Questions about advanced microeconomics attached below:

c. In the general equilibrium theory, why do consumer and producer interact each other to determine the equilibrium? using the Edgeworth box explain that voluntary exchange can improve the welfare of society! Explain the concept of Feasible Allocation, Pareto Optimal allocation, Core Allocation and Competitive Allocation! (7 points) d. A firm has the following production technology/ function: q(21, Z2) = azz + bZ where Z is the input of good-1, 2, is the input of good-2, w and weare the input price of good-land good-2 respectively and P is a price of product. Find the input demand function, the supply function and the profit function! (20 points)