Unformatted text preview: t of Economics, ECO 204, 2013  20143 We know that
which means that we can calculate change in
applying the envelope theorem on: due to a small change in a parameter by [ )
)
(d) Derive an equation for ) in terms of the parameters. What does this equation tell us about the parameter From the FOCs we have: By the envelope theorem, we know this is: It tells us that as . For what value of is maximized? When: That is, with
when
unconstrained solution (i.e.
convince yourself of what’s going on here.
Question 3
Consider the function defined on (a) Solve the problem (a special case of Where the parameter [ from ). You should draw and ). Assume the parameters
) ) where ) ): . We solve inequality constrained problems by the “KuhnTucker method”: [ [ 5 University of Toronto, Department of Economics, ECO 204, 2013  20143 Start with [ this will be true when either and/or . Case A: Suppose
If this is the solution then we need to see if/when . From the FOC: Thus, so long as and the solution will be . Case B: Suppose
If this is the solution then we need to see if/when Thus, so long as the solution will be (b) All else equal, what is the change in
“case” separately. . From the FOC: and . due to a small change in Hint: You will have to consider each Case A: When You should think about the last result – why is it that a, suppose, one unit increase in also makes increase by 1 unit? Case B: Suppose 6 University of Toronto, Department of Economics, ECO 204, 2013  20143 (c) All else equal,...
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 Winter '13
 AJAZ
 Derivative, Convex function, Parametric equation, small change

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