The beer market in Tanzania is currently at equilibrium selling 10 million bottles per week of Tshs 80 per bottle. It has been established that a percentage change in price results in a 0.5 percent change in the demand for beer and 0.8 percentage change in its supply, consistent with the laws of demand and supply. The government has announced at a Tshs 10 tax for every bottle of beer sold in order to raise revenue. The tax burden rest on both consumers and producers of beer.
Required
Define the terms “Consumer surplus” and “Producer surplus”. With the help of well labeled diagrams, show that the consumer surplus and producer surplus before and after the tax
Determine the demand and supply functions of beer in the market
How much will consumer pay per bottle after the tax. Compute the Consumer surplus lost due to the tax
How much will the beer producers/retailers receive per bottle after the tax. Compute the Producer Surplus due to the tax
How do the surplus lost in (c) and (d) above compare with the price elasticity of demand and supply?
How much does the government raise revenue per week from the tax
Compare the dead weight loss due to the tax
Consumer surplus refers to the difference between the maximum price a consumer is willing to pay for a product and the actual price they pay. It represents the value that consumers receive from purchasing a product at a price lower than their willingness to pay.
Producer surplus, on the other hand, refers to the difference between the minimum price a producer is willing to accept for a product and the actual price they receive. It represents the additional profit that producers receive from selling a product at a price higher than their willingness to accept.
Before the tax is imposed, the beer market is in equilibrium with a price of Tshs 80 per bottle. The demand and supply functions can be represented as follows:
Demand function: Qd = 10 - 0.5P
Supply function: Qs = 0.8P
To determine consumer surplus and producer surplus before the tax, we can calculate the area of the triangles formed by the demand and supply curves.
Consumer surplus before tax:
Consumer surplus = (1/2) * (10 - P)(10 million) = (1/2) * (10 - 80)(10 million) = 400 million Tshs
Producer surplus before tax:
Producer surplus = (1/2) * (P - 0)(10 million) = (1/2) * (80 - 0)(10 million) = 400 million Tshs
After the tax is imposed, the price per bottle increases by Tshs 10, resulting in a new price of Tshs 90 per bottle.
Consumer surplus after tax:
Consumer surplus = (1/2) * (10 - 90)(10 million) = 100 million Tshs
Consumer surplus lost due to the tax:
Lost consumer surplus = Consumer surplus before tax - Consumer surplus after tax
Lost consumer surplus = 400 million Tshs - 100 million Tshs = 300 million Tshs
Producers/retailers will receive Tshs 80 per bottle after the tax.
Producer surplus after tax:
Producer surplus = (1/2) * (90 - 0)(10 million) = 450 million Tshs
Producer surplus due to the tax:
Producer surplus due to tax = Producer surplus after tax - Producer surplus before tax
Producer surplus due to tax = 450 million Tshs - 400 million Tshs = 50 million Tshs
The surplus lost due to the tax is inversely related to the price elasticity of demand and supply. If demand and supply are elastic, the surplus lost will be greater. If demand and supply are inelastic, the surplus lost will be smaller.
To calculate the government revenue per week from the tax, we need to determine the quantity of beer sold after the tax is imposed. This can be found by setting the demand and supply functions equal to each other and solving for P:
Qd = Qs
10 - 0.5P = 0.8P
1.3P = 10
P = 7.69
The quantity sold after the tax is 10 - 0.5(7.69) = 6.15 million bottles.
Government revenue per week from the tax:
Revenue = Tax per bottle * Quantity sold
Revenue = 10 Tshs/bottle * 6.15 million bottles = 61.5 million Tshs
The deadweight loss due to the tax is the loss of total surplus in the market caused by the distortionary effects of the tax. It is represented by the area of the triangle formed between the demand and supply curves after the tax is imposed. The deadweight loss can be calculated by subtracting the consumer and producer surpluses after the tax from the consumer and producer surpluses before the tax:
Deadweight loss = Consumer surplus before tax + Producer surplus before tax - Consumer surplus after tax - Producer surplus after tax
Deadweight loss = 400 million Tshs + 400 million Tshs - 100 million Tshs - 450 million Tshs = 250 million Tshs