Question

Suppose that the government is considering a tax of $12 per bottle of champagne. Calculate each of the following: i. The change in equilibrium quantity due to the tax. ii. The change in the price buyers pay (PB) due to the tax. iii. The change in the net price sellers receive (PS) due to the tax. iv. The change in consumer surplus due to the tax. v. The change in producer surplus due to the tax. vi. The Government revenue from the tax (assume that it was zero before the tax).

Answer 1

Answer:

i. The equilibrium quantity will shift towards the left side of Demand Supply curve.

ii. The Price Buyer pay (PB) will increase by $6.

iii. The net price seller receive will decrease by $12.

iv. Consumer Surplus will decrease.

v. Producer Surplus will decrease.

vi. Government Revenue will be total decrease in Consumer and Produce surplus minus the dead weight loss.

Explanation:

i. The consumer only cares about the price that is charged to him. So when tax is passed on to consumer in form of increase in price, then the demand curve will shift left.

Usually in order to control the shift, the supplier only passes a portion of the tax to the consumer, and pays the rest himself. So in that case the supplier will get less money. So, the supplier curve will also shift upwards.

So the quantity traded will shift towards left.

ii. It depends upon the tax that is transferred by supplier to the consumer. So if supplier decides to transfer half of the tax to consumer, the PB will increase by $6.

iii. Price received by the supplier will be reduced by the amount to tax payed by the consumer, with is $6. And the supplier will also have to pay $6 tax himself. So total PS will reduce by $12.

iv. The consumer surplus will reduce by the amount of revenue that went to government in form of tax revenue, and inform of the dead weight loss, that is the lost quality traded due to decreased demand. It can be calculated as

$ConsumerSurplusLost = (Increase In PB)*(Qe_{new} ) + \frac{1}{2}*(Increase In PB)*(Q_{eOld}-Q_{eNew})$

v. Similarly the supplier surplus will be reduced by the amount of revenue that went to government in form of tax revenue, and inform of the dead weight loss, that is the lost quality traded due to decreased demand. It can be calculated as

$ProducerSurplusLost = (Decrease In PS)*(Qe_{new} ) + \frac{1}{2}*(Decrease in PS)*(Q_{eOld}-Q_{eNew}$

vi. Government tax will be the loss of consumer and producer surplus minus the dead weight loss that is the lost quality traded due to decreased demand. It can be written in equation form as:

$TaxRevenue = (PB - PS)*(Qe_{new} )$