2. Consider the static model of labor supply in which a representative consumer draws utility from consumption of an aggregated commodity, x, and disutility from supplying labour hours h. The consumer is endowed with H (fully divisible) time units at her disposal and has preferences given by u(x, h) with du/dx > 0 and au/ah <0. The agent has non-labor income y and earns wages w per unit of labor. As usual, we normalize the price of consumption to 1 so that the consumer's budget constraint is x= wh+y (or x+wz = wH+y, where z = H - h). Suppose the agent participates in the labour market (i.e. she supplies a positive number of hours). i) Take first order conditions of the agent's maximization problem and rearrange the expressions you get to equate the cost of leisure to the marginal rate of substitution between labor and consumption. ii) Totally differentiate the optimality condition above with respect to w to obtain an expression for h/aw as a function of h, w and the derivatives Ur, Urh = Uhx and Uhh. iii) Totally differentiate the optimality condition above with respect to y to obtain an expression for h/ay as a function of w and the derivatives Ur, Urh = Uhr and Uhh. iv) Use Slutsky equation to get an expression for ah/ow where he denotes the compensated (or Hicksian) labor supply. v) Compute the Marshallian and Hicksian elasticities using the expressions you ob- tained in in (b) and (d) respectively. (Hint: the denominators of both these elasticities coincide). vi) Explain which of these elasticities is larger and why.

Fig: 1