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IEonsitfler a model where a labor union has monopoly on the sale of labor. Its utility function reects the Fact that it cares about wages and employment levels and does not mind trading oFF higher wages For lower levels of employment. The monopoly's utility function is given by: U=WL, where W is the wage rate and L is the labor hours. Suppose that the utility-maximizing union sells Labor hours, L to a prot maximizing competitive rm whose labor demand is given by: l. 1.1. In this model, explain the sequence of decision puking by the union and the rm' 1.11 the determination of wages and employment 1.2. Show the utility maximization problem of the UNION and Fold the optimal level of wages and employment. 1.3. Now suppose that in an alternative model, the rm and the union simultaneously bargain over wages and employment and agrees on a wage and employment level. (I) Is this agreement \"efcient\" from a production point of view? (2} Is this agreement Pareto optimal? (3) re the agreed upon wages less or greater than the marginal product of labor of the worker