Question

1. Let the demand function be Q(d) = 100 – 3P(X). a. What is the own price elasticity of demand when P = 10? b. What is the own price elasticity of demand when P = 20? c. What is the own price elasticity of demand when P = 30? d. Find the inverse demand function and graph the demand curve. Note for each of the questions above whether it is along the price elastic or price inelastic portion of the demand curve. Assume the firm is operating at P = 10 and is thinking about lowering price by 1%. Would you recommend such a price decrease? Provide evidence for your conclusion

Answer 1

Q(d) = 100 – 3P(X) ........1 is the demand function

so P(x)=100- Q(d)/3

a) own price elasticity when p =10 and Q= 70

e_p,q= (slope of the line )*P/Q slope of line is   which is differentiating the demand function

so we get   = -3

so elasticity is -3*(10/70) = -3/7 = -0.428 which is less than 1 in absolute terms

|e_p,q|<1 so it is price inelastic . a change in price brings less effect to change in quantity demanded.

when p = 20 so q= 40

elasticity would be -3*(20/40) = -1.5

since |e_p,q|= 1.5>1 we have price elastic behaviour

next when p= 30 so q= 10

e_p,q= -3*(30/10)= -9

so |e_p,q|= 9 which is again greater than 1 so has elastic price , a small change in price leads to huge change in quantity,

inverse demand function is given by P(x)= [100-Q(D)]/3

the graph of the demand function is as

when p= 10 and the firms want to reduce the price so 10% would be $1 and the new price is $ 9

so q given p=9 is 73

e_p,q= -3* (9/73)= -0.369

so |e_p,q | = 0.369 which is less than 1 so the price change is inelastic . which is even less than when price was 10 . so we conculde that its better to keep price at 10 . decreasing it at 9 would mean that the quantity is not increased much so revenues would be less.