Consider the possibility of migration between cities. Suppose a region's workforce of 14 million is initially split equally between two cities,XandY. Further suppose that utility is measured in dollars (along the vertical axis) and that the urban utility curve peaks at 4 million workers in both cities. Beyond that point the slope is-$3 per million workers.

The initial equilibrium utility level is $60. Suppose cityXexperiences technological innovation that shifts its utility curve upward by $12. That is, at every population size, utility is $12 higher than before the technological change.

a. Draw a pair of utility curves, one forXand one forY, and label the positions immediately after the innovation (before any migration) asxfor cityXandyfor cityY. Use arrows along the curves to indicate the migration that follows.

b. In the new equilibrium, the utility level is $__and the population ofXis __million, while the population ofYis __ million.