Labor supply and taxation. To interpret the evidence over extended periods of time on the link between the level of economic development and hours of work, some economists have used the following utility function for a representative agent u(c, h) = Ln(c-7) - av(h) where crepresents consumption (price equal to 1), h number of hours of work, a>0, and vis an increasing and concave function (for example, v(h) = 112), and > 0. We can see cas a "subsi- stence" term. This representative agent maximizes the utility function subject to the budget con- straint c= wl, where w is the wage rate. We want to know how labor supply changes when w increases

a. Since v () is concave, we have that for low values of w, the supply of labor increases in w, but after a sufficiently high value of wit will decrease

b. Depending on the magnitude of the value of a>0 we can have that hours of work is not a monotonic function in the wage (for some values of wit increases and for others it decreases)

c. Starting a low level of wages, there will be a period of decreasing hours of work as a function of w, but as w becomes very high, the number of hours will tend to stay almost constant

d. As with quasi-linear functions, labor supply here does not depend on wages as long as v is concave and increasing