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**CFA Practice Question**

The demand curve for a monopolist is P = 16 - Q. If the monopolist's marginal cost is $10, what output should the monopolist choose? At the profit-maximizing output, what price should the monopolist charge?

B. $13

C. $14

A. $12

B. $13

C. $14

Correct Answer: B

Total Revenue = Q * P = 16Q - Q

^{2}, MR = ΔTR/ΔQ = 16 - 2Q = MC => 16 - 2Q = 10 => Q = 3, Price = 16 - 3 = $13###
**User Contributed Comments**
38

User |
Comment |
---|---|

akanimo |
this can be solved by simulaenous equations i) MC = 10 ii) MR = MC (at optimal price) ... MR = 10 iii)MR = P - ( Q * Slope ) iv) P = 16 - Q => Q = 16 - P Okay lets simplify... MR = P - ( Q * Slope ) ..where MR = 10, slope = 1 10 = P - Q .... but we can subst Q = 16 - P 10 = P - ( 16 - P ) 10 = 2P - 16 26 = 2P P = 13 |

kalps |
Marginal revenue at profit max point marginal revenue = marginal cost solve this for Q Enter Q in demand function and hey ur there |

bigzero |
The problem is confusing. For both Q=3 and Q=4,the profit are the same. You will see at Q=3, MC=MR which means producing one more unit doesn't change the profit. |

BADGUY |
thanks akanimo, you are the best!i was almost going crazy! |

sivenkova |
Why slope=1? |

motoloco |
I think the slope of the MR curve is 2 (1 the the slope of the demand curve)...For mi the answer is 3.5 and 12.5 |

myzec |
Slope is 1 as in the notes it states that a Monopoly will maximise profit where it is unit elastic. Since Unit elastic = 1 the slope will be 1 |

raychow |
I agree with motoloco, the answer should be Q=3.5 P= 12.5 |

ljamieson |
well simple calculus gives: TR = QP = 16Q - Q^2 TC = integral wrt Q of MC = 10Q + const. profit = TR - TC = 16Q-Q^2 - 10Q - const. max over all {Q,P}: dprofit/dQ = 0 = 6 - 2Q => Q = 3 => P = 13. |

MikeB |
P=(16-Q) MR=P-(slope*Q) Let's say MR's slope is 1, MR=MC=10, sub for P 10=(16-Q) - (1*Q) 10=16-2Q -6=-2Q 3=Q P=16-3=13 not sure why calculus is need for a simple substitution. |

jassosahan |
Q=2,P=14 or Q=4,P=12 both the cases profit is maximised.Ask me how? remember MR=Mc=10 AT Q=3 profit is $9 |

Yannicklin |
MR = P - ( Q * Slope ) I can't find this formulae in the book :( help plzz |

Mariecfa |
Yannicklin! MR=P-(Q * Slope) Slope is Change in price divided by change in quantity. |

marinachow |
Why is profit being maximized at Q=2 P=14 or Q=4 P=12, if MC=10, profit/unit at P=12 = 12-10=2, total profit = 2X4=8 at P=13 Q=3, total profit: 3X3=9, wouldn't it be better?? |

qazwsxedcrfvtgb |
Here is the determination of the marginal revenue function. Given demand function: P = 16 - Q Implying Revenue function: R = P*Q =(16-Q)*Q = 16*Q - Q^2 The marginal revenue is the derivative of the revenue function with respect to the quantity, such that: MR = dR/dQ = 16 - 2*Q Given MC = 10, and we know the firm is maximizing profit when MC = MR, so MR = 10. Solving the equation: 10 = MR = 16 - 2*Q Q = 3 Substitute Q=3 into the demand function: P = 16 - Q We get: P = 13 |

SuperKnight |
I am confused here. Myzec states that a monopoly maximizes profit when it is unitary elastic, elasticity of 1. This question uses this assumption, the slope having a value of 1. Yet the next question asks at which point does a Monopoly maximize profit, and the answer is when the demand is elastic, one of the choices is unitary elastic, but it is not the correct answer? |

SaeedAlam |
I vote for the site's solution, as it was what I was taught at Uni. |

BandB |
4 is the correct answer, as 4*12=48 & 3*13=36 My assumption to this answer - as it is carefully said => MR = INITIAL Price- (INITIAL Q * SLOP) in this question, INITIAL Q is 3 instead of 4. but it didn't say that you reach the profit maxmizing position at the inital Q. so the profit maxmization Q is 4 instead of 3. |

Swiki |
MR=dR/dq R=P*R (assuming P=16-Q) R=16Q-Q^2 MR=dR/dq => 16-2Q we Know, MR=MC for MONOPOLY MC=10 so, 10=16-2Q Q=3 Substituting this value to P=16-Q [Price=13] |

alallstar |
BandB - 3*13=39 |

jppogo |
the price follows the model y=ax+b so the slope is a=-1 and we take the absolute value:1 |

poomie83 |
I haven't performed calculus calcs in 15 years so pardon my ignorance but how do you turn 16Q-Q^2 to 16-2Q? Is it a matter of square rooting all the numbers? |

poomie83 |
Also a monopolist maximizes profit when D is elastic (see next question) and not when unitary elastic as some of you have suggested |

sogah |
all i hear is a lot of bs haha |

jqian |
I am totaly lost. I guess the key is the slope. I don't know where the 1 from? |

dipu617 |
Too many convincing explanations from too many knowledgeable people!!! Really lost.... |

chuamj |
1 came from the equation (P = 16 - Q). The slope is (-1) if you differiate the equation. 1 is just the abs of it. |

dybacis |
Can someone explain me how is that formula for MR correct if MR=change in TR/change in quantity so at Q=4 MR=((4*12)-(3*13))/(4-3)=9 NOT 10 |

moneyguy |
I calculated exactly like Swiki, and thought I was right. Still do. |

2014 |
Thanks qazwsxedcrfvtgb ... life becomes easy ... keep up good work |

CHUCKYT |
MR=P-(slope*Q) Slope is 1 because the demand curve for the monopolist(given P=16-q) is a unit elastic downward sloping straight line from point p=16 q=0, to point p=0 q=16. When p=16-q, slope=1 and mc=mr so mr=10 then, 10=(16-Q)-(1*q) 10=16-2q q=3 If q=3 then p=13 |

sgossett86 |
I was in economics class and the right answer based on my U of Michigan course is Q=3.... |

Yass0707 |
I have use same logic as "gazwsxedcrfvtgb" and I get also MC=MR 1O=MR=16-2*Q but I get Q=2 what do i do wrong? |

Yass0707 |
omg im tired... 16-10=6 not 4 :) so Q=3 :) |

kay136 |
I give up on this question. |

chesschh |
LOS: Explain, describe, describe explain (not calculate). I dont see why this question should be in the exam |

Logaritmus |
On common sense let's find a profit maximizing quantity: Our profit is P - 10, and we want to maximize total profit. Total profit is Quantity * profit from sale = Q*(Price - 10) = Q(16-Q-10)=Q(6-Q) - a quadratic function which have max at Q = 3 so maximizing profit quantity is 3, price must be 13 and profit is 9. |

pigletin |
it's very easy, just solve the first derivative for total revenue, and set it equal to marginal cost, then you have the quantity, and solve the price |