You are given the following information for a firm: Demand: p = 774 - 3q Cost: 1
ID: 1189708 • Letter: Y
Question
You are given the following information for a firm:
Demand: p = 774 - 3q
Cost: 1q2 + 383q + 996
Find the quantity of output that maximizes the firms profit, and round your answer to one decimal. Answer: 48.9
You are given the following information for a firm:
Demand: p = 827 - 1q
Cost: 3q2 + 242q + 432
How much profit will this firm earn when it produces the quantity of output that maximizes their profit? Answer: 20,957.1
Can someone please explain these?? I need help with them and don't understand. The answers are below the question.
You are given the following information for a firm:
Demand: p = 774 - 3q
Cost: 1q2 + 383q + 996
Find the quantity of output that maximizes the firms profit, and round your answer to one decimal. Answer: 48.9
You are given the following information for a firm:
Demand: p = 827 - 1q
Cost: 3q2 + 242q + 432
How much profit will this firm earn when it produces the quantity of output that maximizes their profit? Answer: 20,957.1
Can someone please explain these?? I need help with them and don't understand. The answers are below the question.
Explanation / Answer
Firm maximises profit where marginal cost is equal to marginal revenue.
MR=MC
Revenue=PQ
MR=dR/dQ
1.
Revenue=PQ= (774 – 3Q)*Q=774Q-3Q^2
MR=dR/dQ=774-6Q
Cost=C= 1q2 + 383q + 996
MC=dC/dQ=2Q+383
Maximisation point MR=MC
774-6Q=2Q+383
Q=391/8 =48.875=48.9
2.
Demand: p = 827 - 1q
R=PQ=827Q-Q^2
MR=827-2Q
Cost: 3q2 + 242q + 432
MC=dC/dQ=6Q+242
Profit maxmisation point: MR=MC
827-2Q=6Q+242
Q=585/8=73.125
Profit=Revenue-Cost Putting the value of Q* in the cost and revenue function
=827*73.125-(73.125)^2-3*(73.125)*(73.125)-242*(73.125)-432
=20975.07
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