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Ting (2009) - Organizational Capacity (view source)
Revision as of 19:15, 29 September 2020
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|Has article title=Organizational Capacity
|Has author=Ting
|Has year=2009
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*This page is referenced in [[BPP Field Exam Papers]]
The variables are:
*Policy set by the principal is <math>x_t \in X\,</math>, for <math>t=\{1,2\}\,</math>.
*Agents have ideal points of <math>x^A\,</math> and <math>x^P\,</math>.
*Agents can invest in capacity <math>c\,</math>, at a cost <math>k(c)\,</math> which is continuous, increasing and convex
In the first period, <math>P\,</math>'s best response to any <math>c\,</math> is <math>x^P\,</math>. <math>A\,</math> then maximizes utility by choosing <math>c_1\,</math> subject to this. However, as <math>z\,</math> is independent of <math>x\,</math> (and <math>y\,</math>), and as <math>A\,</math>'s utility is concave in <math>c\,</math>, but costs are convex, <math>A\,</math> chooses the interior maximum irrespective of <math>P\,</math>'s choice to maximize <math>z\,</math> and hence <math>u\,</math> (subject to the constraint that <math>x=x^p\,</math>). Any <math>y\,</math> can be choosen as it will have no effect.
===Specialized Capacity (SC)===
<math>A\,</math> doesn't want policy to move beyond <math>x_A\,</math>. In addition, <math>A\,</math> prefers policies closer to <math>x^A\,</math> than <math>x^P\,</math> and can prevent <math>P\,</math> from choosing <math>x^P\,</math> by investing in some <math>y \,</math> closer to <math>x^A\,</math>. Therefore, the equilibrium is:
:<math>x_1^* = x_2^* = y^* \mbox{ and } y^* \in \left ( x^P, x^A \right]\,</math>
**If <math>p\,</math> is low and the agent's utility is independent of policy, then implementation <math>z\,</math> strictly increases as with the distance between the agent's and the principal's ideal points.
**If <math>p\,</math> is high then an agent might be willing to shift the target policy away from <math>x^A\,</math>, and in doing so reduce the implementation needed to satisfy the principal.
===Endogenous Specialization===
Whether specialization would occur if it were endogenously choosen depends on both who is choosing, and if the prinicpal is choosing where the agent's ideal point is:
*The utility of the agent is strictly higher in SC than in GC
*The utility of the principal is strictly lower in SC than in GC if <math>x^A \ge x_c\,</math>.
===Delegation===
In this section the paper first considers what would happen if the principal gave the agent the authority to choose policy in the first period, and then considers whether the principal would endogenously choose to do so.
In the GC game:
*The principal's choices in period 2 remain unchanged.
*However, the agent now chooses his ideal point as the policy in period 1.
*Recall that the total utility is the sum over the two periods with the second period discounted.
**Therefore the agent invests more heavily in capacity and realized implementation is higher, as compared with the standard GC model, particularly if the discount factor is low so the second period gets little weighting.
*<math>\hat{c}_1^* > c_1^*\,</math> and <math>\hat{z}_1^* > z_1^*\,</math>.
In the SC game:
*There are three possibilities for the agent:
**Choose <math>x_1 = y\,</math> and the game is as before
**Choose <math>x_1 = x^A\,</math> and pay twice for the capacity investment that is only realized once (in period 2), but get some benefits from <math>x^A\,</math> in the first period.
**Choose <math>x_1 = x^A\,</math> and invest nothing, taking just the benefits from the first period - this can be particularly ideal if <math>\delta\,</math> is very low.
In choosing delegation endogenously:
*The payoffs from the two GC games (to the principal) are compared. Under "many functional assumptions" <math>P\,</math> is less likely to delegate as the distance between <math>x^A\,</math> and <math>x^P\,</math> diverge.
*In the SC game, delegating authority to the agent is weakly dominated.
