I think:
A)
((ΔQ/Average of Q)*100) /((ΔP/Average of P)*100)
If P= 2 Q= 34.04
If P= 4 Q= 15
(19.04/24.52)/(2/3) = .7765/.667 =1.164 >1 = elastic
B) Q= 16.8671
16.8671-15= 1.867/15= .1244= 12%
C)
4*15=60
3.92*16.8671=66.11
Decrease in price = increase in demand = increase in profit
The demand equation for a product is:
q=60/p + ln(65-p^3)
A) Determine the point of elasticity of demand when p=4, and classify the demand as elastic, inelastic, or of unit elasticity at this price level.
B) If the price is lowered by 2% (from $4.00 to $3.92), use the answer in part (a) to estimate the corresponding percentage change in quantity sold.
C) Will the changes in part (b) result in an increase or decrease in revenue? Explain.
4 answers
Can someone tell me if this is right? Pretty please?
...anyone?
Yes, your approach is correct, except watch for the following.
(1) In principle, part (A) should be done using calculus. If you have not done calculus before, what you did is appropriate, EXCEPT that the interval for p between 4 and 2 is way too large because q(p) varies rapidly between p=2 and p=4.
The theoretical result using calculus should give E(4)=-13.8
Remember that elasticity is always negative, although we only use the absolute (positive) value.
(2) You have given the exact answer correctly, but not using the result of part (A) as requested.
Using part (A),
E(p)=E(4)=-13.8
Δp=-0.02
so
Δq=E(p)*Δp=-13.8*(-.02)=0.276, or 27.6%
(compared with the correct value of 12%).
The enormous error is due to the rapidity of change of E(p) at this point. If we had used a change of 0.1%, it would have been 1.38% vs 1.27% and the approximation would have been acceptable.
(3)
Also, you need to watch the use of equal sign.
Equal sign means just that, values on each side are equal.
In your statement:
16.8671-15= 1.867/15= .1244= 12%
you have added the division of 15 on the second expression, which tips the equality. The proper way to present it is as follows:
(16.8671-15)/15= 1.867/15= .1244= 12%
This ensures that equality is true throughout.
(4) Part (C)
Your calculation of the revenues is correct. The increase is 10.2%.
(1) In principle, part (A) should be done using calculus. If you have not done calculus before, what you did is appropriate, EXCEPT that the interval for p between 4 and 2 is way too large because q(p) varies rapidly between p=2 and p=4.
The theoretical result using calculus should give E(4)=-13.8
Remember that elasticity is always negative, although we only use the absolute (positive) value.
(2) You have given the exact answer correctly, but not using the result of part (A) as requested.
Using part (A),
E(p)=E(4)=-13.8
Δp=-0.02
so
Δq=E(p)*Δp=-13.8*(-.02)=0.276, or 27.6%
(compared with the correct value of 12%).
The enormous error is due to the rapidity of change of E(p) at this point. If we had used a change of 0.1%, it would have been 1.38% vs 1.27% and the approximation would have been acceptable.
(3)
Also, you need to watch the use of equal sign.
Equal sign means just that, values on each side are equal.
In your statement:
16.8671-15= 1.867/15= .1244= 12%
you have added the division of 15 on the second expression, which tips the equality. The proper way to present it is as follows:
(16.8671-15)/15= 1.867/15= .1244= 12%
This ensures that equality is true throughout.
(4) Part (C)
Your calculation of the revenues is correct. The increase is 10.2%.
1 answer