Suppose that people consume only two goods, cheese and bread

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Suppose that people consume only two goods, cheese and bread. They consume these two goods in a fixed ratio: One slice o

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Suppose that people consume only two goods, cheese and bread. They consume these two goods in a fixed ratio: One slice of bread is always eaten with one slice of cheese. Both cheese and bread are produced using only labor as an input. Their production functions are: Yb = AbLb, Yc = AcLc, where Yb is the quantity of bread, Yc is the quantity of cheese, Lb is the amount of labor devoted to producing bread, and Lc is the amount of labor devoted to producing cheese. The total quantity of labor in the economy, L, is constant, and Lb + Lc = L. In the year 2000, Ab = Ac = 1. But technological progress takes place at different speeds in the two industries. Specifically, Anb = 2%, and Anc = 1%, where these growth rates of technology are exogenous. a. What quantities of labor will be devoted to producing bread and cheese in 2000? b. What will the growth rate of total output be in 2000? (Hint: Because the quantity of bread produced will always be the same as the quantity of cheese produced, the growth rate of total output equals the growth rate of the quantity of bread produced, which equals the growth rate of the quantity of cheese produced.) c. Draw a graph showing the growth rate of output from the year 2000 onward. Show whether growth rises, falls, or stays constant, and explain why it does so. What will the growth rate of output be in the long run?

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