Calibrated CES Utility Functions: A Worked Example

As is the case for all interesting questions in economics, the only good answer to this problem is “It depends.”. It is fairly easy to see how this works on intuitive grounds. Thomas’s offer in Zürich does not pay him enough to live exactly the lifestyle that he enjoys in Ann Arbor, as he would need a 60% raise to cover rent and consumption. The elasticity of substitution is key. If it is high, he more willing substitutes consumption of goods and services for housing and thereby lowers his cost of living in Zürich. On the other hand, if the elasticity is low, he is “stuck in his ways”, and the move is a bad idea. Before thinking about how to solve this model I want to reflect on how we proceed. We are given information about Thomas’s choices in Ann Arbor. This information is essentially an observation of a benchmark equilibrium, consisting of the prevailing prices and quantities of goods demand. The benchmark equilibrium data together with assumptions about elasticities are used to evaluate Thomas’s choices after a discrete change in the economic environment. The steps involved in solving this little textbook model are identical to those typically employed in applied general equilibrium analysis. A general equilibrium model involves the simultaneous interaction of agents on both sides of each market, a benchmark equilibrium dataset describes all relevant economic transactions in a reference period, and calibrated functions are used to characterize choices by consumers and producers following a discrete change in the economic environment. Economic impacts are evaluated on the basis of observed choices and assumed elasticities. ∗I wish to thank Torben Mideksa and Todd Caldis for the comments and corrections they communicated based on on an earlier draft of this paper. I remain responsible for remaining errors and inconsistencies. Prices and income levels employed in this exposition were arbitrarily defined. Any resemblence to the actual circumstances of specific individuals is purely coincidental.