WeekofMar30

WeekofMar30 - l ² ³=² with ²> and ³> If q = q>...

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W3211 Spring 2009 Professor Vogel Recitation Week of 03/30/09 1. Suppose that the rental rate of capital and the wage rate of labor facing OsCorp is a function of the amount of capital and the amount of labor Oscorp hires. In particular, let the rental rate for capital as a function of capital hired be v ( k ) and let the wage rate for labor as a function of labor hired be w ( l ) . (a) Draw an isocost line if v 0 ( k ) = 0 and w 0 ( l ) = 0 (i.e. v ( k ) = v > 0 and w ( l ) = w > 0 ) (b) Draw an isocost line if v 0 ( k ) > 0 and w 0 ( l ) = 0 (c) Draw an isocost line if v 0 ( k ) = 0 and w 0 ( l ) > 0 (d) Draw an isocost line if v 0 ( k ) > 0 and w 0 ( l ) > 0 (e) Finally, when might you think it is reasonable for v 0 ( k ) > 0 and when do you think it might be reasonable for v 0 ( k ) = 0 ? 2. Suppose that the production function is q ( l;k ) = k l ± , with &;± > 0 . If q = q 0 > 0 and the rental rates for capital and labor are v > 0 and w > 0 respectively, solve for the derived demand for l and k . 3. Suppose that the production function is q ( l;k ) = ( k ²
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Unformatted text preview: + l ² ) ³=² , with ² > and ³ > . If q = q > and the rental rates for capital and labor are v > and w > respectively, solve for the derived demand for l and k . 4. Suppose that the total cost is C ( q ) = 10 + 2 q & 1 2 q 2 + 4 q 3 (a) Solve for marginal cost, MC ( q ) (b) Solve for average cost, AC ( q ) (c) Graph C ( q ) ;MC ( q ) , and AC ( q ) 5. Suppose that the price of hang-gliders for villians is p > . Oscorp&s production function for hang-gliders for villians is q ( l;k ) = ( l & k 1 & & ) ³ , where & 2 (0 ; 1) and ³ 2 (0 ; 1) . The cost per unit of l is w > and the cost per unit of k is v > . (a) Solve for Oscorp&s demand for l and k , and call these l ± and k ± . (b) How does l ± vary with i. p ii. & iii. w...
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