Please solve the question clearly providing a step by step explanation on how to do it. Do everything the question asks you to do. Do not miss anything out.

This problem set tells the story of three friends Alice, Bob, who are consumers, and C arol, who owns a firm. Alice, and Bob have preferences over two goods, Dumplings and Free time. Each of them have Ti available hours each day with i=A,B. Carol's firm produces dumplings using two inputs, L abour and K apital with respective prices w and r. Denote the market price of dumplings as p. 1. [12 points] Compute the market demand for dumplings in the region Alice and Bob live assuming they are the only inhabitants. Assume now that p=1 and TA=TB=16, how does the market demand change with a 1% increase in the wage w