Consider a tree that is planted at time t=0, and let V(t) denote its value at time t. The rate of interst is 100r per cent per year and is continously compounded.

a) Derive an expression for the present value of the tree.

b) The optimal time to cut down the tree is the value of t that maximise the present value of the tree. Derive the condition this optimal time must satisfy.

c) Explain what the condition means in plain language.

Consider the following model of an open economy          Y- C(Y) - X(e) = C

Question:   Consider a firm that sells in two separate markets. The inverse demand functions in the two market are  p₁= a₁-b₁.q₁    

                     and   p₂ = a₂ -b₂.q₂      and the total production   c(q) = a. (q₁+q₂)