Question 1 (5 points)

Here is a diagram showing that free trade results in exports (x), compared with Autarky at A.
p stands for price and Q for quantity. The world price is pw

(a) Comparing autarky at A with the free trade outcome, prove that free trade improves
welfare (measured as the sum of consumer and producer surplus). (2 marks)

(b) Does your proof in (a) work if there are consumption externalities both under autarky
and under free trade? Why (not)? (1 mark)

(c) Does your proof in (a) work if there are production externalities (with no consumption
externalities) both under autarky and under free trade? Why (not)? (1 mark)

(d) How can the benefits of free trade be made the most of without unacceptable
externalities? (1 mark)

Question 2 (7 points)

Here is a slide from the lecture in week 3. You may assume the demand curve and the cost of
extraction is the same in both periods in the two period model.

(a) What economic quantity is measured by the length of the dashed line? (1 mark)

(b) What is the discount rate in this model? [Hint: it is positive] (1 mark)

(c) What would happen to period one consumption if the discount rate halved? (1 mark)

(d) What would happen to period one consumption if the discount rate were multiplied by
negative one? [That is, if it changed sign to be negative.] (1 mark)

(e) What would happen to the diagram if more of the non-renewable resource were
discovered? (1 mark)

(f) The marginal net benefit in period one is given by: MB1 = 6 – 0.4Q1. Derive optimal
consumption in periods 1 and 2 using the discount rate calculated in b) and any other
information you need from the diagram above. Show all steps of your working out. (2
marks)