Macro 1

Q7. Good weather in Central and South America increases the supply of coffee beans by 25%. This can be expected to cause ____ in the price of coffee due to a shift of the ____ curve.

A.) An increase : demand

B.) An increase : supply

C.) A decrease : supply

D.) A decrease : demand

2. Workers in an industry successfully form a union. Wages in the industry are likely to decrease over time. T/F

3. Suppose that in two months time the minimum wage is set to increase by $1 per hour. This is likely to

A.) benefit some workers who are presently earning the minimum wage

B.) have no effect on unemployment

C.) benefit all workers who are presently earning the minimum wage

D.) cause a reduction in unemployment

4. As the baby boom generation retires in larger numbers, this is likely to increase wages in the economy (all else the same). T/F

5. Unemployment results when

A.) there is a shortage of workers

B.) the quantity of labor demanded is greater than the quantity of labor supplied at the going wage rate

C.) the quantity of labor demanded is less than the quantity of labor supplied at the going wage rate

D.) the wage is below the level that balances supply and demand for labor

6. A decrease in the price of coffee will cause

A.) an upward movement along the demand curve for coffee

B.) a leftward shift of the demand curve for coffee

C.) a rightward shift of the demand curve for coffee

D.) a downward movement along the demand curve for coffee

7. A decrease in the supply of a good can be expected to cause ____in the equilibrium price of the good and ____in the equilibrium quantity of the good bought and sold, all else the same.

A.) a decrease : a decrease

B.) a decrease : an increase

C.) an increase : a decrease

D.) an increase : an increase

8. All else the same, when the supply of a good or service rises, then equilibrium price will also tend to rise. T/F

The number of claims per annum from a certain type of medical insurance policy sold to policyholders over the age of 60 is believed to follow a Poi()) distribution, where the parameter A is unknown. A sample of 10 policies gave rise to the following numbers of claims: 0, 1, 0, 0, 3, 0, 1, 0, 2, 2 (i) Use a normal approximation to calculate an approximate 99% confidence interval for the Poisson parameter 1. [3] (ii) Comment on the accuracy of the interval obtained in part (i). [2] (Hii) Write down the equations that you would use to obtain the confidence interval for 1 using an accurate method. [2] You are not required to solve these equations. [Total 7] A random sample ( x1,...,*, ) is taken from a Poisson distribution, with parameter /. (i) Show that the maximum likelihood estimator of / is: A = X [3] (ii) Determine the bias and mean square error of u . [2] (ii) Show that the variance of / attains the Cramer-Rao lower bound. [2] [Total 7]A random sample of 10 pet insurance claims had an average size of f680. It is believed that claim amounts are exponentially distributed. (i) Using the fact that if X1,..., X,, are exponentially distributed with parameter 1, then 2nix has a X2, distribution, where X is the mean of X1,...,X , calculate an exact 90% confidence interval for the mean pet insurance claim size. [3] (ii) Write down the likelihood function in terms of the mean / of the exponential distribution and hence show that the maximum likelihood estimator of / is X . [5] (iii) (a) Show that the Cramer-Rao lower bound for estimators of the mean of the exponential distribution is given by: n (b) Hence, calculate the estimated asymptotic standard error of the mean, X. [3] (iv) (a) Use your results from (iii) and the asymptotic properties of estimators to calculate an approximate 90% confidence interval for the mean claim size. (b) Comment on the confidence intervals produced in (i) and (iv)(a). [4]