This problem set tells the story of three friends Alice, Bob, who are con- sumers, and Carol, who owns a rm. 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. Carols rm produces dumplings using two inputs, Labour and Kapital with respective prices w and r: Denote the market price of dumplings as p: 6. [14 points] Assuming p = 3 and that w can take any value, what is the total labour supply in the region Alice and Bob live? What is Carols labour demand? Use the two to nd the expression determining the equi- librium wage in the local labour market (do not solve this expression as it would be too complicated). Use all the above and your economic reason- ing to, without doing any further calculation, discuss how an increase in the price of capital r will aect the welfare of these three friends. 7. [16 points] Assume now that capital is no longer xed. Use the Lagrange method to calculate Carols long-run total, average and marginal cost functions when r = 2 and w can take any value. Find her output supply as a function of p and w. Will Carols rm exit the market for some dumpling price p? If she doesnt exit, what will be her labour demand assuming p = 3? Finally, use again your economic reasoning but no additional calculations to discuss how the transition from the short to the long run will aect the welfare of the three friends.