Question 1

a) Consider a fish species that is caught with nets. The quantity of fish caught is assumed to

be a fraction, a, of the fish population. The rate of change of the fish species overtime is

the difference between the growth rate and the quantity of fish caught. Given that the

growth function of the fishery is

g(y)= y-y²

y(0)= y0

(i) Solve for the fishing population, y, as a function of t.

(ii) What will happen to the fish population as t ? ?? Justify your response.

b) Suppose that only two firms supply the market and each firm chooses its output in period

t + 1 to maximize profit in the belief that the other firm will maintain its output level at

the period t value.

Let the demand function be

p(x+y) = 126 - (x+y)

Now suppose the firms have cost functions given by

C(x)=x²

C(y)=y²

(i) Derive the linear second order difference equation.

(ii) Given x(0) = 28 and x(1) = 56, solve the difference equation for x.

Question 2

a) Determine whether the following statements are true or false and justify your response.