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This problem set tells the story of three friends Alice, Bob, who are consumers, and Carol, who owns a firm. Alice, and Bob have preferences over two goods, Dumplings and F ree time. Each of them have Ti available hours each day with i=A,B. Carol's firm produces dumplings using two inputs, Labour and K apital with respective prices w and r. Denote the market price of dumplings as p. 4. [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 ? 5. [12 points] Carol's firm is the only supplier of dumplings in the region but she wants to be nice to her two friends, so she behaves as a perfectly competitive (i.e. price taker) firm in both the input and output market. Her firm has the following technology: f(L,K)=(L)31(K)21. Assume that r=2,w can take any value and that capital is fixed at K=8. What is Carol's short-run conditional labour demand? Calculate her total, average and marginal short-run cost functions. Suppose the price for dumplings is p=1, will Carol shut down her firm? And if p=2 ? Graph her marginal, average and average variable cost curves for the case w=1. [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 Carol's labour demand? Use the two to find the expression determining the equilibrium wage in the local labour market (do not solve this expression as it would be too complicated). Use all the above and your economic reasoning to, without doing any further calculation, discuss how an increase in the price of capital r will affect the welfare of these three friends. This problem set tells the story of three friends Alice, Bob, who are consumers, and Carol, who owns a firm. Alice, and Bob have preferences over two goods, Dumplings and F ree time. Each of them have Ti available hours each day with i=A,B. Carol's firm produces dumplings using two inputs, Labour and K apital with respective prices w and r. Denote the market price of dumplings as p. 4. [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 ? 5. [12 points] Carol's firm is the only supplier of dumplings in the region but she wants to be nice to her two friends, so she behaves as a perfectly competitive (i.e. price taker) firm in both the input and output market. Her firm has the following technology: f(L,K)=(L)31(K)21. Assume that r=2,w can take any value and that capital is fixed at K=8. What is Carol's short-run conditional labour demand? Calculate her total, average and marginal short-run cost functions. Suppose the price for dumplings is p=1, will Carol shut down her firm? And if p=2 ? Graph her marginal, average and average variable cost curves for the case w=1. [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 Carol's labour demand? Use the two to find the expression determining the equilibrium wage in the local labour market (do not solve this expression as it would be too complicated). Use all the above and your economic reasoning to, without doing any further calculation, discuss how an increase in the price of capital r will affect the welfare of these three friends