Answer to Question #300573 in Microeconomics for dennis

Question

1. The elasticity of demand for home computers is -2.5, the elasticity of demand for business computers is -.90, and the elasticity of supply for computers for both purposes is 1.
2. A per-unit tax of $200 is imposed on the suppliers of computers. How much does the gross price increase in each market? [Hint: first find the tax incidence/shares.]

Answer 1

Tax incidence

Tax incidence on consumers for home computers:

Tax incidence (TI) = Supply elasticity (Se)/ (Supply elasticity+Demand elasticity (De))

$TI = \frac{Se}{(Se+De)}= \frac{1}{(1+2.5)}=0.4857$

Tax incidence on suppliers for home computers:

$TI = \frac{Se}{(Se+De)}= \frac{2.5}{(1+2.5)}=0.7143$

Tax incidence on consumers of business computers:

$TI = \frac{Se}{(Se+De)}= \frac{1}{(1+0.9)}=0.5263$

Tax incidence on suppliers of business computers:

$TI = \frac{Se}{(Se+De)}= \frac{0.9}{(1+0.9)}=0.4632$

Gross price changes.

Consumers for home computers will pay 0.2857 of the tax imposed plus the actual price of a computer as shown:

$Gross increase=0.2857\times200=57.14$

Consumer price will therefore increase by $57.14

Price that suppliers for home computers will charge will be less by 0.7143 of the tax imposed.

In this case, price will decrease by 0.7143 of tax

$Gross decrease=0.7143\times200=142.86$

Price received will be less by $142.86

Price increase for consumers of business computers

$Gross increase=0.5263\times200=105.26$

Price will increase by $105.26

Price change for suppliers of business computers:

$Gross decrease=0.4632\times200=92.64$

Suppliers price received will decrease by $92.64.