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Unformatted text preview: York University Department of Economics Professor Ahmet Akyol AS/ECON 2400 - INTERMEDIATE MACROECONOMIC THEORY I Final Exam, Summer 2010. Duration 2 hours SOLUTIONS 1.-35 points- Consider the representative consumer with preferences over the consump- tion good, c , and leisure, l described by the utility function U ( c,l ) = ln c + ln l (1) She is endowed with h hours of time. She faces a wage rate, w , measured in consump- tion units per hour, in the labour market. She receives dividend income from the firm. In addition, she faces a labor income tax rate of t . In other words, for each w she earns, she pays tw to the government. The representative firm has a technology that converts labour hours to output: Y = zN d (2) where z is the exogenous total factor productivity, and N d is the hours of labour employed by the firm. The firm faces a wage rate w in the labor market. (a) Solve the firms profit maximization problem. Calculate the firms demand for labour, and the profit. Graph the firms labour demand function. The profit of the representative firm is given by: = zN d- wN d (3) = ( z- w ) N d . (4) Taking the derivative of this function with respect to N d and setting it equal to zero, we get: z- w = 0 , (5) which implies that the demand for labour N d is infinitely elastic at w = z , as shown in Figure 5.15 on page 155 in the textbook. (An alternative to using calculus is the discussion at the beginning of page 155 in the textbook.) Notice that when w = z , we have zero profits (i.e. = 0) for the firm. 1 (b) Set up the Lagrangian and solve for the demand of the consumption good, c , and the leisure, l ....
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- Summer '09