Suppose the market for grass seed can be expressed as Demand: Qd=40-5p Supply: Qs=10P-20

Change in quantity demanded due to tax = 5

Tax incidence on buyers = 15

Price received by the sellers = 3.5

The given demand function is

Qd = 40 -5P

The given supply function is

Qs = 10P -20

A market is in equilibrium when quantity demanded is equal to the quantity supplied

40 - 5P = 10P - 20

40 + 20 = 10P +5P

60 = 15P

P = 60/15

P = 4

Equilibrium price = 4

Equilibrium quantity = 40 - 5*4 = 20

Equilibrium quantity = 20

When government impose a 1.5 per unit tax, the supply function become

Qs = 10(P-1.5) -20

= 10P - 15 -20

= 10P - 35

Qs = 10P - 35

Equilibrium after tax is reached when

10P - 35 = 40 - 5P

10P + 5P = 40 + 35

15P = 75

P = 75/15 = 5

The equilibrium price after tax = 5,

At this price quantity demanded in the market = 40 - 5*5 = 15

Demand after tax = 15

Change in quantity demanded = 20 - 15 = 5

After tax price paid by the consumers = 5

Before tax price = 4

Change in price = 5-4 = 1

After tax quantity demanded = 15

Tax incidence on buyers = 15*1 = 15

Tax incidence on buyers = 15

After tax price received by the sellers = Price paid by the consumers - Tax

Tax = 1.5

Price paid by the Consumers = 5

Price received by the producers = 5-1.5 = 3.5

Price received by the sellers = 3.5

2)  The given supply function is

P = 3Q + 24

This is the inverse supply function.

The given supply function can be written as Q = f(P) as follows

Q = (P - 24)/3b