Question

The demand for milk is represented by: P = -0.5 QD + 7.2

The supply for milk is represented by: P = 1.2QS + 2.8

Qty are in millions of gallons per week.

Now suppose that the government levies a $.51 excise tax per gallon on the sellers. Calculate the part of the tax borne by the consumers in this market and enter using 2 decimal places. Help please, thank you! Where can I find your solution to the problem? I'm new at Chegg... thanks.

Answer 1

Equilibrium price is when supply quals demand, so at equilibrium point we can equate the two supply and demand equations to find the market price and quantity P* and Q* at equilibrium before taking the tax into consideration.

Since the two equations are:

Supply: P = 1.2QS + 2.8

Demand: P = -0.5 QD + 7.2

we can equate the two equations. Since the left hand side contains price in both equations

by equating the price we get -0.5Q*+7.2=1.2Q*+2.8 where Qs=Qd=Q* is equilibrium quantity and for this Q* the equilibrium price would be P*=Ps=Pd (for both supply and demand equations)

solving it gives Q*=4.4/1.7=2.588 gallons

So P*=(-0.5)x(2.588)+7.2=$5.906 per gallon (by putting value of Q* in demand equation as any one equation will give same P*)

Now new supply curve with tax is P=(1.2Qs+2.8)+0.51 because imposing tax shifts the supply curve upwards by the amount of the tax in absolute terms, hence $0.51 is added into the price equation of supply.

Suppose the actual price paid by buyer is Pb at the quanittity of Qb, now if we want to calculate price paid by buyer we equate new supply curve to original demand curve (demand curve remains the same) as this new equilibrium is what the current position of the graphs will be after tax,

The tax causes the buyer to pay price Pb which is more than the previous market price P* and accordingly the supplier receives the price Ps which is less than P*. The difference between Pb and Ps is the tax amount with the market price P* (before taxes) in between.

New equilibrium: New supply curve equation=original demand curve equation

(1.2Qb+2.8)+0.51=-0.5Qb+7.2 (again since price is common in left hand side of both equations)

So Qb=3.89/1.7=2.288 gallons

So Pb=(-0.5)x(2.288) + 7.2=$6.056 per gallon

So Pb is the actual price paid by buyer after tax while P* was the market price without tax

Therefore,

Tax burden borne by consumer is price paid by consumer minus the market price when no tax was present

So, Tax borne by consumer=Pb-P*=6.056-5.906=$0.15

(To calculate price paid by supplier Ps, we find the price from the old supply curve before tax by inputting quantity Qs as the new Qb found)