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You have decided to begin a new practice in a market subject to the demand function P = 300 - 10Q which would allow you to earn revenue at a marginal rate of MR = 300 - 20Q
You have decided to begin a new practice in a market subject to the demand function P = 300 - 10Q which would allow you to earn revenue at a marginal rate of MR = 300 - 20Q. You have determined your practice exists with a total cost of TC = 2.5Q2 + 20Q + 50 and a marginal cost of MC = 5Q + 20. Based on this information determine:
a) The number of products provided for this market.
b) The maximum willingness to pay your consumers have for that many units (and thus the price you will charge).
c) The total amount of revenue your practice will generate.
d) Your total production cost.
e) Your total profit.
Expert Solution
a) The quantity produced in this market is determined by equating the MR to the MC.
=> 300-20Q = 5Q+20
=> Q = 11.2 units.
b) The maximum willingness to pay is P = 300 - 10 x 11.2 = $188.
c) Total Revenue = P x Q = 188 x 11.2 => $2105.6
d) Total Cost = 2.5 x 11.2 x 11.2 + 20 x 11.2 + 50 = $587.6
e) Total Profit = Total Revenue - Total Cost = 2105.6-587.6 = $1518.
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