Answer:
Please refer to the below for explanation.
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
