1. Arnold takes special steroids to build muscle. The ounces of muscle built per

Question

1. Arnold takes special steroids to build muscle. The ounces of muscle built per year (Q) is:

Q = 5 + 61 S –S2

where   Q = the ounces of muscle built per year

                  S = ounces of steroid used

Steroids costs $300 per ounce. Arnold is paid by a promoter $20 for each ounce of muscle built. He also spends $400 per week in food.

Show your work/thought process:

What is the optimal amount of steroids (S) to purchase?

Given your answer in part a, what is the total amount of muscle that Arnold will build?

Explanation / Answer

Decision rule:

Marginal revenue product of labour = Marginal cost of labor

MRPL = MCL

First lets estimate MRPL

MRPL = Marginal revenue * MPL = $20 * (61-2S) = 1220- 40S

now

MCL = 300

So

1220-40s=300

40S = 920

S=23 is the optimal amount

Muscle built will be calculated by putting S=23 in equation

ounces of muscle built = 5+61*23-(23)^2 = 879

$

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