Problem: Two people are sharing an apartment in New York City, including all the food in the fridge. Currently, the fridge is ?lled with 30 sodas and 30 burgers. Assume person 1's utility from consuming burgers (b) and sodas (s) is u_{1}(b_{1}; s_{1}) = b_{1} * s_{1}, while the utility of person 2 is u_{2} = 3 * b_{2} + s_{2}.
a) Fixing the utility level of person 2 at u2, solve for the number of sodas person 2 has to drink as a function of the burgers he/she eats.
b) Using the results from part a), write down the resulting utility of person 1 as a function of the number of burgers b1 only, where the number of sodas is given by the requirement that person 2's utility remains at level u_{2}.
c) Solve part b) for the optimal number of burgers and sodas as a function of u_{2}.
d) Solve for the contract curve and plot it.
e) Suppose individual 1 has 10 burgers and 10 sodas. Is this a Pareto Optimum? If so argue why, if not provide a di?erent allocation that would make both individuals better off.