Question

A contrast is designed by these equations: MB = 1000- 10L MC = 76 + 4L2...

A contrast is designed by these equations: MB = 1000- 10L MC = 76 + 4L2 Calculate the optimal contract length. Can you show me how to calculate the optimal length step by step not sure how the answer is 14

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Answer #1

Optimal contract length is that length corresponding to which MB equals MC.

MB = 1000 - 10L

MC = 76 + 4L2

Equating MB and MC

1000 - 10L = 76 + 4L2

1000 - 10L - 76 - 4L2 = 0

-4L2 - 10L + 924 = 0

4L2 + 10L - 924 = 0

Dividing the both sides by 2

2L2 + 5L - 462 = 0

Soving above quadratic equation -

2L2 + 33L - 28L - 462 = 0

L(2L + 33) - 14(2L + 33) = 0

(2L + 33) (L - 14) = 0

Putting each equal to 0 -

2L + 33 = 0

L = -33/2

L - 14 = 0

L = 14

The value of contract can not be in negative.

So,

The optimal length of contract is 14.

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