Consider a pure exchange economy with two goods and two consumers. Let F denote food and C denote clothing. Lacy has the utility function U(F;C) = F1=3C2=3. Roy has the utility function V (F;C) = F2=3C1=3. Each consumer has an initial endowment consisting of 9 units of F and 9 units of C. Normalize the price of F to one. Let P denote the price of C. (a) Is the initial endowment a Pareto ecient allocation of F and C between the two con- sumers? Explain brie y. (b) What is each consumer's demand for F and C as a function of P? [Hint: the wealth of each consumer is 9 9P.] (c) What is the price of C in a competitive equilibrium? (d) What is the allocation of F and C between the two consumers in a competitive equilibrium