It is not surprising that the quantity of one product demanded may depend not on

Question

It is not surprising that the quantity of one product demanded may depend not only on the price of the product, but also on the price of another product (for instance the demand for cars is affected not only by the price of cars, but the price of gas). Suppose that the quantities demanded, q1 and q2, of two products depend on their respective prices, p1 and p2, as follows:

q1= 150 - 2p1 - p2

q2 = 200 - p1 - 3p2

Suppose one manufacturer sells both of these products. How should the manufacturer set prices to earn the maximum possible revenue? What is the maximum possible revenue?

Explanation / Answer

For revenue=p1*q1+p2*q2

From formula put q1 & q2 value

=150p1-2(p1^2)-p1*p2+200p2-p1*p2-3(p2^2)

=-2(p1^2)-3(p2^2)-2p1*p2+150p1+200p2

partially differentiate revenue by p1 put it equal to zero

-4p1-2p2+150=0

2p1+p2=75 ....(i)

partially differentiate revenue by p2 put it equal to zero

-6p2-2p1+200=0

p1+3p2=100 ...(ii)

Solving (i) & (ii) will give us max revenue

p1=100-3p2

put p1 to eq (i),

200-6p2+p2=75

5p2=125

p2=25

p1=100-75

p1=25

q1=150-50-25

q1=75

q2=200-25-75

q2=100

max revenue=p1*q1+p2*q2

=25*75+100*25

=1875+2500

=4375

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