Together with some anthropologists, you're studying a sparsely populated region of a rain forest, where 50 farmers live along a 50-mile-long stretch of river. Each farmer lives on a tract of land that occupies a 1-mile stretch of the river bank, so their tracts exactly divide up the 50 miles of river bank that they collectively cover. (The numbers are chosen to be simple and to make the story easy to describe.) The farmers all know each other, and after interviewing them, you've discovered that each farmer is friends with all the other farmers that live at most 20 miles from him or her, and is enemies with all the farmers that live more than 20 miles from him or her. You build the signed complete graph corresponding to this social network, and you wonder whether it satisfies the Structural Balance property. This is the question: is the network structurally balanced or not? Provide an explanation for your answer.

Suppose that fixed costs for a firm in the automobile industry (start-up costs of factories, capital equipment, and so on) are $5 billion and that variable costs are equal to $17,000 per finished automobile. because more firms increase competition in the market, the market price falls as more firms enter an automobile market, or specifically, , where n represents the number of firms in a market. assume that the initial size of the u.s. and the european automobile markets are 300 million and 533 million people, respectively.a. calculate the equilibrium number of firms in the u.s. and european automobile markets without trade.b. what is the equilibrium price of automobiles in the united states and europe if the automobile industry is closed to foreign trade? c. now suppose that the united states decides on free trade in automobiles with europe. the trade agreement with the europeans adds 533 million consumers to the automobile market, in addition to the 300 million in the united states. how many automobile firms will there be in the united states and europe combined? what will be the new equilibrium price of automobiles? d. why are prices in the united states different in (c) and (b)? are consumers better off with free trade? in what ways?