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2 answers:
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Answer:
1. 13x/760-13x
2. X = 29.23
3. X> 29.23
4. X<29.23
5. Max price = 29.23c
Step-by-step explanation:
1. D(x) = 760-13x
To get Elasticity, we differentiate the equation
D'x = -13
Elasticity is expressed as:
E(x) = -x*D'(x)/760-13x
= X(-13)/760-13x
B. Price elasticity with demand = 1
13x/760-13x = 1
We cross multiply
13x = 1(760-13x)
13x = 760-13x
Collect like terms
26x = 760
X = 29.23
C. When elasticity of demand is elastic
13x/760-13x > 1
We cross multiply
13x > 1(760-13x)
13x > 760-13x
Collect like terms
26x > 760
X > 29.23
C. Greater than 29.23
D. When inelastic
This follows same solution as 2 and 3 but the sign is different.
E(x) <1
13x/760-13x < 1
We cross multiply
13x < 1(760-13x)
13x < 760-13x
Collect like terms
26x < 760
X < 29.23
B. less than 29.23
E. We get total revenue
X(760-13X)
= 760x - 13x²
We differentiate this
760-26x = 0
760 = 26x
X = 29.23
revenue is a maximum at price is 29.23c
f. The last question is incomplete