By the usual happenstance, my classes today were kidnapped by a not-totally-off-subject spur of the moment idea. We were doing consumer surplus in micro principles and benefit-cost analysis and I was getting the "wow, this is so totally irrelevant looks." So, I decided to answer what I thought was an interesting question: the price of gas has fallen from about $4 to $3 in the past few months, so what are the consumer surplus gains? Taking the abstract to the concrete ...
The data:
- Monthly gas consumed in August = about 280 million gallons [source]
- August price = about $4 [source]
- Short run gas demand elasticity = about -1/4 [source]
The elasticity formula gives the slope of demand:
- e = (dQ/dP)*(p/Q)
- -1/4 = (dQ/dP)*(4/280)
- dQ/dP = -17.5
Plug the slope into the assumed linear demand:
- P = a + (dP/dQ)Q
- 4 = a + (-1/17.5)*280
- a = 20
Determine consumption at P = 3:
- Q = (P - a)(dQ/dP)
- Q = (3 - 20)(-17.5)
- Q = 297.5
Plug into the change in CS formula:
- dCS = dP*Q + .5*dP*dQ
- dCS = 1*280 + .5*1*17.5
- dCS = 288.75
The monthly welfare gains are $288.75 million.
