Business
Introduction to Economics
Exercise 4 - Outline solutions
1. Let us return to the butter market of Question 2 from Exercise 3: The demand for butter is given by:
Qd = 20 – 0.05P
And supply is given by:
Qs = – 10 + 0.20P
Where P is pence per kilogram of butter, Qd is the number of kilograms of butter demanded per day, expressed in thousands and Qs is the number of kilograms of butter supplied per day, expressed in thousands. (a) Take the market equilibrium calculated in Exercise 3, Question 2 (a), as your starting point. Now suppose the government imposes a per unit sales tax of 20 pence per kilogram in the butter market. What are the implications for the market equilibrium price and quantity?
[Tutors: Please start by drawing a diagram to show the impact of the tax and the compute the new equilibrium.]
The post-tax price paid by consumers is computed by recognising that the consumer and producer prices are different. We can thus restate the demand and supply functions for butter as:
Qd = 20 – 0.05Pc
Qs = – 10 + 0.20Ps ,
where Ps is the price suppliers receive and Pc is the price paid by consumers. The tax drives a wedge between the price consumers pay and the price suppliers receive, such that t = Pc – Ps. If we substitute Ps = Pc - t into the supply equation we obtain:
Qs = – 10 + 0.20(Pc - t) ,
If we set demand equal to supply we have:
20 – 0.05Pc = -10 + 0.2(Pc – t)
Hence: Pc = (30 + 0.20×20)/0.25 = 136.
Thus, the post-tax price is £1.36 per kilogram.
Substituting the price into demand (it could also have been substituted into the supply function), we can compute the post-tax equilibrium quantity:
Qd = 20 – 0.05×136 = 13.2 thousand kilograms of butter per day.
The price received by suppliers is given by Ps = Pc – t = 136 – 20 = 116. (b) Who incurs the greater burden of the tax – consumers or producers? We know that the pre-tax price was £1.20. After the tax, the consumer pays 16 pence more and the
Exercise 4 - Outline solutions
1. Let us return to the butter market of Question 2 from Exercise 3: The demand for butter is given by:
Qd = 20 – 0.05P
And supply is given by:
Qs = – 10 + 0.20P
Where P is pence per kilogram of butter, Qd is the number of kilograms of butter demanded per day, expressed in thousands and Qs is the number of kilograms of butter supplied per day, expressed in thousands. (a) Take the market equilibrium calculated in Exercise 3, Question 2 (a), as your starting point. Now suppose the government imposes a per unit sales tax of 20 pence per kilogram in the butter market. What are the implications for the market equilibrium price and quantity?
[Tutors: Please start by drawing a diagram to show the impact of the tax and the compute the new equilibrium.]
The post-tax price paid by consumers is computed by recognising that the consumer and producer prices are different. We can thus restate the demand and supply functions for butter as:
Qd = 20 – 0.05Pc
Qs = – 10 + 0.20Ps ,
where Ps is the price suppliers receive and Pc is the price paid by consumers. The tax drives a wedge between the price consumers pay and the price suppliers receive, such that t = Pc – Ps. If we substitute Ps = Pc - t into the supply equation we obtain:
Qs = – 10 + 0.20(Pc - t) ,
If we set demand equal to supply we have:
20 – 0.05Pc = -10 + 0.2(Pc – t)
Hence: Pc = (30 + 0.20×20)/0.25 = 136.
Thus, the post-tax price is £1.36 per kilogram.
Substituting the price into demand (it could also have been substituted into the supply function), we can compute the post-tax equilibrium quantity:
Qd = 20 – 0.05×136 = 13.2 thousand kilograms of butter per day.
The price received by suppliers is given by Ps = Pc – t = 136 – 20 = 116. (b) Who incurs the greater burden of the tax – consumers or producers? We know that the pre-tax price was £1.20. After the tax, the consumer pays 16 pence more and the