Question

The demand and supply curves are given by q=110−2p and q=3p−50, respectively; the equilibrium price is $32 and the equilibrium quantity is 46 units. A sales tax of 7% is imposed on the consumer. (a) Find the equation of the new demand and supply curves. Enter the exact answer. Demand: q= Supply: q= (b) Find the new equilibrium price and quantity. Round your answers to two decimal places. p=$ Number q= Number units

Answer 1

1. The Demand is given by
   `q^d=110-2p^d(1.07)`
2. The supply curve is by
   `q^s=3p^s-50`

Consumers will face a price of 33.29 and the equilibrium quantity will be 43.42.

These results illustrate that as a consequence of the tax, the price faced by consumers will be higher, quantity sold be lower, and producers will receive less for their product sale.

Step-by-step explanation:

1. The Demand is given by
   `q^d=110-2p^d`
2. The supply curve is by
   `q^s=3p^s-50`

In the absence of taxes
`p^s=p^d` and
`q^s=q^d`.

An ad-valorem tax
`t=0.07` generates now that

`p^s=p^d(1+t)`

So the new equilibrium is

`110-2p(1.07)=3p-50`

`110+50=5.14p`

`p^s=31.12`

`p^d=33.29`

Replacing in the demand equation we get the equilibrium quantity

`q=43.42`