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Unformatted text preview: 76 CHAPTER 11 111. Suppose the firm’s labor demand curve is given by: w = 20  0.01 E , where w is the hourly wage and E is the level of employment. Suppose also that the union’s utility function is given by U = w × E . It is easy to show that the marginal utility of the wage for the union is E and the marginal utility of employment is w . What wage would a monopoly union demand? How many workers will be employed under the union contract? Utility maximization requires the absolute value of the slope of the indifference curve equal the absolute value of the slope of the labor demand curve. For the indifference curve, we have that E w MU MU w E = . The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization requires that 01 . = E w . Substituting for E with the labor demand function, the wage that maximizes utility must solve 01 . 100 000 , 2 = − w w , which implies that the union sets a wage of $10, at which price the firm hires 1,000 workers. 112. Suppose the union in problem 1 has a different utility function. In particular, its utility function is given by: U = ( w w * ) × E where w * is the competitive wage. The marginal utility of a wage increase is still E , but the marginal utility of employment is now w – w * . Suppose the competitive wage is $10 per hour. What wage would a monopoly union demand? How many workers will be employed under the union contract? Contrast your answers to those in problem 1. Can you explain why they are different? 77 Again equate the absolute value of the slope of the indifference curve to the absolute value of the slope of the labor demand curve: 01 . * = − = E w w MU MU w E . Setting w* = $10 and using the labor demand equation yields: 01 . 100 000 , 2 10 = − − w w . Thus, the union demands a wage of $15, at which price the firm hires 500 workers. In problem 1, the union maximized the total wage bill. In problem 2 the utility function depends on the difference between the union wage and the competitive wage. That is, the union maximizes its rent. Since the alternative employment pays $10, the union is willing to suffer a cut in employment in order to obtain a greater rent. 113. Using the model of monopoly unionism, present examples of economic or political activities that the union can pursue to manipulate the firm’s elasticity of labor demand. Relate your examples to Marshall’s rules of derived demand. Marshall’s rules state that the elasticity of labor demand is lower the 1. lower is the elasticity of substitution; 2. lower is the elasticity of demand for the output; 3. lower is labor’s share of total costs; and 4. lower is the supply elasticity of other factors of production....
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This note was uploaded on 08/06/2008 for the course ECON 324 taught by Professor Hamermesh during the Spring '05 term at University of Texas.
 Spring '05
 HAMERMESH
 Utility

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