Imagine the supply curve for sweets in Whoville is given by: P = 270 + Q/10 and the demand curve is given by: P = 300 Q/5

Suppose the Grinch levies a sugar tax of 12 per sack, collected from Whovillians. What is the tax revenue and what fraction of the tax does the buyer bear?

The problem i am having is when i try to draw a diagram, how do i know the supply curve shifts or the demand curve shifts?

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gsgaurav104Answered18 hours ago

Note that if it is not given whether tax is imposed on buyer or seller, then you can shift either supply or demand curve. Your answer won't change by shifting either of the curve. This is because effect of tax just depends on the relative elasticity of buyers and sellers and not on the party at which tax is imposed.

However, if it is given that tax is imposed on buyers then shift demand curve and if imposed on sellers then shift supply curve.

Explanation:

P= 270 + Q/10

Q/10 = P - 270

Qs = 10Ps - 2700 ( supply curve) where Ps = price received by sellers, Qs = quantity supplied

P = 300 - Q/5

Q/5 = 300 - P

Qd = 1500 - 5Pb (demand curve) where Pb = price paid by buyer, Qd = quantity demanded

At equilibrium without tax,

Qd = Qs

1500 - 5P = 10P - 2700 (Pb = Ps = P without tax)

4200 = 15P

280 = P ( equilibrium price before tax)

Q= 1500 - 5P = 1500-5(280) =100 ( equilibrium quantity before tax)

Once the tax is imposed,

Price paid by buyers will exceed the price received by sellers by the amount of the tax.

So, Pb = Ps + 12

Therefore,

Qs = 10Ps - 2700 ( new supply curve)

Qd = 1500 - 5Pb = 1500-5(Ps + 12) = 1440 - 5Ps ( new demand curve)

At new equilibrium after tax,

Qd = Qs

1440 - 5Ps = 10Ps - 2700

4140 = 15Ps

276 = Ps ( price received by sellers after tax)

Pb = Ps + 12 = 276 + 12 = 288 ( price paid by buyers after tax)

New equilibrium quantity is:

Qd = 1500 - 5Pb = 1500 - 5(288) = 60

So, tax revenue = new equilibrium quantity after tax * tax per sack = 60*12 = 720

Tax borne by buyer per sack = price paid by buyer after tax - price paid by buyer before tax =288-280 = 8 per sack

Fraction of tax borne by buyer = 8/12 = 2/3 = 67%.

I have shifted demand curve in this figure, but it really doesn't matter. You can also shift the supply curve leftwards

Will the answer different by shfting the supply curve instread of the demand curve?