1) With the help of appropriate figures, show how utility possibility frontier is derived.

2) The utility function for Abe (A) and Bro (B) are as follow: UA = XAYA UB = XBYB 0.5

Where the initial endowment of X and Y are: XA = 20, YA = 20, XB = 8, YB = 100

(a) Calculate the marginal rate of substitution of X and Y for Abe and Bro at their initial endowment point.

(b) Assume that the amount of X and Y is fixed, draw the Edgeworth diagram and label the initial allocation for both consumers as 'W'.

(c) Next, explain exchanges that are mutually beneficial for both consumers. In your explanation, please include the discussion on the different goods that each consumer would like to offer, the concept of Pareto improvement, Pareto efficient and Pareto inefficient allocations.

3) If a monopoly's inverse demand curve is p(Q) = 18 - 2Q and its cost function is C(Q) = 10 + 3Q + 0.5Q2 , what is Q* maximizes the monopoly's profit (or minimizes its loss)? At Q*, what is the price and the profit? Should the monopoly operate or shut down?