Exercise 8.16: Suppose the producer is required to pay a specific tax of $1.00 per unit (as with fuel, liquor, or tobacco). If the before-tax demand and supply were D(p) = 100-30*p and S(p) = 20*p - 50, what are the before- and after-tax equilibrium prices? How much of the tax per unit is actually paid by the consumer and how much by the producer?

We first compute the before-tax equilibrium, setting supply equal to demand: 

    20*p - 50 = 100 - 30*p
         50*p = 150
	    p = 3
With a tax of $1.00 per unit, the supply function will change as follows. The new supply equals the old supply function evaluated at p-1: 
    S(p-1) = 20*(p-1) - 50 = 20*p - 70
So the new supply function has still the same slope, but lies below the old supply, as the constant -70 is less than -50. Let us now compute the new after-tax equilibrium price: 
    20*p - 70 = 100 - 30*p
         50*p = 170
	    p = 3.4
So the equilibrium price increased from $3.00 to $3.40 per unit. The consumer does absorbs $0.40 of the tax, while the remaining $0.60 is the tax on the producer.