Solve the Problem $1 + 9 r + 7 r ^ { 2 } + 9 r ^ { 3 } + r ^ { 4 } + 9 r ^ { 5 } + 7 r ^ { 6 } + 9 a ^ { 7 } + r ^ { 8 } \ldots$

question 21

Multiple Choice

Solve the problem.
-Find the sum of the infinite series $1 + 9 r + 7 r ^ { 2 } + 9 r ^ { 3 } + r ^ { 4 } + 9 r ^ { 5 } + 7 r ^ { 6 } + 9 a ^ { 7 } + r ^ { 8 } \ldots$ for those values of $r$ for which it converges.

• A) \(\frac { 9 r ^ { 3 } + 7 r ^ { 2 } + 9 r + 7 } { 1 - r ^ { 4 } }\)
• B) \(\frac { 7 r ^ { 3 } + 9 r ^ { 2 } + 7 r + 1 } { 1 - r ^ { 4 } }\)
• C) \(\frac { 7 r ^ { 3 } + 9 r ^ { 2 } + 7 r + 9 } { 1 - r ^ { 4 } }\)
• D) \(\frac { 9 r ^ { 3 } + 7 r ^ { 2 } + 9 r + 1 } { 1 - r ^ { 4 } }\)

Understand the conditions for long-run equilibrium in purely competitive markets and the achievement of normal economic profits.

Recognize the allocation efficiency in pure competition where production occurs at the output level where P = MC.

Comprehend the differences between short-run and long-run supply curves in purely competitive industries.

Describe the effect of new firms entering or existing firms leaving a purely competitive market on market supply and equilibrium.

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Definitions:

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Additional amount above the par value that an investor must pay to call in a callable bond before its maturity date.

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Refers to the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.