Help in answering the questions below.

1.

(i) 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.

(ii). 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.

(iii). 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.

The number of claims arising in a year on a certain type of insurance policy has a Poisson distribution with parameter 1. The insurer's claim file shows that claims were made on 238 policies during the last year with the following frequency distribution for the number of claims: Number of claims Frequency 174 50 PAWN 10 4 25 No information is available from the policy file, that is, only data concerning those policies on which claims were made can be used in the estimation of the claim rate A (This is why there is no entry for the number of claims being 0 in the table.) (i) Show that the truncated probability function is given by: P(X = x) =- x!(1-e- ) x = 1, 2,3. ... (ii) Hence show that both the method of moments estimator and the MLE of 1 satisfy the equation 1 = x(1-e-*), where x is the mean number of claims for policies that have at least one claim. (iii) Solve this equation, by any means, for the given data and calculate the resulting estimate of 1 to two decimal places. (iv) Hence, estimate the percentage of all policies with no claims during the year.A random sample of n observations is taken from a normal distribution with mean and variance of. The sample variance is an observation of a random variable S-. Derive from first principles E( $2 ) and var($2)