Expected Utility Function and Cobb-Douglas Production Function

Parameters involved

Suppose a representative household’s expected utility function is given by:



The utility function depends on the expected discounted sum of consumption and leisure, and is hours worked in “market activities”. The expectations operator is E, and the discount rate is which specifies the degree of patience. A high value means more patience for consumption and leisure. The parameter is  and denotes the value of the non-market productive time per household. It could be the relative value of the time spent working at home. Typically, it is the relative value of leisure. The production using this time is untaxed.

There is a stand-in firm with a Cobb-Douglas production function