 7.87 9.03 10.56 12.66 In /, (3 s.f.) -7.45 -7.40 -7.34 -7.26 - 7.15 -7.01 - 6.85 -6.67 Ex; = 296 x/ =11,120 _In/x, =-57.129 _(In /x, )? = 408.50 _x, In /x =-2,104.5 (a) Apply a transformation to the original formula, M, = Be*, to make it suitable for analysis by linear regression. Hence, write down expressions for Y, o and B in terms of Ax , B and c. (b ) Plot a graph of In /, against the age of the policyholder, x. Hence comment on the suitability of the regression model and state how this supports your transformation in part (a). [4] (ii) Use the data to obtain least squares estimates of B and c in the original formula. [3] (iii) (a) Calculate the coefficient of determination between In /, and x. Hence comment on the fit of the model to the data. (b) Complete the table of residuals and use them to comment on the fit. [5] Age, X 30 32 34 36 38 40 42 44 Residual, e; 0.08 -0.03 -0.06 0.02 0.09 (iv) Calculate a 95% confidence interval for the mean predicted response In /35 and hence obtain a 95% confidence interval for the mean predicted value of /35 . [4] [Total 16]The government of a country suffering from hyperinflation has sponsored an economist to monitor the price of a "basket" of items in the population's staple diet over a one-year period. As part of his study, the economist selected six days during the year and on each of these days visited a single nightclub, where he recorded the price of a pint of lager. His report showed the following prices: Day (i ) 8 29 57 92 141 148 Price ( P.) 15 17 22 51 88 95 In P 2.7081 2.8332 3.0910 3.9318 4.4773 4.5539 [i=475 [ =54,403 [InP, = 21.5953 _(In P)? =81.1584 Liln P, =1,947.020 The economist believes that the price of a pint of lager in a given bar on day i can be modelled by: In P = a + bite; where a and b are constants and the e, 's are uncorrelated /(0,o ) random variables. (i) Estimate a , b and o. [5] (ii) Calculate the linear correlation coefficient r. [1] (iii) Obtain a 99% confidence interval for b . [2] (iv) Determine a 95% confidence interval for the average price of a pint of lager on day 365: (a) in the country as a whole (b) in a randomly selected bar. [7] [Total 15]