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This problem set tells the story of four friends Alice, Bob, Carol, who are consumers, and Fanny, who owns a firm. Alice, Bob and Carol have preferences over two goods, Dumplings and Eggs. Fanny's firm produces eggs. In what follows you should use \( m_{i} \) for \( i=A, B, C \) to denote the income of each of the three consumers and \( p_{j} \) for \( j=D, E \) to denote the prices of each of the two goods. Similarly, \( d_{i} \) and \( e_{i} \) denote the consumption of dumplings and eggs respectively by consumer \( i=A, B, C \). Fanny uses two (non-fixed) inputs, called 1 and 2, to produce eggs; the price of these inputs is denoted by \( w_{j} \) for \( j=1,2 \). 7. Assume that Alice, Bob and Carol have the same budget \( m_{A}=m_{B}= \) \( m_{C}=50 \) and that \( p_{D}=1 \). Use your responses to (1), (2) and (5) to find the market (aggregate) demand for eggs (if you failed to obtained any of these demands, compute the market demand with the individual demands you found rather than leaving this question blank). Use the market demand for eggs you just found and Fanny's supply function of eggs you found in (6) to find the equilibrium in the eggs market. Write the integral across prices that measures the total consumer surplus in equilibrium (you do not need to solve it). What is the producer surplus in equilibrium?

We are given that N + 1 eggs are as good as 1 dumpling, or with N = 4, (N + 1) = (4 + 1) = 5 eggs are as good as 1 dumpling, so we can