Question

Q1 Social Welfare. Natural gas is in high demand as a clean-burning energy source for home heating and air conditioning, especially in major metropolitan areas where air quality is a prime concern. The domestic supply of natural gas is also plentiful. Government reports predict that gas recoverable with current technology from domestic sources is sufficient to satisfy production needs for more than 50 years. Plentiful imports from Canada are also readily available to supplement domestic production. To illustrate the net amount of social welfare generated in this vigorously competitive market, assume that market supply and demand conditions are

QS=–500+500P (Market Supply)

QD=3,500–500P (Market Demand)

where Q is output in million Btus (in millions), and P is price per unit. A British thermal unit (Btu) is an English standard unit of energy. One Btu is the amount of thermal energy necessary to raise the temperature of one pound of pure liquid water by one degree Fahrenheit at the temperature at which water has its greatest density (39 degrees Fahrenheit).

(1). Graph and calculate the equilibrium price/output solution.

(2). Use this graph to help you algebraically determine the amount of consumer surplus.

(3). Determine the amount of producer surplus.

(4). What is the amount of social welfare?

Answer 1

1) -

Price	Quantity Demanded	Quantity supplied
7	0	4000
6	500	3500
5	1000	3000
4	1500	2500
3	2000	2000
2	2500	1500
1	3000	1000
0	3500	500

The equilibrium point is E where the equilibrium price is 3 and the equilibrium quantity is 2,000 units.

2) -

Consumer surplus = 1/2* Equilibrium quantity *( Price when demand is 0- Equilibrium price )

=1/2*2000*(7-3)

=1/2*2000*4

=4000

3)-

Producer surplus =(1/2* Equilibrium price *(Equilibrium quantity - supply at price 0 )+(Supply at price 0* Equilibrium price )

=(1/2(2000-500)3)+(500*3)

=(1/2*1500*3)+(5003)

=2250+1500

=3750

4)-

Social welfare = Consumer Surplus + Producer Surplus

= 4000+3750

=7750