7. Consider the following income-expenditure model of a closed economy. The aggregate consumption function is C = 100 +0.8(Y – T); taxes are T = 380; investment, I, is 300 and government expenditure, G, is 200.

(a) Calculate the multiplier, equilibrium income and the government budget surplus [6 marks]

(b) Now let taxes, T = 10 + 0.25Y. Recalculate the multiplier, equilibrium income and the government budget surplus. Try to explain any differences between your answers and your answers to part (a). [10 marks]

(c) Now we further extend the model and open the economy to trade. Let net exports be NX = 444 - 0.3Y. Keep the tax function as in (b). Recalculate the multiplier and equilibrium income and again explain any differences between your answers and those in part (b).

True or False

On April 9th 2020, the S&P500 was trading at 2,750, implying a current P/E ratio of 18. The expected cash payout ratio (dividends + buybacks) is 92% of earnings (in perpetuity). Analysts’ consensus annual growth forecast in earnings for the index is 3.5% for the next 5 years. Use a risk free rate of 0.8% and set the long term growth rate equal to the risk free rate. 1) Estimate the implied equity risk premium using a two-stage growth model given the current level of the S&P500 index and expectations of cash flows. 2) All else equal (i.e. for a given level of the S&P500 index), what would happen to the iERP if the COVID crisis led investors to lower substantially their expectations of dividends and buybacks? (Would it go up or down?)

A production line operation is tested for filling weight accuracy using the following hypotheses.

Hypothesis       Conclusion and Action
H ₀:  = 16         Filling okay, keep running
H _a:     16       Filling off standard; stop and adjust machine

The sample size is 37 and the population standard deviation is  = 0.8. Use  = .05. Do not round intermediate calculations.

1. What would a Type II error mean in this situation?
   SelectConcluding that the mean filling weight is not 16 ounces when it actually isConcluding that the mean filling weight is 16 ounces when it actually isn'tItem 1
2. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?
   
3. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?

A production line operation is tested for filling weight accuracy using the following hypotheses.

Hypothesis       Conclusion and Action
H ₀:  = 16         Filling okay, keep running
H _a:     16       Filling off standard; stop and adjust machine

The sample size is 36 and the population standard deviation is  = 0.8. Use  = .05. Do not round intermediate calculations.

1. What would a Type II error mean in this situation?
   Concluding that the mean filling weight is not 16 ounces when it actually isConcluding that the mean filling weight is 16 ounces when it actually isn'tItem 1
   
2. What is the probability of making a Type II error when the machine is overfilling by .5 ounces (to 4 decimals)?
   
   
3. What is the power of the statistical test when the machine is overfilling by .5 ounces (to 4 decimals)?
   

Based on current dividend yields and expected capital gains, the expected return on portfolios A and B are 11% and 14% respectively. The beta of A is 0.8 while that of B is 1.5. The rate of exchange fund bill is currently 6%, while the expected return of the Hang Seng Index is 12%. The standard deviation of portfolio A is 10%, while that of B is 31%, and that of the index is 20%.

a. If you currently hold the Hang Seng Index, would you choose to add portfolio A or B to your holdings?

b. If you currently hold the exchange fund bills, which one would you choose (i.e. portfolio A, portfolio B or the Hang Seng Index) to add to your holdings?

c. What would happen if we measure the performance of a poorly diversified portfolio using Treynor measure? (6marks)

Pennsylvania Company has a monthly gross payroll (paid on the last day of each month) of $516,000, which is subject to unemployment taxes (Federal at 0.8% and State at 5.4%). All earnings are subject to 7.65% FICA tax (combined Social Security and Medicare). Federal income tax withholdings are 25%, and state income tax withholdings are 8% of total earnings.

Assuming no individual employee has reached the maximum limit for Social Security tax or for unemployment tax, which of the following is not true for the month ended January 31?

a) Pennsylvania Company will record a liability for Federal Unemployment Taxes of $4,128.

b) Pennsylvania Company will record a net payroll of $306,246.

c) Pennsylvania Company will record a liability for State Income Taxes of $41,280.

d) Pennsylvania Company will record a total liability for FICA Taxes of $39,474.

Please answer the following 2 questions using the probabilities of different scenarios below.

• What is the expected return and standard deviation of the S&P 500 portfolio and the Bond?

• Suppose AAPL has a beta of 0.8. If the risk-free rate is 3% and the market return is 9%, according to CAPM, the expected return for AAPL is? If the stock price for AAPL is $100 today, according to the expected return you calculate, what is the expected price for AAPL in a year if AAPL is not paying a dividend? What is the expected price if AAPL will pay a dividend of $3?

Suppose that the mean weight of newborn babies is normally distributed with a mean of 6.9 pounds and a standard deviation of 0.8 pound. A developmental psychologist wants to test whether newborn babies of mothers who use drugs during pregnancy differ in weight from the average baby. The psychologist takes a random sample of 30 mothers who used drugs during pregnancy and computes the mean birth weight of these mothers’ babies. This sample of 30 mothers has a sample mean of 6.7 pounds. Using an alpha level of .01, test whether mothers’ drug use during pregnancy affects newborn babies’ birth weight. Which of the following is the most accurate mathematical null hypothesis?

A) μ < 6.7

B) μ ≠ 6.7

C) μ ≠ 0

D) μ = 6.9