Question

Consider an industry with market demand Q=550-2p and market supply Q=100+10p. Determine the equilibrium price and quantity. Suppose the govrenment imposes a tax of $6 per unit to be paid by consumers. What is the impact on equilibrium price and quantity? What if the sales tax is paid by the seller instead of the buyer?

Suppose that demand is instead given by Q=280-2p.

a) Show that the equilibrium levels of p and q are the same as in the initial equilibrium

b) Determine the impact of a $6 sales tax in terms of the price effectively paid by buyers and sellers

c) Compare the results in b) and those in the initial part of the exercise. Explain the economic intuition.

Answer 1

a) When demand is Q=550-2p

and aupply is Q= 100+10p

Equilibrium is when market demand and supply are equal, the point where they cut each other is equilibrium point with some quantity and price.

Demand is the quantity that the consumers are willing to buy for a particular price and supply is the quantity that the producers are willing to sell at a given price.

For equilibrium,

Demand = Supply

550-2p = 100+10p

550-100= 10p+2p

450=12p

p= 450/12

p=37.5 $

Now, equating this price in demand function to find the equlibrium quantity:

Q= 550-2(37.5)

Q= 475 units

Therefore. equilibrium quantity is 475 units abd equilibrium price is $37.5

b) If sales tax is imposed on consumers, they will be willing to buy less units because they will be needing to pay extra 6$ amount with every additional unit they purchase. Due to the tax, the demand decreases forcing the producers to decrease the price.

Effect on price- One of the most obvious impact which is seen in supply and demand is on the price of the commodity. Due to inclusion of tax, the prices increases.

Due to sales tax supply curve will shift inwards. Since sales tax means increase in price, but the overall equilibrium price wil decrease.

c) Initially, the consumers were demanding more, but due to introduction of sales tax, their quantity demanded will decrease and the price they will be willing to pay will also decrease.

In case of supply, the producers will want to increase the price of good, but due to demand curve the overall result would be decrease in equilibrium price and quantity