Consider a person who has a total of T units of time that the person can allocate to leisure (h), time spent consuming (kc), and working (whatever time (T – h – kc) is left after leisure and time spent consuming). This person is paid w per unit of time worked, and hence has an income of w(T – h – kc), which the person spends on consumption (c). The price of consumption is 1 and the person has no other income. If consumption is c, then the person must spend kc units of time doing the consuming, where k is a parameter. Utility is given by u(c, h) = ch.
a) Formulate the budget constraint for this person. Start with a constraint (of the form c = ...) with c on the left-hand side and income on the other
b) Find the demand function for consumption
c) Now suppose that k decreases. What happens to the optimal consumption? Does the saying "time is money" make sense in this context?