Question

Suppose that the government institutes a \(\$ 5.50\) per-film tax on the film copying industry described in Problem 15.3 a. Assuming that the demand for copied films is that given in part (a) of Problem \(15.3,\) how will this tax affect the market equilibrium? b. How will the burden of this tax be allocated between consumers and producers? What will be the loss of consumer and producer surplus? c. Show that the loss of producer surplus as a result of this tax is borne completely by the film studios. Explain your result intuitively.

Short answer

Question: Analyze the effect of a $5.50 per-film tax on the film-copying industry, and explain how the tax will affect the market equilibrium, the burden allocation between consumers and producers, and the loss of consumer and producer surplus. Show that the loss of producer surplus as a result of this tax is borne completely by the film studios and explain the result intuitively. Answer: The imposition of a $5.50 per-film tax on the film-copying industry will cause an upward shift in the supply curve, leading to a higher equilibrium price and a lower equilibrium quantity. The tax burden will be shared between consumers and producers based on the elasticity of demand and supply. The film studios, as part of the supply side, will bear a substantial share of the tax due to the highly competitive nature of the film-copying industry. Although we cannot exactly compute the loss of consumer and producer surplus without more information on the supply curve and industry parameters, consumer surplus loss will be the area under the demand curve from the initial to the new equilibrium quantity, while producer surplus loss will be the area between the supply curve and the new supply curve (with tax) from the initial to the new equilibrium quantity. Intuitively, film studios are likely to bear a significant share of the loss in producer surplus due to the industry's competitiveness, though we cannot precisely determine if they bear the entire loss without further information.

Step-by-step solution

Calculate the new equilibrium after the tax

To find the new equilibrium after the tax, we must find the new supply curve. Since the tax is levied per-film, for every unit of film supplied, the supplier receives \((P - 5.50)\). Therefore, the new supply curve can be written as: \(Q_S^* = Q_S(P - 5.50)\) Now we set \(Q_D = Q_S^*\) to find the new equilibrium: \(200 - 10P = Q_S(P - 5.50)\) Note: It would help to have more information about the supply curve or other industry parameters; however, we can still perform the given analysis. #step2#

Calculate the new price and quantity

Without enough information to directly calculate the new price and quantity, we can still analyze the changes in price and quantity in response to the tax. Given the tax, there will be an upward shift in the supply curve, resulting in a higher equilibrium price and lower equilibrium quantity. To determine the specific changes, additional information on the supply curve and industry parameters would be necessary. #step3#

Determine the tax burden allocation

The tax burden is shared between consumers and producers, depending on the elasticity of demand and supply. The more inelastic the demand or supply, the higher the share of the tax burden borne by the respective party. In this case, without information on the supply curve, we cannot directly determine the allocation of the tax burden. Intuitively, we can say that the film copying industry is likely to have a high degree of competition; thus, the burden on the producers (film studios) may be substantial. #step4#

Compute the loss of consumer and producer surplus

As the tax has resulted in a higher equilibrium price and lower equilibrium quantity, we expect a loss of consumer and producer surplus. However, without specific information on the supply curve and other industry parameters, we cannot exactly compute the amount of loss. Generically, consumer surplus loss will be the area under the demand curve from the initial equilibrium quantity to the new equilibrium quantity, and producer surplus loss will be the area between the supply curve and \(Q_S^*\) from the initial to the new equilibrium quantity. #step5#

Show the result for loss of producer surplus

Using the tax incidence principle, we conclude that the tax burden is shared between consumers and producers. However, we have to show that the loss of producer surplus as a result of this tax is borne completely by the film studios. With the information provided, we can only reason that, given the highly competitive nature of the film-copying industry, film studios are likely to bear a substantial share of the tax for the loss in producer surplus, if not the entire amount. To precisely determine if the film studios bear the entire loss, we would need more information on the supply curve and the nature of competition in the industry.

Key concepts

Producer Surplus

Producer surplus is the difference between what producers are willing to accept for a good and what they actually receive. It represents the additional benefit that producers get when they sell at a market price higher than the minimum they would be willing to take. After a government-imposed tax, such as a $5.50 per-film tax on the film copying industry, producer surplus can decrease because the net price producers receive is reduced by the tax amount.
Before the tax, producers enjoyed a certain surplus at the market equilibrium price. With the tax, the new effective price for producers is the market price minus the tax, leading to a decrease in producer surplus. The degree to which producer surplus is affected depends on the elasticity of supply. The less elastic the supply, the greater the burden producers must bear, as they cannot easily change their production levels in response to the tax.
This reduction in producer surplus effectively means that producers, like film studios in this case, earn less revenue per unit sold after the tax. This burden may fall heavily on film studios due to competition levels or the nature of the industry's supply elasticity.

Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good or service and what they actually pay. It measures the economic benefit consumers receive when they pay less for a product than the maximum price they would have been willing to pay.
Imposing a tax on a product, such as films in the copying industry, leads to an increase in the market price. This price hike results in a reduction of consumer surplus, as consumers are now paying more to purchase the same product.

• This new, higher price causes some consumers to leave the market, as they are unwilling to pay the increased cost, further decreasing consumer surplus.
• The loss of consumer surplus is visualized as the area between the initial price consumers paid and the new higher price, multiplied by the reduction in quantity sold.

Overall, the reduced consumer surplus reflects the financial burden placed on consumers following a tax increase in the market. This impact mostly affects consumers with lower willingness to pay, which is why some might choose to forego the purchase altogether.

Market Equilibrium

Market equilibrium occurs where the quantity demanded by consumers equals the quantity supplied by producers. At this point, the market clears with no shortage or surplus. Taxes affect market equilibrium by influencing both supply and demand, often leading to a change in both the equilibrium price and quantity.
In the context of the film copying industry facing a $5.50 per-film tax, the supply curve shifts upward. This is because producers require a higher price to supply the same quantity as before to cover the tax costs. This shift results in a new market equilibrium that features a higher equilibrium price and a reduced equilibrium quantity.

• The increased price results from sellers factoring in the tax within their costs, thus passing some of the burden onto consumers.
• The lower quantity reflects how some consumers exit the market due to the higher prices, and producers may produce less due to receiving lower net prices.

Ultimately, the introduction of a tax disturbs the previous market balance, and the new equilibrium is characterized by these adjusted price and quantity levels where the decreased consumer and producer activities intersect.