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
![2038_31b4c236-590e-4a05-bd3c-6ff9b8f337be.png](https://secure.tutorsglobe.com/CMSImages/2038_31b4c236-590e-4a05-bd3c-6ff9b8f337be.png)
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
![976_2ba6236c-2165-44bd-9b8a-ebff7dfc384b.png](https://secure.tutorsglobe.com/CMSImages/976_2ba6236c-2165-44bd-9b8a-ebff7dfc384b.png)
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.