Demand function: Q = 48 - 2P
a) 2P = 48 - Q
Therefore the inverse Demand function is
P = 24 - Q/2
b) P = 24 - Q/2
Total Revenue = PQ = (24 - Q/2)*Q
TR = 24Q - Q2/2
MR = differentiating TR with respect to Q
MR = 24 - Q
We know a firm will maximize profit at MR = MC
TC = 6 + 3Q + Q2
MC = 3 + 2Q
Putting MR = MC, we have
24 - Q = 3 + 2Q
24 - 3 = 2Q + Q
21 = 3Q
Q = 21/3 = 7
Q = 7
Putting the value of Q in the equation P = 24 - Q/2
P = 24 - 7/2
P = 24 - 3.5
P = 20.5
Therefore the profit-maximizing output is 7 and the price is $20.5
c) TR = PQ = 20.5*7 = $143.5
TC = 6 + 3Q + Q2 = 6 + 3*7 + 7*7 = 6 + 21 + 49 = $76
Profit = TR - TC = 143.5 - 76 = $67.5
Therefore the firm's maximum profit is $67.5
d) a) entry will occur until profits are zero
In the long run, more and more firms will enter the market and the economic profit will be zero in the long run.
In economics, a Demand function is a graph depicting the connection between the price of a sure commodity and the amount of that commodity that is demanded at that fee. call for curves may be used both for the price-amount courting for a person client, or for all purchasers in a selected marketplace.
Learn more about the Demand function here: brainly.com/question/24384825
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