Question 1: Changing growth in wages over time (5% out of 45%)

The following data on average weekly earnings for all employees was obtained from the Reserve Bank websitehttp://www.rba.gov.au

a)    From December 1970 to December 1980, what was the average annual growth rate in   average weekly earnings?  Give your answer to 3 decimal places. HINT: Consider using a version of the compound interest formula.

At this rate of growth, calculate when (month and year) average weekly earnings doubled on December 1970 levels.

b)   Using the same approach from part (a), calculate the average annual growth rate in average weekly earnings from December 1980 to December 1990.   Give your answer to two decimal places, but retain the unrounded answer in your calculator to calculate when  (month and    year) average weekly earnings doubled on December 1980 levels.

c)    Wages growth has been considerably slower in more recent times.  From December 2010 to December 2020, what was the average annual growth rate in average weekly earnings?        Report this rate to three decimal places, but retain the unrounded answer in your calculator for use in part d).

d)   If this growth has continued since December 2020, what would we expect the average weekly earnings to be as of June 2022? Report your result to two decimal places.

Question 2:  Using Indices and Compounding Interest (10% out of 45%)

A 24-year-old economics graduate has just secured their first full time position and is aiming to save a reasonable deposit to buy a small apartment. As such, the graduate must consider a savings strategy. The graduate is aiming to have $100 000 saved over 5 years.

Task – Part 1

Using information given below, determine the average rate of return required for the employee to reach this savings target:

     The graduate’s initial annual salary (at age 24, after tax) is $51 000, of which they can

contribute between 9.5% and 12% towards superannuation

     After making their superannuation contribution, the graduate’s living expenses must be

accounted for.  During the first year, these amount to $26 000.  In subsequent years,               expenses are assumed to increase by 3.25% each year. Anything left remaining after living    expenses represents potential savings to be put aside for the house deposit.  In this instance, the account that the graduate is depositing these savings into is a non-interest bearing           account (with a commencing balance of zero).

     The graduate’s salary over the next 5 years is predicted to change as follows:

•     At the end of Year 2, a pay increase of 1.5%

•     At the end of Year 3, a pay increase of 2%

•     At the end of Year 4, a final pay increase of 0.75%

Steps to answer Part 1

a)  Determine the graduate’s salary for each of the five years.

b)  Determine the graduate’s superannuation contributions for each of the five years.  For this section you must pick your own value between 9.5% and 12% and use this value for all five years.

c)  Determine the graduate’s living expenses for each of the five years. Then, from there, determine the amount remaining that could be put towards a housing deposit per year over 5 years.

d)  If the graduate does not reach their savings target at the end of 5 years, determine the time  required for the graduate to reach their savings goal if they were to place all of the savings     accumulated up to that point (i.e. by end of Year 5) into a savings account which accumulates interest compounded annually at 4.65%.

Task – Part 2

At the age of 29, due to circumstances beyond their control, the graduate has to withdraw $25 000  back out from the account into which they have been depositing their savings.  The graduate is then faced with a choice:

    Put the remaining balance into an interest-bearing account with a guaranteed return of 6.99%

per annum, compounding monthly.

    Put the remaining balance into an interest-bearing account with a guaranteed return of 2.49%

per annum, compounding quarterly.

Step to answer Part 2

For both interest-bearing account options, determine how long it would take the graduate’s account balance to reach $100 000.  Express your answers in months and years (to two decimal places).

Question 3: Determining range of profitability, optimum profitability and optimum employment (15% out of 45%)

Stephen operates a business that makes microwave ovens from a warehouse in an industrial estate. It costs Stephen $108 (in parts and labour) to make each microwave. In addition to this, there are     further fixed costs of $336 per microwave.  On average, Stephen sells 32 machines per week for a    price of $152 each.

Stephen then decides to have a sale and reduces the price of each microwave oven to an even   numbered price between $120 and $130 inclusive.  During the sale, Stephen sells on average 48 machines per week.

Task

1.    Select your own price value between $120 and $130 and determine the price-demand (p) function for this situation. HINT: Consider creating a pair of simultaneous equations.

2.    Determine the Total Revenue (TR) function and Total Profit (∏) functions.  HINT: TR = pq and ∏ = TR – TC.

3.    Determine Stephen’s break-even point(s).  If there is more than one break-even point, what do the values obtained represent?

4.    Plot the Total Cost (TC), Total Revenue (TR) and Profit (∏) functions on the same set of axes (i.e. single graph with three lines).

5.    Find the Marginal Revenue (MR) and Marginal Cost (MC) functions by differentiation and        determine the level of output (i.e. the value of q on the horizontal axis of your plot) at which  MR = MC.  With reference to your Excel plot, what conclusion can you make about this value?

6.    Confirm the maximum profit point by differentiation in a way that proves that the point is indeed a maximum. Also, confirm the amount of profit at that point by substitution.

7.    The productivity of labour function for the business is: Q = 5.6√L – 0.97L. Stephen currently employs 16 workers.  Determine

a.    marginal productivity of labour () for this number of workers and

b.   the number of workers that would optimise productivity

8.   Write a conclusion in which you summarise your interpretation of the results obtained.

a.    Is the sale a viable proposition for Stephen based upon your calculations?

b.    Is the current number of workers ideal for Stephen’s business?

c.    State any underlying assumptions and limitations that could influence your               calculations and what might occur if these assumptions and limitations did not hold firm over time.