ajaz_204_2013_2014_HW_2

# D derive an equation for due to a small change in due

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Unformatted text preview: ue to a small change in due to a small change in Hint: You will have to consider each Hint: You will have to consider each “case” in terms of the parameters. What does this equation tell us about the parameter 2 University of Toronto, Department of Economics, ECO 204, 2013 - 20143 ANSWERS Question 1 Consider the function defined on [ ). Assume the parameters (a) Is the function concave, convex, concave and convex, or neither concave nor convex? Since we see that “straight line” portions). which means that this equation is strictly concave (i.e. decelerating and does not have (b) Solve the following optimization problem (a special case of )): Given this function is strictly concave we know that if we find a stationary point then it must be the only solution to this problem and that it will be an interior solution. Now: We have found a stationary point and know that this is the solution. (c) All else equal, what is the change in due to a small change in (d) All else equal, what is the change in due to a small change in By the envelope theorem: 3 University of Toronto, Department of Economics, ECO 204, 2013 - 20143 ) Question 2 Consider the function defined on (a) Solve the problem (a special case of Where the parameter [ ( ) ( ) ). Assume the parameters ) ) where ) ): . We solve equality constrained problems by the “Lagrangian method”: [ [ (b) All else equal, what is the change in due to a small change in You should think about the last result – why is it that a, suppose, one unit increase in also makes (c) All else equal, what is the change in increase by 1 unit? due to a small change in 4 University of Toronto, Departmen...
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## This homework help was uploaded on 02/15/2014 for the course E 204 taught by Professor Ajaz during the Winter '13 term at University of Toronto.

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