Quantitative Methods With Economics

QUESTION 1  

Task 

You have been asked to investigate whether energy-saving light globes have lower total costs than  standard globes.  

Steps to complete to undertake the investigation 

1. Find cost and wattage of an energy saving globe and a regular light globe  

to complete the table below. Use the Internet or get these values from a  

local supermarket. 

1. Form an equation relating total cost of a light globe over time (t, in hours) to purchase cost  (P) and the running costs (R) for each type of light globe. One equation is for energy saving  globes and the other is for regular light globes.  
2. Use algebra to find the number of hours the light-globes will run when their total costs are the same. 
3. Graph your equations relating total cost to time on the same set of axes using Excel or a  similar program 
4. Summarise your findings in 200 words. In your conclusion  
5. Compare the two types of globes, in particular describing which has the lower  total costs 
6. Provide a recommendation on which of the globe is preferable 
7. Note any assumptions you have made and any limitations of your findings.  

Relevant information:  

∙ Assume that electricity for a standard house costs 25.38 cents per kiloWatt hour (kWH) ∙ It is estimated that electricity usage in Australia was 10 712.18 kWH per capita.

MAT10706 Assessment 2: Project Session 1 2017 4

QUESTION 2 

Task 

Costs for an airline have increased by $80 per passenger. To compensate for this, they are  introducing a fuel surcharge of $100 per passenger. Your task is to determine the  consequences of the surcharge.  

The supply and demand equations are given by; 

∙ Demand Equation: �� = 1500 − 10���� 

∙ Supply Equation: �� = 0.0001��2 + 2���� + 200 

where qis the number of passenger flights (in thousands per year) andpis the market price in  dollars.aandbare coefficients to be chosen below. 

Steps to complete to undertake the investigation 

1. Obtain two random numbers for a and b between 0.1 and 0.9 inclusive. Use the Excel random  function =Rand() or the RANDOM key on your calculator. Rewrite the demand and supply  equations above using these numbers. 
2. Use algebra to find the equilibrium price and quantity, without the proposed surcharge.  3. Update the demand equation to include the $100 surcharge. 
3. Use algebra to find the new equilibrium price and quantity, with the surcharge. 5. Use Excel to graph on the same set of axes, the original supply and demand equations (from part  1) and the updated demand equation with the proposed surcharge (part 3). 
4. Use your results to complete the following summary table. Round answers to two decimal places,  except for total revenue amounts which round to 0 decimal places 

Summarise your findings in 200 words. In your conclusion  

1. Discuss the effect of the surcharge on price, quantity and revenue 
2. Provide a recommendation to the airline on whether to introduce the fuel  surcharge or not  

c. Note any assumptions you have made and any limitations of your findings.

Comparative study on Energy Saving and Standard Glove

Real Cost of Lighting Your Home: Most of the time, we overlook the cost of lights to run. In this study, an attempt has been made to do the analysis of different types of light bulbs or Gloves. For the sake of this study, only two different types of light bulbs are considered.

1. Energy Saving Light Bulb (CFL or LED)
2. Standard Regular or Incandescent Bulb.

Energy-saving bulbs like CFL, LED has high installation cost as compared to the regular ones. But the watt usage of these bulbs is quite less as compared to the regular one.

An Incandescent bulb (Regular bulbs) usually comes with 60 watts with a price of $2-$3. At the same time, a CFL bulb ranges from 8 watts to 40 watts. A CFL bulb with 8 watts (which is equivalent to 60 watts in terms of luminosity of regular bulbs) costs $8-$10.

The information for the average prices for the energy-saving and regular gloves can be found in the Reference Section.

Table -1 provides information on a different type of light bulbs based on Australian Market Price,

Table – 1 

Energy Cost Equation

Equation for Total Cost (Rubinfeld, 2013)for Energy Saving Gloves,     …. (1)

Similarly, the total cost equation for Regular gloves can be written as,   …. (2)