# Graphing Demand Curve and Finding Price Quantity

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.

https://brainmass.com/economics/game-theory/graphing-demand-curve-finding-price-quantity-399085

#### 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 ...

#### 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.

Finding Equilibrium Price & Quantity, Elasticities

In the following table is data that describe the market for gasoline in a small town. For each given price there is a quantity supplied (QS) and a quantity demanded (QD).

Price QS QD

0.5 30 193

0.6 35 186

0.7 40 180

0.8 45 173

0.9 50 166

1 55 160

1.1 60 153

1.2 65 146

1.3 70 140

1.4 75 133

1.5 80 126

1.6 85 120

1.7 90 113

1.8 95 106

1.9 100 100

2 105 93

2.1 110 86

2.2 115 80

2.3 120 73

2.4 125 66

2.5 130 60

1)Use the date to draw the supply and demand curves. Label the curves completely.

2)Calculate the equilibrium price and quantity in the gasoline market.

3)What would happen if the price goes up to 2.4 ( show graphically )

4) What would happen if the price goes down to 0.7 ( show graphically )

5)Calculate the price elasticity of demand at the equilibrium price using the exact (point) elasticity measure.

6)Calculate the price elasticity of the following ranges

a.Between P=0.5 and P=0.9

b.Between P=2.2 and P=2.5

7)Imagine that the small town introduces trolley service that will allow most of the residents to get around easily. What would you expect to happen to the demand for gasoline in the area? Would it become more or less elastic? Explain.

8)Draw the total revenue curve and show in the graph where are the elastic and inelastic regions.

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