A government subsidised a new factory in a rural area to create jobs. It also provided training

courses at a college. Objectors claimed the development would destroy an area of natural beauty.

What concepts are involved in this statement?

A economic growth, resource allocation, free market equilibrium

B government intervention, monetary policy, opportunity cost

C public good, market prices, fiscal policy

D supply-side policy, negative externalities, factors of production

3 Reena makes a living by selling paintings of the town in which she lives. She sells them in an

open-air market once a week.

In order to be able to sell more pictures in a week she decides to buy a studio, pay someone to

help in the studio and try to increase demand by advertising in the local paper.

Which factors of production were changed?

A capital only

B labour and capital

C labour and land

D labour only

(4 points) A binomial lattice is used to model the price of a non-dividend paying stock up to time T. The time interval (0, 7) is subdivided into n intervals of length Ar = -. It is assumed that, at each node in the binomial lattice, the share price will either increase by a factor of: or decrease by a factor of where >0. The movements at each period are assumed to be independent. (a) (1.5 points) Show that the price at time T will be: S, = S, exp HT +OVT 24. -n , where X,, is the total number of up jumps. (b) (1 point) Specify the distribution of X",, and state how this distribution can be approximated when n is large, assuming the share price will be equally likely to increase or decrease. (c) (1.5 points) Determine the distribution of ST when n approaches infinity, using part (b).(7 points) You are working on a Ho & Lee interest rate model for the risk-neutral spot rate: dr, = adt + cdW, where W is a standard Brownian motion. (a) (1 point) Define the technique of calibration as it relates to one-factor interest rate models and explain why the Ho & Lee model facilitates calibration. (b) (1 point) State an argument for and an argument against calibration. (c) (1 point) Show that r =r, + at + cW, (d) (2 points) Derive a formula for the arbitrage-free price B(0, 7) of a default-free zero-coupon bond, as a function of r, a, c, and T. Hint: E(e' (e) (1 point) Derive a formula for the continuously compounded forward rate F(0, T, U) , where U > T > 0, as a function of r, a, c, T, and U. (f) (1 point) Derive a formula for the instantaneous forward rate f(0, 7) as a function of r, a, c, and T