Question

In a particular town there are 100 cars and 50 motorcycles. Each car owner has a demand curve for petrol given by: Qdc = 20 – 5p for p ≤ 4 and Qdc = 0 for p > 4. Each motorcycle owner has the following demand function for petrol: Qdm = 15 – 3p for p ≤ 5 and Qdm = 0 for p > 5. Prices are expressed as SR per gallon, and quantities as gallons per week. b) Sketch the market demand curve for petrol (that is, the combined demand from car and motorcycle owners)
c) Write an algebraic expression for the market demand function.

Answer 1

Answer on Question # 71125, Economics / Microeconomics

In a particular town there are 100 cars and 50 motorcycles. Each car owner has a demand curve for petrol given by: Qdc = 20 - 5p for p ≤ 4 and Qdc = 0 for p > 4. Each motorcycle owner has the following demand function for petrol: Qdm = 15 - 3p for p ≤ 5 and Qdm = 0 for p > 5.

a) If the price is SR 3, then:

(i) each car owner will buy Q = 20 - 5*3 = 5 gallons of petrol per week.

(ii) each motorcycle owner will buy Q = 15 - 3*3 = 6 gallons of petrol per week.

Question: Write an algebraic expression for the market demand function.

Solution:

$$QD = 100*(20 - 5p) + 50*(15 - 3p) = 2750 - 650p, \text{ where } p \leq 4;$$ $$QD = 50*(15 - 3p) = 750 - 150p, \text{ where } p \leq 5;$$ $$QD = 0, \text{ where } p > 5.$$

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