CFA Practice Question

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CFA Practice Question

Company A is the only producer of widgets. At a price of $10, the quantity of widgets demanded is 200, while at a price of $8, the quantity demanded is 300. What is the marginal revenue Company A receives when production is at 200 widgets?
Correct Answer: $6

Use the formula: marginal revenue = price - (quantity * slope).

User Contributed Comments 21

User Comment
isida shouldnt the asnwer be 4?? (2400-2000)/100
kalps yes, your formula is correct old boy the answer is $4 change in total revenue divided by change in quantity = marginal revenue
zglacier the answer is correct !
because the formula MR = P -(Q * slope )is more precise !!
danlan slope=(10-8)/(300-200)=0.02, Q=200, P=10
so MR=10-200*0.02=6
msns How can there be a marginal revenue in this case. We are actually selling more units at a lower price of $8. So aren't we actually incurring a loss.
bobert Nope, just look at the math.

200 * 10 = 2000
300 * 8 = 2400

There is no loss, so just use the formula as stated above and you'll be good to go. Remember, a monopoly allows you to supply at a lower price, and have more sales which outweighs the extra you would earn if you sold at a higher price.
qazwsxedcrfvtgb Revenue
R = p(q) * q
where p(q) is the price function of q.

Marginal Revenue
MR = dR/dq
= p'(q)*q + p(q)

Given: q = 200, p(q) = 10
And: p'(q) = (8-10)/(300-200)= -1/50

So: MR = -(1/50)*200 + 10 = 6
nneks Thanks qazwsxedcrfvtgb....i was now about to comment on the sloppy calculation of the slope above...posted by danlan.
Beret Or:
p = -0.02*q + 14
R = p*q = (-0.02*q + 14)*q
MR = dR/dq = -0.04*q + 14
Fill in current point of q = 200 and find
MR = 6
desertfox27 i really do not understand the logic of the formula. in the book, it only says MR = change in TR over change in quantity. Thus, the answer should be 4.
desertfox27 thanks. i only got the explanation in the next question, MR = initial price - (initial quantity X slope). slope is change in price over change in quantity. please note it is in absolute value.
bundy Change in Rise/ Change in Run X Price = MR
southeuro tend to agree with isida. shouldn't MR be change in revenue over change in quantity therefore 400/100 = 4?
Sam123456 Thanks Left Handed Typing Rule. That clears it up.
dmfz i agree with desertfox
Shaan23 You can use the Change in TR/ Change in Q if it's a perfectly competitive market(Perfectly elastic Demand). Here the demand function is downward sloping. You have to use the other method stated above in the comments
schweitzdm How do you decide to use P=10 instead of P=8?
robbiecow alternative calc to use is MR = P x (1 - 1/|elasticity|)

1. inelastic demand (D<1), selling more will decrease TR
2. elastic demand (D>1), selling more will increase TR
Yrazzaq88 First of all:

Step 1: Calculate the slope:
Take ($8-$10) / (300-200) = -2/100 = -0.02 << Remember, that the slope is in negative format.

Step 2:
Now that we have the slope of -0.02, we will do the following to get MR= -0.02 x 200 (our quantity) + 10 (our price) = 6
praj24 Thanks Yrazzaq!
Freddie33 Yrazzaq, based on the formula given in the answer, then with a negative slope you would get a MR of $14. It is when slope = 0.02 (positive) that results in MR = $6 (correct answer)
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