need help Name Student IO Revenue vs. Profit Maximization. On weekends during su
ID: 1136068 • Letter: N
Question
need help
Name Student IO Revenue vs. Profit Maximization. On weekends during summer months, Eric Cartman rents jet skis at the beach on an hourly basis. Last week, Cartman rented jet skis for 20 hoursper day at a rate of S50 per hour. This week, rentals fell to 15 hours per day when Cartman raised the price to S55 per hour. (10 points) 3. Using these two price-outpu marginal revenue curves can be estimated as: P- S70-S10 and MR - $70-S20 Caleulate the revenue-maximizing price-output combination. How much are these maximum revenues? If marginal cost is $30 per hour, caleulate profits at thts activity level assuming TC = MC ) calawlate doe tirelatemsavinmtzine price -outt combination alonh reive and profits at this activity level. Answer:Explanation / Answer
P = 70 - Q
Total Revenue, TR = P*Q
TR = (70-Q)*Q
TR = 70Q - Q^2
MR = 70 -2*Q (given in question)
A.
The revenue maximizing output level is the one where MR = 0.
70 -2*Q = 0
2*Q = 70
Q = 70/2
Q = 35
The corresponding price (to Q=35), P = 70 - 35 = 35
The revenue maximizing price-output level = (P,Q) = (35,35)
Profit = TR - TC
= P*Q - MC*Q
= 35*35 - 30*35
=1225 - 1050
= 175
B.To solve for the profit maximizing output level, we use the MR-MC rule:
MR = MC
70 -2*Q = 30
2*Q = 40
Q = 20 is profit maximizing output level.
The corresponding price (to Q=20), P = 70 - 20= 50
Profit = TR - TC
= P*Q - MC*Q
=50*20 - 30*20
= 1000 - 600
=400
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