This question deals with an economy in which the issue of production efficiency does not arise, perhaps because there is only one factor of production. The requirement that a Pareto optimal allocation be production efficient is then replaced with the simpler requirement that a combination of goods lying on the production possibility frontier be produced.
Consider an economy inhabited by George and Harriet, whose utility functions are
The total quantities of ale and bread that can be produced by the economy are a and b, and they are constrained by the production function
There are infinitely many Pareto optimal allocations. In one of them, Harriet's utility is 8.
a) An allocation in this economy is described by a list of four variables. What are these variables?
b) What four equations describe the Pareto optimal allocation in which Harriet's utility is 8?
c) Find this Pareto optimal allocation.