Question

A bakery works out a demand function for its chocolate chip cookies and finds it to be q = D(x)= 760-13x​, where q is the quantity of cookies sold when the price per​ cookie, in​ cents, is x.

Required:
a. Find the elasticity.
b. At what price is the elasticity of demand equal to 1?
c. At what prices is the elasticity of demand elastic?
d. At what prices is the elasticity of demand inelastic?

Answer 1

Please refer to the below for explanation.

Step-by-step explanation:

From the above, the demand function is given as ;

D(x)=760-13x

a) Find the elasticity

It means finding the derivative of the function

D'(X)=-13, hence elasticity is expressed as

xD'(x) / D'(x)

= x(-13) / 760 - 13x

= 13x / 760 - 13x

The elasticity expression is thus ; E(x)= 13x / 760 - 13x

b) At what price is the elasticity demand equal to 1.

The above means that E(X) = 1

Putting 1 for E(X) in the elasticity equation,

E(x) = 13x / 760 - 13x

1 = 13x / 760 - 13x

When you cross multiply, you'll have

760 - 13x = 13x

Collecting like terms, you'll have

760 = 13x + 13x

760 = 26x

Dividing both sides by 26, you'll have

x = 760 /26

x = 29.23

It means that the elasticity at the price of demand = 1 is 29.23

c) At what price is the elasticity of demand elastic.

The above means that E(X) > 1

Thus;

13x / 760 - 13x > 1

When you cross multiply, you'll have

13x > 760 - 13x

Collecting like terms, you'll have

13x + 13x > 760

26x > 760

Dividing both sides by 26, you'll have

x > 760/26

x > 29.23

It means that the elasticity of demand is elastic at x > 29.23

d) At what price is the elasticity of demand inelastic

The above means that E(X) < 1

Hence;

13x / 760 - 13x < 1

When you cross multiply, you'll have

13x < 760 - 13x

Collecting like terms, you'll have

13x + 13x < 76

26x < 760

Dividing both sides by 26, you'll have

x < 760/26

x < 29.23

It means that the elasticity of demand is inelastic at x < 29.23