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?