Definition
Example: effect of tax on producer
(1)
PS = PM × TO:
PS: price of producer
PM: market price, or price of consumer.
TO: Power of tax.
ps = pm + to
(2)
QO = S(PS)
S: supply curve
qo = 
: elasticity of supply, or the percentage of output with respect to percentage change of producer's price
(3)
QD = D(PM)
By setting qd = qo, we have
when to > 0, the producer has a subsidy
since 
> 0, 
< 0, we know pm < 0
Special cases
If perfectly elastic demand ( = - infinity), or perfectly inelasticity supply ( = 0), pm = 0, so all subsidy benefit goes to producer
If perfectly inelastic demand ( = 0), or perfectly elasticity supply ( = infinity), pm = -to, ps = 0, so all subsidy benefit goes to consumer
Note
- In PE, we only consider the supply and demand of the sector with tax / subsidy