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 _b() = (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 k_a units of capital and consumer "B" has of k_b capital units.

a) Assemble the Pareto problem of this economy.