# 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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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please refer attached file for complete solution. Graphs and some formulas are missing here.

Solution:

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.

Equilibrium point is the price at which Qd=Qs

We find the equilibrium point at P=1.9 where Qd=Qs=100

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

Refer to the graph. We find that at P=$2.4, Qd=66 and Qs=125

Qs>Qd, Surplus=Qs-Qd=59

There is a surplus of 59 units in the market.It is indicated by green line above.

Market forces will push the prices to decrease sothat surplus is cleared and equilibrium is attained.

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

Refer to the graph above, At P=$0.7, Qs=40 and Qd=180

Qs<Qd, Shortage=Qd-Qs=140

There is a shortage of 140 units In the maeket indicated by red line.

Market forces will push the prices to increase the prices sothat there is no shortages and equilibrium is attained.

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

Let us find the slope of the demand line=m= -66.63636364

Equilibrium Quantity=Qd=100

Equilibrium Price=P=1.9

Point elasticity of demand=slope*P/Qd=-1.266090909

6)Calculate the price elasticity of the following ranges

a. Between P=0.5 and P=0.9

Q1=193 Q2=100

P1=0.5 P2=0.9

Ep =

Where Ep = Coefficient of price elasticity

Q1 = original quantity demanded

Q2 = new quantity demanded

P1 = Original Price

P2 = New Price

Plug in the values in formula above and get

Ep= -1.11

Absolute value of elasticity is greater than 1, arc price elasticity of demand is elastic

b.Â Â Â Â Â Between P=2.2 and P=2.5

Q1= 80 Q2=66

P1=2.2 P2=2.5

Ep =

Where Ep = Coefficient of price elasticity

Q1 = original quantity demanded

Q2 = new quantity demanded

P1 = Original Price

P2 = New Price

Plug in the values in formula above and get

Ep=-1.50

Absolute value of elasticity is greater than 1, arc price elasticity of demand is elastic

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.

On introduction of trolley services, demand curve will such that gasoline demand for each price level will decrease

Slight change in prices can force the people to switch over.

Demand will become more elastic.

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

Price QD Revenue=P*Qd Point elasticity=slope*(P/Qd)

0.5 193 96.5 -0.17

0.6 186 111.6 -0.21

0.7 180 126 -0.26

0.8 173 138.4 -0.31

0.9 166 149.4 -0.36

1 160 160 -0.42

1.1 153 168.3 -0.48

1.2 146 175.2 -0.55

1.3 140 182 -0.62

1.4 133 186.2 -0.70

1.5 126 189 -0.79

1.6 120 192 -0.89

1.7 113 192.1 -1.00

1.8 106 190.8 -1.13

1.9 100 190 -1.27

2 93 186 -1.43

2.1 86 180.6 -1.63

2.2 80 176 -1.83

2.3 73 167.9 -2.10

2.4 66 158.4 -2.42

2.5 60 150 -2.78

Refer to the table and graph above.

Â© BrainMass Inc. brainmass.com October 3, 2022, 12:26 am ad1c9bdddf>https://brainmass.com/economics/demand-supply/finding-equilibrium-price-quantity-elasticities-239415