MAT10706 Quantitative Methods With Economics

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MAT10706 Quantitative Methods With Economics

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MAT10706 Quantitative Methods With Economics

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Course Code: MAT10706
University: Southern Cross University

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Country: Australia

Questions:
a. Explain the meaning and significance of any points of intersection.b. Discuss any differences in profitability between each type of heater (pay particular attention to the break-even point)
Answers:
The three different type of casting used by factory workers and their respective data and information is shown below.

Chromium

Titanium

Zirconium

Cost of casting

$75

$150

$240

Cost of gas fittings

$38

$36

$42

Sale price

$150

$220

$320

Fixed cost

$400

$500

$600

Investigation

Total cost and total revenue function along with excel graph

Total cost is a function of fixed cost and variable cost (Samuelson and Marks, 2013).
Variable cost
VC = Cost of casting + cost of gas fittings
For Chromium = 75 +38 = $113
For Titanium = 150 +36 =$186
For Zirconium = 240 +42 = $282
Total cost
TC = (Variable cost * Number of units) + Fixed Cost
Let number of units = Q
For Chromium = $113 Q +400
For Titanium =$186 Q +500
For Zirconium = $282 Q +600
Total revenue is a function of sale price and number of units (Nicholson and Snyder, 2014)  .
TR = P Q
For Chromium 
For Titanium 
For Zirconium 
Excel graph for TR and TC 

Point of intersection with the help of algebra

At point of intersection the total cost and total revenue would be same.
For Chromium
Sale price P = 150
TR = TC
PQ =113 Q +400
150Q = 113Q +400
Q = 10.81
TR and TC are intersection at Q =10.81 
For Titanium
Sale price P = 220
TR = TC
PQ =$186 Q +500
220Q = 186 Q+500
Q =14.7058
TR and TC are intersection at Q =14.7058 
For Zirconia
Sale price P = 320
TR = TC
PQ =$282 Q +600
320Q =282 Q+600
Q =15.789
TR and TC are intersection at Q =15.789 

Profit function and break-even point for each of the heater

Profit = TR – TC
At break-even point the TR and TC would be same (Paul and Wells, 2015). 
For Chromium
Profit function = TR -TC = PQ – (113 Q +400) = 150Q -113Q -400 = 37Q -400
Intersection point is 10.81 which is the break-even point.
For Titanium
Profit function = TR -TC = PQ- ($186 Q +500) =220Q – 186Q -500 =34Q -500
Intersection point is 14.705 which is the break-even point.
For Zirconium
Profit function = TR -TC = PQ-($282 Q +600) = 320Q -282Q -600 =38Q -600
Intersection point is 15.789 which is the break-even point.
Summary
a) The points of intersection highlight the breakeven point i.e. where there is no profit and no loss for the firm. These points are important as they convey the amount of sales that needs to be generated in order to ensure that the operations break even (Besanko and Braeutigam, 2015). Based on the expected demand of the underlying product, the firm can determine whether the expected sales would be able to be higher than the break even or not. Also, the margin of safety may be determined.
b) Taking into consideration the respective break even points for the various heaters, it may be concluded that highest profitability is observed for the Chromium model which achieves break even at the lowest unit sale. The next in line is Titanium model and finally the Zirconium model which has the highest breakeven unit requirement and hence the lowest profitability (Arnold, 2013).
c) The key assumption that has been made is that there is no change in the variable cost per unit irrespective of the volume and also the company can achieve and produce the requisite quantity of various heaters. These assumptions tend to limit the utility of breakeven analysis. 
Demand equation 
Supply equation 
Where,  

Two random numbers a and b between 0.1 and 0.9 has been obtained through =RAND() function and is show  below (Besanko and Braeutigam, 2015). 

Equilibrium price and quantities

Demand equation 
Supply equation 
At equilibrium 
Quantity cannot be negative and therefore, the equilibrium quantity would be 362.78 (Nicholson and Snyder,  2014).
Now,
Equilibrium price 
Therefore, equilibrium price would be $591.94 

New demand equation with $50 surcharge

Demand equation  
$50 surcharge hence, p would be p +50 
(New updated demand equation) 

New equilibrium price and quantity with levy 

Or 
Quantity cannot be negative and therefore, the equilibrium quantity would be 351.83.
Now,
Equilibrium price 
Therefore, equilibrium price would be $578.40. 

Supply and demand curve  

Summary table

Before levy

After levy

Difference

Equilibrium quantity

362.78

351.83

10.95

Equilibrium price: consumer pays

591.94

578.40

13.54

Equilibrium price: before levy

591.94

578.40

13.54

Revenue government receive (without levy)

188624

203499

-14.875

Revenue government receive (with levy)

203499

203499

Summary
a) It is apparent that after the levy in the form of surcharge is put, owing to which there is a decrease in consumption as the burden of levy needs to be borne. Further, the levy does seem to be productive from the perspective of the government as it has not impacted the consumption of services but has led to higher revenue generation for the government. This is on expected lines as for train service the demand would be expected to be inelastic (Pindyck and Rubinfeld, 2014).
b) Considering the positive impact of the levy on the government revenues, it makes sense that levy ought to be introduced. This would provide much needed support for the financial situation of the government and help it to maintain the quality of the services in the wake of the higher operating costs (Mankiw,2014).
c) The tacit assumption is that the supply can adjust without any changes in cost to the variations in demand in a short period of time. Typically this is not the case owing to which the utility of the analysis conducted may be limited.  
Referencing
Arnold, A.R. (2013). Microeconomics (9th ed.). Sydney: Cengage Learning.
Besanko, D. and Braeutigam, R. (2015). Microeconomics (4th ed.). New York: John Wiley & Sons.  
Mankiw, G. (2014) Microeconomics (6th ed.). London: Worth Publishers.
Nicholson, W. and Snyder, C. (2014). Fundamentals of Economics (11th ed.). New York: Cengage Learning.
Paul, K. and Wells, R. (2015). Microeconomics (2nd ed.). London: Worth Publishers.
Pindyck, R. and Rubinfeld, D. (2014). Microeconomics (5th ed.). London: Prentice-Hall Publications.
Samuelson, W. and Marks, S. (2013). Managerial Economics (4th ed.). New York: Wiley Publications.

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