Would the result that L is increasing in the wage change if we changed the utility function?

. Consider the consumption maximization problem of young John D. Rockefeller in 1855. He chooses to work hours L for wage w, since he is only a clerk in the merchant house of Hewitt & Tuttle. He must choose how to spend his income on two goods: clothing C and housing H, from which he derives utility via utility function U = C + H L where 2 (0; 1). Suppose that prices of one year of rent for housing and on yearís worth of clothing are r and p, respectively. 1. Solve for Rockefellerís optimal choice of L1; C1, and H1: 2. It is now 1872, and John D. Rockefeller has just Önished consolidating his competitors in oil reÖning to form Standard Oil. His hourly wage has now jumped to w. He still lives in the same small house in Cleveland as he did in 1855, though, since he still has time left on his lease. Solve for his optimal choice of C2 and L2, as well as his indirect utility as a function of model parameters. 3. At the end of the year, Rockefellerís lease is Önally up, so he can choose housing freely. Solve for his new choices of L3; C3; and H3, as well as his indirect utility. Show formally that the utility function is convex is the price of housing r. 2 4. In which of the time periods does Rockefeller work the most? The least? What is the intuition for these e§ects? Would the result that L is increasing in the wage change if we changed the utility function?

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