1. Solve the following quadratic equations.

(a) x2 − 6x + 5 = 0

(b) Q2 + 6Q + 5 = 0

(c) 2/(P + 1) = (P – 1)/6

(d) Q/2 + 12/Q = 5

2. The demand function for a good is given by Q = (200/P) − 1 and the (inverse) supply functions is P = 5 + 0.5Q. Solve for the equilibrium level of P and Q.

3. Consider a monopolist who faces an inverse demand function P = 10 − Q and no production costs.

(a) Compute total revenue (TR).

(b) Plot total revenue as a function of Q.

(c) Find the points Q at which the monopolist breaks even.

4. Solve the following equations. (a) 2x /4 = 2.

(b) e5x = 1/ ex−5

(c) 2 + ln(t − 5) = 2.5

5. The spread of a carrot fly through an untreated crop is modelled by the equation Y = 500(1 − e−0.5t), where Y is the weight of infected carrots in tons, t is time in days.

(a) Graph Y for as a function t in the interval [0, 6]. Hence describe the spread of carrot fly during the next 6 days.

(b) Calculate the time taken to infect 300 tons of carrots.

6. Consider a utility maximization problem that we briefly touched up in Lecture 1. Let   the consumer’s utility function be given by U(x1, x2) = x1x2. This functional form is called the Cobb Douglas utility function.