Consider the following economy: Consumers maximize their utility U(C, l) = (l C)^0.

6. Consider the following economy: • Consumers maximize their utility U(C, l) = (l ⋅ C)^0.5 subject to the budget constraint Y = w(ℎ − l) + a, where l is leisure, C is consumption, w is the real wage, h is the given amount of time and a is the inherited wealth. All these variables are 'real' as opposed to 'nominal.' (Notice that the relative price of consumption is equal to 1.) Producers produce consumption goods by using labor (N) only, according to the production function y= ln(N + 1) and maximizes their profits π = ln(N + 1) − wN. • For simplicity, we ignore the government, so there are no taxes. a. Verify whether the following statement is true or false: For consumers, substitution effect always dominates the income effect, in other words, the labor supply curve is upward sloping. And the law of demand applies to labor demand. (Hint: Derive the labor supply and demand curves as a function of real wage and the available time.) b. If the amount of available time, h, is 24 (hours) and = 11, find the equilibrium real wage, employment level, and consumption of this economy. You can ignore the producers' profits, if any, to answer these questions. Simply assume that the profits will be saved in the firms for some future uses (no dividend income for households)