Question

The equations for the demand and supply curves for a particular product are P = 10...

The equations for the demand and supply curves for a particular product are P = 10 - .4Q and P = 2 + .4Q respectively, where P is price and Q is quantity expressed in units of 100. After an excise tax is imposed on the product the supply equation is P = 3 + .4 Q. a- Compute equilibrium price and quantity before and after tax. b-Calculate government's revenue from this tax. C- Calculate share of producers and consumers from this tax.

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Answer #1

(a) Equilibrium occurs when demand equals supply.

Before tax: 10-0.4 Q = 2+0.4Q

8 = 0.8Q

Q= 10 hundred units (equilibrium quantity before tax)

And P= 10-0.4(10)= $6 (Equilibrium price before tax)

After tax : Supply curve shifts upward by $1 as shown by new supply equation P= 3+0.4Q

After tax : Equilibrium occurs where new supply equation equals demand .

10-0.4Q= 3+0.4Q

0.8Q = 7

Q= 8.75 hundred units (Equilibrium quantity after tax)

P= 10-0.4(8.75)= $6.5 (Equilibrium price after tax)

(b) Government revenue = ($1)(8.75) = $8.75 hundred

(c) Share of consumer for this tax = $(6.5-6)= $0.5

Share of producer for this tax = $(1-0.5)= $0.5

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