Q1 Take a typical worker, Jordan. Before the onset of COVID-19, Jordon earned $30 per hour (after taxation) in their job. Assume that Jordan has no other sources of income or savings. Write down the equation of Jordan’s consumption budget constraint (for a single working day). Using a model with consumption on the vertical axis and hours of free time on the horizontal axis, plot Jordan’s budget constraint. Label all relevant elements of this diagram and state the value of the horizontal and vertical intercepts.

Q2 Now, add an indifference curve to the model you developed in Q1 and label it IC1. This indifference curve should be at a utility maximising point and show Jordan’s corresponding choice of consumption and hours of free time. As you have not been given any information regarding Jordan’s preferences, state one assumption that you have made about Jordan’s utility maximising choice and one assumption that you have made about the slope of Jordan’s indifference curve.

Q3 The arrival of COVID-19 brought financial hardship for Jordan’s employer. As a result, Jordan has had their hourly wage cut by 20% (a common occurrence around the world at the moment). Write down a new equation for Jordan’s consumption budget constraint (for a single working day). Using the same model developed in Q1-Q2, plot Jordan’s new budget constraint. Clearly state the value of the horizontal and vertical intercepts. MACQUARIE BUSINESS SCHOOL Department of Economics

Q4 Now, add a second indifference curve to the model you developed in Q1-Q3 and label it IC2. This indifference curve should be at a new utility maximising point and show Jordan’s corresponding choice of consumption and hours of free time. State what has happened to Jordan’s choice of consumption and free time. What can be said about Jordan’s overall level of utility after the onset of COVID-19?

Q5 Using the model created in Q1-Q4, show the income effect, substitution effect and overall effect of Jordan’s wage decrease. Compare the relative size of the income and substitution effects shown on your model. What can be inferred about Jordan’s preferences for free time and consumption from this comparison?

Sarah is a freshman high school student who is also holding down a 20-hour-a-week job. She drinks diet cola several times a day to keep her energized without adding calories, and she has given up all dairy products as part of her newly embraced vegan diet. At a routine checkup, her physician warned against excessive soda consumption and recommended that she add more sources of calcium to her diet. Why?

Timothy quits his job which pays $86000 a year , to enroll in a 3 year graduate program. His annual school expenses are $64900 for tuition, $8500 for books, and $1300 for food.

1. What is his opportunity cost for attending the graduate program?

A motor vehicle assembly plant requires the use of both capital and labour. The Tesla manufacturing plant is considering increasing the numbers of workers to production.

1. Does Diminishing Return hold in this scenario? (YES/NO)

2. Explain answer

The researcher conducted a hypothesis test and found the 95% confidence interval to examine whether there is a difference in high school students completion rate in percent with respect to the size of the teachers' salary (low or medium). The hypothesis test result showed p-value of 0.59 and the CI was [-2.45, 4.45].

In the space provided below,

a) Explain whether the hypothesis test result and the confidence interval are in agreement.

b) Explain whether and why Type 1 error or Type 2 error could occur in this study.

Please show answer using R commands.

Exercise 3: Bob is a high school basketball player. He is a 60% free throw shooter. That means his probability of making a free throw is 0.60. Use R commands to answer the following questions. (

(a) During the season, what is the probability that Bob makes his third free throw on his sixth shot? 

(b) What is the probability that Bob makes his first free throw on his sixth shot?

Amelia wants to estimate what proportion of her community members favor a tax increase for more local
school funding. She wants her margin of error to be no more than 2% at the 95% condence level. What is
the smallest sample size required to obtain the desired margin of error?

(2) Suppose a preliminary poll reveals that 45% of 50 voters support a presidential candidate. At 95% condence,
how large a sample is needed to obtain a margin of error of 4 percentage points?

Recently a researcher reported a correlation of -.57 across 30 high schools in the state between mean teacher salary and the per student vandalism rate of the school (these are not actual data and should be used only for purposes of this take-home). Interpret this finding. What do you believe is the most likely reason that these two variables correlate? (Be specific: if, for example, you believe that there is a third, fourth, etc., variable operating here, please indicate what variable it is and how it may affect the correlation.)

Suppose you are interested in measuring the amount of time, on average, it takes you to make your commute to school. You've estimated that the average time is 35.68 minutes with a standard deviation of 6.17 minutes. Assuming that your estimated parameters are correct and the commute time is normally distributed, what is the probability that the average commute time of 11 random days is greater than 36.86 minutes? Question 8 options: 1) 0.2629 2) 0.7371 3) 0.5758 4) 0.8246 5) 0.4242

List the type of correlation and casual relationship that you would expect to find for each of the following pairs of variables. a) the price of gasoline at the pump, the current world price of crude oil b) the fish population in a lake, the number of cottages around the lake c) the humidex rating (an index based on air temperature and humidity), the number of respiratory ailments reported d) the stock price of a telephone company, the cost of car insurance e) parents’ educational level, their children’s success in school?

While direct sunlight is unpolarized, light coming from a clear blue sky is linearly polarized to some extent. Assume all the light from the blue sky is linearly polarized in the same direction. Suppose a school library has installed skylight windows in the ceiling of the atrium to allow for natural lighting. The windows are polarized so that the intensity of light from the polarized blue sky is reduced by 58%. What is the angle between the polarization direction of the light and the polarization axis of the windows? __________°