Question 1.

Suppose an economy with two individuals: Mrs. A and Mr. B. They each seek to smooth their consumption over two periods: the present (t -1) and the future (t -2).They each have an income of $100 per period and no initial wealth.The present consumer price, c1, is p1=1, while the nominal interest rate, i, and the rate of inflation , are both 5%.

a) Write down the intertemporal budget constraint of these two individuals and represent it graphically, taking care to specify the staffing point, the slope, as well as the intersections with the axes.

b) Mrs A's intertemporal preferences are such that her marginal substitution rate (MRS) between present and future consumption is c2/2c1, while Mr B's MRS is 2c2/c1. Find their optimal consumption choices. Are they lenders or borrowers at this interest rate?

c) Suppose that in this economy, there is no way to save at a rate i without finding someone to lend to (i.e. a borrower). Based on your answer in b), describe what should happen for the credit market to balance. Out of balance, would it be possible for both Mrs A and Mr B to lend (save)? Or that they both want to borrow? Detail your reasoning.

Question 2

Suppose a beekeeper, who produces honey. Its marginal cost of producing honey is constant, c>0 while its marginal profit decreases with the amount of honey produced - a reflection of a market price that must fall in order for a larger quantity of honey to flow. In addition, the production of honey generates an external benefit for an apple grower, next door to the beekeeper, because of pollination of his orchard. The external marginal profit, b > 0, is also assumed to be constant.

a) Describe and graphically represent the situation described above. In doing so, take care to contrast the balance of the market with the social optimum and explain why they differ from each other.

b) Suppose the two neighbours, the beekeeper and the apple grower, negotiate to jointly determine honey production. The status quo (in the absence of a negotiated agreement) is the market balance found in a) and the negotiating costs are zero. What would then be the minimum payment to be paid to the beekeeper by the apple grower to encourage him to produce the optimum amount of honey? And what would be the maximum amount that could be paid by the apple grower? Represent your answer graphically and detail your reasoning.