ECO 3352 Troy University Demand Equation of P Exercise

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I’m working on a economics question and need an explanation and answer to help me learn.

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Suppose a pure monopolist faces the demand equation of P = 200 – 0.75Q. MC = Q + 50.
Solve for Total Revenue.
Total Revenue= P*Q = 200Q – 0.75Q^2
Solve for Marginal Revenue.
MR= d(TR)/ dQ = 200- 1.5Q
Find the profit-maximizing price.
Profit-maximization: Set Q where MR=MC
200-1.5Q= Q+50
P= 200-0.75*60= 155
Find the profit-maximizing quantity.
Suppose Average Total Cost is $145. How much is the profit/loss?
TC= ATC*Q= 145*60=8700
TR= 200*60- 0.75*60*60= 9300
TR-TC= 600
The profit is 600
Draw a graph showing the demand, the firm’s marginal revenue, its marginal cost, and its
average total cost. Shade in and indicate the profit/loss.

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total revenue

Marginal Revenue

demand equation

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