The Bramwell Corporation has estimated its demand function and total cost functi
ID: 1221851 • Letter: T
Question
The Bramwell Corporation has estimated its demand function and total cost function to be as follows:
Q = 25 – 0.05P
TC = 700 + 200Q
Answer the following questions either by developing demand and cost schedules (hint: Use quantities from 1 to 14) or by solving the equation.
What will be the price and quantity if Bramwell wants to
Maximize profits
Maximize revenue
Maximize revenue but require the profit to be a minimum of $300
Now assume the cost function is TC = 780 + 200Q while the demand function remains the same. What will the price and quantity be if Bramwell wants to
Maximize profits
Maximize revenue
Maximize revenue but require the profit to be a minimum of $300
Explanation / Answer
1. Q = 25 - 0.05P therefore, P = 500 - 20Q
TR = 500Q -20Q2 , MR = 500-40Q -(1)
TC = 700 + 200Q ttherefore, MC = dTC/ dQ = 200 -(2)
Profit maximisation exists where MR= MC
I.E. 500 - 40Q =200 , Q = 300/ 40 = 7.5 ~ 8 and P = 350
Total revenue, TR = P×Q = 75×35 = 5×5×7×5×3 = 375 × 7 = 2625
Total cost = 2200
total profit = 2625 - 2200 = $425
2. If TC = 780 + 200Q, MC WOULD still be 200.
that's why P* = 350 and Q* = 7.5 ~8
TC = 2280 and TR = 2625
total profit would be = 2625 - 2280 = $345
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