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Unformatted text preview: Number 3 Given a Cobb- douglas production function, we calculate the change given by a unit change for labor and capital. Solving for the derivatives of the Cobb- Douglas wrt to each variable D @ Q = 4 * k ^ H 0.5 L * l ^ H 0.5 L , k D 2.` l 0.5` k 0.5` Marginal product of capital D @ Q = 4 * k ^ H 0.5 L * l ^ H 0.5 L , l D 2.` k 0.5` l 0.5` Marginal product of labor k = 50 l = 600 50 600 Plugging in the values of l & k to their Marginal Products, we get : 2.` l 0.5` k 0.5` 6.928203230275509` H The effect of 1 unit change in K L 2.` k 0.5` l 0.5` Adding the changes to get the total change 6.928203230275509 + 0.5773502691896258 7.505553499465135`-- fi The total effect of a 1 unit change i capital H k L and labor H l L Number 4 Solving for the monopoly ' s optimal Q to maximize production . We get the MR and MC. By solving : In:= D @H 1400- 7.5 * Q L * Q, Q D 1400- 15.` Q Marginal Revenue In:= D @ Q ^ 3- 6 * Q ^ 2 + 140 * Q + 750, Q D 140- 12 Q + 3 Q 2 Marginal Cost Equating MR & MC which is the condition for maximization in a monopoly,...
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- Spring '11