Consider an economy with two consumers, A and B, and a single firm. 25% of the firm belongs to consumer A and 75% belongs to consumer B. The utility function of consumer A is given by _a() =(1/4).C⁴ The utility function of consumer B given by () = (1/8).C⁸ Where "C" is a consumer good desired by both consumers. The consumer good "C" is produced by the firm through the production function given by C = 2.(k)^(1/2), where "k" is the amount of capital used by the firm for produce "C". Consumer "A" has ka units of capital and consumer "B" has of kb capital units.

a) Assemble the Pareto problem of this economy. b) Does this economy satisfy Walras' Law? Show how you got your answer. c) Find the demands of consumers "A" and "B" for the consumer good. d) Find the firm's demand for capital. e) Find the firm's supply of consumer goods.

Now, find the competitive balance and indicate in the balance found: f) What is the equilibrium relative price (r/p) (where "r" is the price of capital and "p" is the price of the consumer good)? g) Allocation of consumer goods of individual "A" h) Allocation of consumer goods of individual "B"