Question

Among the tax proposals regularly considered by Congress is an additional tax on distilled liquors. The tax would not apply to beer. The price elasticity of supply of liquor is \(4.0,\) and the price elasticity of demand is \(-0.2 .\) The cross-elasticity of demand for beer with respect to the price of liquor is 0.1 a. If the new tax is imposed, who will bear the greater burden-liquor suppliers or liquor consumers? Why? b. Assuming that beer supply is infinitely elastic, how will the new tax affect the beer market?

Short answer

a. The liquor consumers will bear the greater burden of the tax because the demand for liquor is inelastic and the supply is elastic. b. The new tax will not affect the price of beer, but it will increase the total quantity of beer demanded because the cross-elasticity of demand for beer with respect to the price of liquor is positive and the supply of beer is infinitely elastic.

Step-by-step solution

Determine who will bear the tax burden

The person that will bear the greater burden of the tax can be determined by considering the price elasticity of demand and supply. The supplier will bear the larger portion of the tax if the demand is inelastic (absolute value less than 1) and the supply elastic (greater than 1). Given the price elasticity of demand for liquor is \(-0.2\) and the elasticity of supply is \(4.0\), it means that the demand is inelastic and the supply is elastic. Therefore, the liquor consumers will bear the greater burden of the tax.

Determine the effect of the tax on beer market

Considering the cross-elasticity of demand for beer with respect to the price of liquor is \(0.1\), it suggests that as the price of liquor increases due to the tax, the demand for beer also increases. More specifically, a 1% increase in the price of liquor leads to a 0.1% increase in the demand for beer. Bearing in mind that the supply of beer is infinitely elastic (can meet demand at the same price), then the tax on liquor won't affect the price of beer, but will increase the total quantity of beer demanded.

Key concepts

Tax Burden

Understanding who bears the greater burden of a tax is crucial for assessing the impact of tax policies. The tax burden is influenced by both the price elasticity of demand and the price elasticity of supply. When demand is inelastic, meaning consumers are not very responsive to price changes - represented by an elasticity less than the absolute value of 1, they tend to bear a larger share of the tax. Conversely, when supply is elastic, indicated by an elasticity greater than 1, suppliers are more capable of altering their production and can pass on most of the tax to consumers.

In the given scenario, the price elasticity of demand for liquor is (-0.2), signifying a relatively inelastic demand. This suggests that consumers will continue to buy liquor even after a price increase due to the tax. The price elasticity of supply for liquor is 4.0, showing a highly elastic supply. Suppliers can adjust their production easily, but because consumers are less responsive to price changes, they will absorb most of the tax. As a result, liquor consumers are expected to bear the greater tax burden, facing higher prices without significantly reducing their consumption.

Price Elasticity of Supply

The price elasticity of supply measures how much the quantity supplied of a good responds to a change in its price. It's a key concept in economics that helps predict how changes in the market, such as taxation, can affect supply amounts. An elasticity greater than 1, as seen with the supply of liquor at 4.0, signals that producers can increase their output significantly if the price rises.

This high elasticity often indicates the presence of alternatives in production, the ability to switch resources to different goods, or spare capacity. It plays a critical role in determining the tax burden, as mentioned earlier. When the supply is elastic, producers have leverage to slightly adjust prices or they can absorb any additional costs, such as a tax, without losing too much in the way of quantity sold. However, ultimately, the price sensitivity of consumers will dictate how much of the tax can be passed on to them, thus determining the division of tax burden between consumers and producers.

Cross-Elasticity of Demand

Cross-elasticity of demand measures how the quantity demanded of one good responds to a price change in another good. It is a reflection of the interconnectedness between different markets. In this case, the cross-elasticity of demand for beer with respect to the price of liquor is 0.1. This positive cross-elasticity indicates that beer and liquor are substitute goods; as the price of liquor rises due to the tax, some consumers will switch to beer.

As liquor becomes more expensive, we expect to see a slight increase in the demand for beer. Since the supply of beer is infinitely elastic, beer suppliers are capable of meeting any increase in quantity demanded at the same price. Therefore, in the wake of the tax on liquor, we won't see a change in beer prices, but we will observe an increase in the total quantity of beer demanded. This analysis offers insight into how closely related goods can influence each other's markets.