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# Graphing Demand Curve and Finding Price Quantity

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Assume for simplicity that a monopolist has no costs of production
(MC=0) and faces a demand curve given by Q = 150-P.
a) Calculate the profit-maximizing price-quantity combination for this monopolist.
Also calculate the monopolist's profit.
b) Suppose instead that there are two firms in the market facing the demand and
cost conditions just described for their identical products. Firms choose quantities
simultaneously as in the Cournot model. Compute the outputs in the Nash
equilibrium. Also compute market output, price and firm profits.
c) Suppose the two firms choose prices simultaneously as in the Bertrand model.
Compute the prices in the Nash equilibrium. Also compute firm output and profit
as well as market output.
2
d) Graph the demand curve and indicate where the market price-quantity
combination from parts (a)-(c) appear on the curve.

##### Solution Summary

Assume for simplicity that a monopolist has no costs of production
(MC=0) and faces a demand curve given by Q = 150-P.
a) Calculate the profit-maximizing price-quantity combination for this monopolist.
Also calculate the monopolist's profit.
b) Suppose instead that there are two firms in the market facing the demand and
cost conditions just described for their identical products. Firms choose quantities
simultaneously as in the Cournot model. Compute the outputs in the Nash
equilibrium. Also compute market output, price and firm profits.
c) Suppose the two firms choose prices simultaneously as in the Bertrand model.
Compute the prices in the Nash equilibrium. Also compute firm output and profit
as well as market output.
2
d) Graph the demand curve and indicate where the market price-quantity
combination from parts (a)-(c) appear on the curve.

##### Solution Preview

Assume for simplicity that a monopolist has no costs of production
(MC=0) and faces a demand curve given by Q = 150-P.
a) Calculate the profit-maximizing price-quantity combination for this monopolist.
Also calculate ...

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