MAT10706 Quantitative Methods with Economics Project Assignment

This document presents a comprehensive solution to a Quantitative Methods with Economics project, focusing on cost-revenue analysis and demand-supply equilibrium. The project involves determining break-even points for different engine part types using cost and revenue functions, calculating pro...Read More

MAT10706 QUANTITATIVE METHDS WITH ECONOMICS
PROJECT ASSIGNMENT
Student Name
[Pick the date]

Question 1
1) Type 1- Chrome Catalyst Engine Parts
Fixed production costs = $ 4000
Unit variable costs = 876 + 65 = $941
Estimated unit sale price = $ 1,100
Total cost function = 4000 + 941 B
Revenue Function = 1100 B
Type 2- Platinum Power Engine Parts
Fixed production costs = $ 4000
Unit variable costs = 1228 + 65 = $1293
Estimated unit sale price = $ 1,500
Total cost function = 4000 + 1293B
Revenue Function = 1500 B
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Type 3- Silver Streak Engine Parts
Fixed production costs = $ 4000
Unit variable costs = 1024 + 65 = $1089
Estimated unit sale price = $ 1,300
Total cost function = 4000 + 1089B
Revenue Function = 1300 B
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2) Point of intersections between cost and revenue functions
Type 1- Chrome Catalyst Engine Parts
Total cost function = 4000 + 941 B
Revenue Function = 1100 B
At equilibrium
Total cost function = Revenue Function
4000+ 941 B=1100 B
4000−159 B=0
B=25.15
B=26 (nearest whole number)
Type 2- Platinum Power Engine Parts
Total cost function = 4000 + 1293B
Revenue Function = 1500 B
At equilibrium
Total cost function = Revenue Function
At equilibrium
Total cost function = Revenue Function
4000+ 1293 B=1500 B
4000+1293 B−1500 B=0
B=19.3
B=20 (nearest whole number)
Type 3- Silver Streak Engine Parts
Total cost function = 4000 + 1089B
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Revenue Function = 1300 B
At equilibrium
Total cost function = Revenue Function
4000+ 1089 B=1300 B
4000+ 1089 B−1300 B=0
B=18.95
B=19(nearest whole number)
3) The profit functions for the three motorcycles can be estimated using the following formula.
Profit function = Revenue Function – Cost Function
Type 1- Chrome Catalyst Engine Parts
Profit function ¿ 1100 B−(4000+941 B)=159 B – 4000
Break-even point = Fixed Cost/Unit Contribution Margin ¿ 4000
1100−941 =25.15∨26 motorcycles
Type 2- Platinum Power Engine Parts
Profit function ¿ 1500 B−(4000+1293 B)=207 B – 4000
Break-even point = Fixed Cost/Unit Contribution Margin ¿ 4000
1500−1293 =19.32∨20 motorcycles
Type 3- Silver Streak Engine Parts
Profit function ¿ 1300 B−(4000+1089 B)=211 B – 4000
Break-even point = Fixed Cost/Unit Contribution Margin ¿ 4000
1300−1089 =18.96∨19 motorcycles
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4) A) The intersection points on the graph represent the points where the cost and revenue are
equal and hence the profit would be zero at these points. This is the same as breakeven point
which has been computed in part 3. Hence, the value of the intersection points for the three
models is the same as the corresponding break-even point computed in part 3.
b) In order to compare the profitability of the various models, it is essential to compare the
break-even points along with the contribution margin. The break=even point is the lowest for
Type 3 (Silver Streak Engine Parts) model and also the contribution margin is the highest for
this model. Since the fixed cost for each of the model is the same, hence the most profitable
model would be one which has the highest contribution margin per unit which is Type 3
only.
c) An assumption has been made about the sale price. Another assumption is that variable
cost remains the same and any number of units for either type can be sold. A major limitation
of this analysis is that the figures would alter if the sale price of either of the motorcycle type
would change.
Question 2
Demand function : P=175−15 aq
Supply function : P=0.00025 q2 +5 bq+35
1. The value of a and b has been determined by using ran function between 0.1 and 0.9.
2.
Demand function : P=175− ( 15∗0.23 ) q=175−3.45 q
Supply function : P=0.00025 q2 + ( 5∗0.51 ) q+35=0.00025 q2 +2.55 q+35
AT equilibrium
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Demand function=Supply function
175−3.5 q=0.00025q2 +2.54 q+ 35
−0.00025 q2−2.55 q−3.45 q+175−35=0
−0.00025 q2−6 q+140=0
q=−24023.3∧23.35
Quantity cannot be negative and thus, q=−24023.3 would be rejected.
q=23.35
P=175−3.45 q=175− ( 3.45∗23.35 )=$ 94.44
It is apparent that price cannot be negative and thus, the equilibrium quantity is 23.35 and price
would be $94.44.
3. Demand equation has included a price reduction of $25
The new demand equation
P−25=175−3.45 q
P=200−3.45 q
4. New equilibrium quantity and price
Demand equation: P=200−3.45 q
Supply equation: P=0.00025 q2 +2.55 q+ 35
At equilibrium
200−3.45 q=0.00025 q2 +2.55 q+35=¿
−0.00025 q2−6 q+165=0
q=−24027.46 , 27.46
Quantity cannot be negative and thus, q=−24027.46 would be rejected.
q=27.46
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P=200−3.45 q=200− (3.45∗27.46 )=105.26
It is apparent that price cannot be negative and thus, the equilibrium quantity is 27.46 and price
would be $105.26.
5) The requisite demand supply graph for the two situations is indicated below.
6) The requisite table is indicated below.
7) A) On the basis of the above table, it is apparent owing to reduction price, there is an increase
in demand while the supply has remained the same. This has led to increase in the
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equilibrium price by $10.82 at the end of the consumer. Also, there is an increase in the
equilibrium quantity by 4.11 units. Further, there is an increase in the revenue considering
the both equilibrium price and equilibrium quantity have witnessed an increase.
B) Considering the positive impact of the price decrease on the overall market, it would be fair to
conclude that the price reduction should be implemented by the company. Also, since the
revenue has increased, it clearly highlights that the demand for flights is elastic in nature. As a
result, reduced prices tend to lead to a disproportionate jump in the quantity consumed and hence
there is a jump in the revenue. Also, there is a better occupancy rate for the flights through this
means and as a result revenues are improving. It is noteworthy that in case of demand being
inelastic, the price discount would have had a unfavourable influence on the revenue of the
airlines.
C) It is assumed that the second airline does not respond by reducing the price. Also, it is
assumed that the market supply does not alter owing to the lower price through the entry or exit
of a particular airline. A major limitation of this analysis is that it does not consider the
possibility of a price war between the airlines which would be advantageous for the consumers
but would adversely impact profitability for airlines.
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