Question: Consider an economy that uses labor and capital to produce two goods, beer (x) and peanuts (y), subject to technologies that exhibit constant returns to scale. The marginal cost of a 12-ounce can of beer is $0.50. The marginal cost of a 12-ounce tin of peanuts is $1.00. Currently, the economy is producing 1 million 12-ounce cans of beer and 2 million 12-ounce tins of peanuts. The marginal rates of technical substitution of labor for capital in the beer and peanut industries are the same. Moreover, there are 1 million identical consumers in the economy, each with a marginal rate of substitution of beer for peanuts given by MRSx,y = 3y/x.
a) Sketch a graph of the economy’s production possibilities frontier. Identify the economy’s current output on this graph.
b) Does the existing allocation satisfy substitution efficiency? Why or why not?
c) Assuming that the current allocation [x = 1 million, y = 2 million] satisfies input efficiency, write down an equation for this economy's PPF. Then calculate the quantity of beer and peanuts that will satisfy the criterion of substitution efficiency. Show your work.