Homework Answers
A monopolist equates MR=MC in order to maximize the profits.
Total revenue during weekdays = P*Q = (50-Q)*Q = 50Q- (Q)^2
Marginal revenue can be calculated by differentiating total revenue with respect to Q
MR during weekdays (MR1) = 50-2Q
MC=0
In order to maximize profits,
MR1=MC
50-2Q=0
Q=25
Put Q in the demand in order to get the profit maximizing price. P= 50-Q = 50-25 = $25
Therefore, profit maximizing price on weekdays = $25
Total revenue during surge hours = P*Q = (100-Q)*Q = 100Q- (Q)^2
Marginal revenue can be calculated by differentiating total revenue with respect to Q
MR during surge hours (MR2) = 100-2Q
MC=0
In order to maximize profits,
MR2=MC
100-2Q=0
Q=50
Put Q in the demand in order to get the profit maximizing price. P= 100-Q = 100-50 = $50
Therefore, profit maximizing price during surge hours = $50
Now, MC =10. MR remains the same so to maximize profits, equate the new MC with original MR.
In order to maximize profits,
MR1=MC
50-2Q=10
Q=20
Put Q in the demand in order to get the profit maximizing price. P= 50-Q = 50-20= $30
Therefore, profit maximizing price on weekdays = $30
In order to maximize profits,
MR2=MC
100-2Q=10
Q=45
Put Q in the demand in order to get the profit maximizing price. P= 100-45 = $55
Therefore, profit maximizing price during surge hours = $55
1) Demand curve during surge hours is drawn in blue color in figure 1
2) MR curve during surge hours is drawn in red color in figure 1
3) MC curve during surge hours is drawn in orange color in figure 1
4) A represent the point in figure 1 which shows the profit maximzing quantity (45) and profit maximizing price ($55)
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