Given the price-demand equation p + 0.005x = 30 Express the demand x as a functi

Question

Given the price-demand equation p + 0.005x = 30 Express the demand x as a function of the price p. Find the elasticity of demand, E(p). What is the elasticity of demand when p = $10? If this price is increased by 10%, what is the approximate percentage change in demand? What is the elasticity of demand when p = $25? If this price is increased by 10%, what is the approximate percentage change in demand? What is the elasticity of demand when p = $15? If this price is increased by 10%, what is the approximate percentage change in demand?

Explanation / Answer

p+0.005x =30

0.005x=30-p

x=(30/0.005)-(1/0.005)p

x=6000-200p

B) dx/dp =-200

elasticity =(dx/dp)(p/x)

elasticity =-200(p/x)

C)p =10, x =4000

elasticity =(-200)(10/4000) =-1/2

-1/2 =(dx/dp)(p/x)

-1/2 =(dx/x)/(dp/p)

(dx/x)=(-1/2)(dp/p)

(dx/x)*100=(-1/2)(dp/p)*100

price increased by 10%

(dx/x)*100=(-1/2)( 10%)

(dx/x)*100=-5%

demand changes by 5%

D)

elasticity =(dx/dp)(p/x)

p =25, x =6000-200*25 =1000

elasticity =(-200)(25/1000) =-5

-5 =(dx/dp)(p/x)

-1/2 =(dx/x)/(dp/p)

(dx/x)=(-1/2)(dp/p)

(dx/x)*100=(-5)(dp/p)*100

price increased by 10%

(dx/x)*100=(-5)( 10%)

(dx/x)*100=-50%

demand changes by 50%

E)

elasticity =(dx/dp)(p/x)

p =15, x =6000-200*15 =3000

elasticity =(-200)(15/3000) =-1

-5 =(dx/dp)(p/x)

-1 =(dx/x)/(dp/p)

(dx/x)=(-1)(dp/p)

(dx/x)*100=(-1)(dp/p)*100

price increased by 10%

(dx/x)*100=(-1)( 10%)

(dx/x)*100=-10%

demand changes by 10%

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