Amy (A) and Brian (B) have the following utility functions:

UA = 2XAYA, UB = XB(YB)^1/2

where their endowments of consumption goods X and Y are as follows:

XA=80 YA=20 XB=20 YB=20

(a)At the endowment point, what is the marginal rate of substitution of X for Y for Amy? For Brian?

(b)Find the competitive equilibrium price of the goods at which the consumers trade with each other.

(c)In the competitive equilibrium, for each unit of good Y , how many units of good X can be exchanged?

(d)Find both Brian and Amy's preferred consumption bundles in the equilibrium.

(e)Is the allocation of resources achieved in (d) Pareto-optimal? Explain.

(f)Draw the Edgeworth box that shows all possible allocations and plot the endowment points. Plot the indifference curves of the two consumers and the contract curve in the Edgeworth box as well.