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Svetllana [295]
3 years ago
13

Given the following Demand Curve: P = 24 - 8Q

Mathematics
1 answer:
KatRina [158]3 years ago
4 0

Answer:

Maximum value of total revenue = 18

Step-by-step explanation:

  • Express this Demand Curve in terms of Q.

<em>P = 24 - 8Q (it is the same equation)</em>

<em />

  • Find P, if Q=2

<em>P= 24-8(2)</em>

<em>P=24-16</em>

<em>P=8</em>

  • Find Q if P = 8.

<em>P = 24 - 8Q</em>

<em>8= 24 - 8Q</em>

<em>8Q= 24-8</em>

<em>8Q=16</em>

<em>Q=16/8</em>

<em>Q=2</em>

  • Total revenue in terms of Q

<em>Total revenue is P times Q, that is</em>

<em>P*Q=TR=(24-8Q)*Q</em>

<em>TR=24Q-8Q^2</em>

<em>TR=24Q-8Q^{2} \\\\</em>

<em />

  • Marginal Revenue

<em>It is the first derivative of TR</em>

<em>TR'(Q)= 24-16Q</em>

  • Find the values of P and Q that will maximize total revenue.

<em>To find them first TR'(Q)=0, that is</em>

<em>0=24-16Q</em>

<em>16Q=24</em>

<em>Q=24/16</em>

<em>Q=3/2</em>

<em>Q=1.5</em>

<em>and we plug in 1.5 in P=24-8Q, which is,</em>

<em>P=24-8Q</em>

<em>P=24-8(1,5)</em>

<em>P=24-12</em>

<em>P=12</em>

  • Calculate this maximum value of total revenue

<em>P=12 Q=1.5</em>

<em>P*Q=Total Revenue</em>

<em>12*1.5=Total Revenue</em>

<em>18=Total Revenue</em>

<em />

<em />

<em />

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