Question

Suppose that the market for rutabagas (in case you don't know, it is a root vegetable that's also known as Swedish Turnip) is competitive. The demand for rutabagas is Q 2,000 100P and the supply of rutabagas is -100+200P. (a) Suppose that Governor Sloop imposes a $2 per unit tax to be paid by consumers. Who bears the statutory incidence of the $2 per unit tax? Who bears the economic incidence of this tax? [A graph can be helpful but not required.] (b) What is the deadweight loss of the tax? (c) Suppose now that Governor instead imposes that the $2 unit tax is to be paid by the stores directly. What will happen to the "sticker price" (i.e. price paid by consumers) on rutabagas? Verify that the consumers' tax burden would stay the unchanged.

Answer 1

First we find equilibrium price without any intervention i.e. free market

Set Qd=Qs

2000-100P=-100+200P

300P=2100

P=7

Equilibrium price is $7 per unit

Quantity demanded=2000-100*7=1300 units

Quantity supplied=-100+200*7=1300 units

So, equilibrium quantity is 1300 units.

a)

In this case, Consumer spends (P+2) for every amount P, paid to seller.

New demand curve is given by

Qd'=2000-100*(P+2)=2000-100P-200=1800-100P

Set Qd'=Qs

1800-100P=-100+200P

1900=300P

P=$6.3333

New equilibrium quantity=(1800-100*6.3333)=1166.67

As per statutory requirement, customer pays the tax.

We can see that in this situation customer is paying $8.3333 ($6.3333 for price+2 for tax). While seller is getting $6.3333 per unit sold.

So, we can see that

Burden of tax passed to consumer=Total per unit amount by customer after tax-Old equilibrium price

=8.3333-7=$1.3333

Burden of tax passed to seller=Old equilibrium price-Total per unit amount received by seller after tax

=7-6.3333=$0.6667

We can see that economic burden is shared between seller and customer.

b)

Dead weight loss=1/2*(Tax amount*Change in equilibrium quantity)=1/2*2*(1300-1166.67)=$133.33

c)

In this case, seller receives price , P but $2 goes to government and P-2 is left with seller.

New supply curve is given by

Qs'=-100+200*(P-2)=-100+200P-400=--500+200P

Set Qd=Qs'

2000-100P=-500+200P

2500=300P

P=8.3333

New Sticker price=$8.3333 (It was $6.3333 in earlier case, in addition to that consumer was supposed to pay a tax of $2 per unit)

Burden of tax passed to customer=Total per unit amount by customer in new situation-Old equilibrium price

=8.3333-7=$1.3333

We observe that consumer's tax burden remains unchanged