Economics Assignment 5

ECONOMICS ASSIGNMENT 5
Economics Assignment 5

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ECONOMICS ASSIGNMENT 5
Calculation
Chapter 14 Exercise # 2
The relation between Marginal Revenue (MR), Price (p) and price elasticity of demand (e) is
as follows:
MR= P(1+1/e)
At profit maximization: MR= MC, so optimal price or profit maximizing price P* is:
MC= P*(1+1/e) or P*= MC/(1+1/e)
Here MC= $120
Price elasticity of demand for first class passengers= -1.3
So, Optimal fare (P*) for first-class passengers = $120/ (1+(1/-1.3)) =$120/ (1-1/1.3)
Or P* for 1st class passenger= $520 per passenger
Price elasticity of demand for unrestricted coach= -1.4
P* for unrestricted coach=$120/ (1+(1/-1.4)) =$420
Price elasticity of demand for restricted discount coach= -1.9
P* for restricted discount coach=$120/ (1+(1/-1.9)) =$250.33
For the same change in price, the section of consumers with higher price elasticity exhibits
greater changes in demand as compared to other section of consumers (Hirschey, 2008).
Hence, the higher the price elasticity of demand, the closer the optimal price to the marginal
revenue/ marginal cost to ensure profit maximization.
Chapter 14 Exercise # 3
(a)
Total profit function= Total Revenue – Total Cost
Demand function for manufactured items: P1= 100 – 2Q1
Revenue from manufactured items (R1) = (P1) *(Q1) = (100 – 2Q1) *(Q1) =100Q1 - 2Q12

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ECONOMICS ASSIGNMENT 5
Demand function for semi-manufactured raw materials: P2= 80 –Q2
Revenue from semi-manufactured raw materials (R2) = (P2) *(Q2)
= (80 –Q2) *(Q2) =80Q2 – Q22
Total Revenue (TR)= 100Q1 - 2Q12 + 80Q2 – Q22
Total Cost (TC) = 20+4(Q1 + Q2)
Total Profit function = TR-TC= 100Q1 - 2Q12 + 80Q2 – Q22 - (20+4(Q1 + Q2))
= - 20+ 96Q1+76Q2- 2Q12 – Q22
(b)
For Profit maximizing levels of price and output for the two freight categories:
MR1=MR2=MC
Profit maximizing levels of price and output for manufactured goods:
MR1= dR1/d Q1 = 1st derivative of revenue function from manufactured goods= 100- 4 Q1
MC= 1st derivative of Total Cost function= dTC/d Q1= 4
MR1= MC
Or, 100- 4 Q1= 4 Or, Q1= 24 tons
P1= 100 – 2Q1= $52 per ton
Profit maximizing levels of price and output for semi-manufactured raw materials:
MR2= dR2/d Q2 = 1st derivative of revenue function from semi-manufactured raw materials
= 80- 2Q2
MC= 1st derivative of Total Cost function= dTC/d Q2= 4
MR2= MC
Or, 80- 2Q2=4
Or, Q2=38 tons
P2= 80 –Q2=$42 per ton

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ECONOMICS ASSIGNMENT 5
(c.)
Marginal Revenue in manufactured goods market= 100- 4 Q1=$4
Marginal Revenue in semi-manufactured raw materials market= 80- 2Q2 =$4
(d)
Total Profits if different prices are charged=Total Revenue – Total Cost= - 20+ 96Q1+76Q2-
2Q12 – Q22=-20+2,304+2,888-1,152-1,444=$2,576
(e)
If charged same rate for all output:
P1= P2
Or, 100 – 2Q1= 80 –Q2
2Q1–Q2=20 or Q1=10+ Q2/2
Total Revenue (TR)= 100Q1 - 2Q12 + 80Q2 – Q22
Substituting for Q1, TR= 1000+50Q2 -2(100+ Q22 /4+10 Q2) + 80Q2 – Q22
Or TR= 800+110Q2 – 1.5Q22
MR= 110-3Q2
TC= 20+4(Q1 + Q2) = 60+6Q2
MC= 6
For Profit maximization, MR= MC
110-3Q2= 6
Or, Q2= 34.67 tons of semi-manufactured raw materials
Price= 80 –Q2=$45.33
Q1=10+ Q2/2=27.34 tons of manufactured goods
Profit= 800+110Q2 – 1.5Q22-(60+6Q2)=800+3,813.7-1,803.01-(60+208.02)= $2542.67