An economy has a total amount of 100 units of a good to allocate between two persons-Amanda and Britney. Amanda's utility level is given by UA = QA, where QA is the number of units she consumes of the good. On the other hand Britney's utility level is given by the function UB = 10V QB where QB is the number of units of the good she consumes.
a) If all of the society's resources are used to make Britney happy, what are the utility levels for Amanda and Britney? If, instead, all the units are used to make Amanda, what are the utility levels for each one of them?
b) Derive the equation for the utilities possibility curve for this two man economy. That is, derive an equation that expresses Britney's utility as a function (measured on the vertical axis) of Amanda's utility measured on the horizontal axis. Including end points plot several points on the graph.
c) Suppose a politician promises a program that will give Amanda and Britney 70 units of utility for each. Should they believe this promise? Why?
d) Suppose resources in the economy are distributed so that Amanda has a utility level of 64 units and Britney has utility level of 50 units. Is this distribution of utility (Pareto Optimal) efficient? If not, why?