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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 supplier receives 4 pence less. The consumer burdens 80% of the tax and the producer only 20%.

(c) Compute and interpret the deadweight loss of taxation in this market.
(Note: the deadweight loss is also known as the excess burden)

The upper triangle is [1.36 – 1.20]×0.5×[14-13.2] = £0.064 thousand or £64 per day. The lower triangle is [1.20 – 1.16]×0.5×[14-13.2] = £0.016 thousand or £16 per day. The overall tax take per day is 0.2×13.2 = £2.64 thousand or £2640 per day. The deadweight losses or the excess burden of taxation represents only £80 per day or 3% of the tax revenue. The small excess burden of taxation in this case is due to the inelastic demand for butter and its corresponding inelastic supply.

2. An economics lecturer is considering leaving the University of Sussex and opening a consultancy business. For his services as a consultant he would be paid £65,000 per annum. To establish the business the lecturer must convert into an office a house he currently owns and from which he collects rents of £1000 per month. He must hire a secretary at a salary of £20,000 per year and must withdraw £10,000 from his 10% per annum fixed rate savings account to use for miscellaneous expenses. The University of Sussex pays the economics lecturer £35,000 per year. On the basis of a purely economic analysis, do you predict that the economics lecturer will leave the University to start up his own business?

In terms of the consulting business an accountant would calculate profit as the difference between revenue and costs. In this case the accounting profit is £65,000 - £20,000 - £10,000= £35,000. However, the accountant’s approach is to neglect the implicit costs because these can be more difficult to measure as they are more subjective. The interest earnings foregone for the year on his savings account are £1000. The annual rent foregone from the house he owns is 12 £1000 = £12,000. The final element foregone as far as the lecturer is concerned is the...
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