Given $\mathbf { r } ( t ) = 7 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$

question 13

Essay

Given $\mathbf { r } ( t ) = 7 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$ .
a. Find $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ .
b. Sketch the curve defined by $\mathbf { r }$ and the vectors $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { t } ( - 1 )$ on the same set of axes.

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Definitions:

Moral Hazard

A situation in economics where one party is more likely to take risks because the costs that could result will not be borne by the party taking the risk.

Unobservable Characteristics

Traits or attributes of an entity that cannot be directly measured or seen but influence outcomes.

Adverse Selection

Adverse selection is a situation in which an asymmetry of information between buyers and sellers results in the failure to facilitate optimal market outcomes, often seen in insurance markets where those most likely to claim insurance are also the most likely to purchase it.

Moral Hazard

The tendency of a person or entity to take risks because the negative consequences of the risk will be borne by another party.