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

Answer:

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.

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

$q=43.42$