asap dealine 1 hour

Problem 4 (Exchange Economy) The inhabitants of two villages lying on the opposite shores of a long lake care about almonds and beans. Inhabitants of village N (North) all have preferences that can be represented by the utility function N N N 1 N u (xa Ix ) 2 b = slogxa +logxff. Inhabitants of village S (South) all have preferences that can be represented by us(x,x) = (510ng + If. Here, x? denotes the consumption of commodity i (= a, b) in village h (= N, S). The number of inhabitants in each village is the same and normalized to 1. Let the price of almonds be given by p, and the price of beans be normalized to 1. Also, assume that inhabitants in each village derive their income from their initial endowments of almonds and beans. In village N, all inhabitants own eff kilos of almonds and 23' kilos of beans. In village S the inhabitants each own a: of almonds and eg of beans. Both villages lie on different sides of a big lake. A ferry for carrying merchandise and passengers from one village to the other is ordered but not yet in place. For the moment, trade between the villages is therefore not yet possible. (a) For each village h = N, S, compute the excess demand functions for almonds and beans. (b) Derive the equilibrium price of almonds pf; in each village. Interpret your result. From now on, suppose the ferry is in place, and thus there exists a common market where trade of almonds and beans occurs. (c) Derive the excess demand functions for almonds and beans in the common market. (d) Check that Walras' law holds. (e) Derive the equilibrium price for almonds in the common market, p: (interpret your result) and check that it also clears the common market for beans. For the remaining problems, we assume that eff = 20, e? = 10, cf = 10 and 33 = 10. (f) What is the equilibrium price for almonds in each village before trade