If $\mathbf { u } ( t ) = \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + 4 t ^ { 4 } \mathbf { k }$

question 1

Short Answer

If $\mathbf { u } ( t ) = \mathbf { i } - 5 t ^ { 2 } \mathbf { j } + 4 t ^ { 4 } \mathbf { k }$ and $\mathbf { v } ( t ) = t \mathbf { i } - \cos t \mathbf { j } + \sin t \mathbf { k }$ , find $\frac { d } { d t } [ \mathbf { u } ( t ) \cdot \mathbf { v } ( t ) ]$ .

Understand the concept of economic growth as indicated by shifts in the production possibilities frontier.

Identify and explain the concept of opportunity cost and how it varies with different production choices.

Recognize the implications of producing at various points on or inside the production possibility frontier (PPF) in terms of efficiency, unemployment, and resource utilization.

Describe the impact of technological advancements on the production possibilities frontier.

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Definitions:

Efficient Level

Refers to the state where resources are allocated in a way that maximizes the net benefit to society, often achieved when marginal cost equals marginal benefit.

Competitive Output

The level of production that firms in a perfectly competitive market produce and sell at the market price, where marginal cost equals marginal revenue.

Competitive Price

A pricing strategy where the price of a product or service is set based on the prices charged by competitors.

Tax

A compulsory financial charge or levy imposed by a government on individuals or businesses to fund public expenditures.