Question

In: Advanced Math

Maximize or minimize the following functions. Be sure to check your second-order conditions. (a) maxQ Π...

Maximize or minimize the following functions. Be sure to check your second-order conditions.

(a) maxQ Π = (20 − Q)Q − 4Q

(b) maxQ Π = (12 − Q)Q − 2Q2

(c) maxL Π = AL1/2 − 4L

(d) maxL Π = ALα − wL (where A and α are exogenous parameters and w is the wage rate on labor, L)

Expert Solution

(a) Given: . Differentiating we get:

As the second derivative is negative, maximum occurs at Q=8, and maximum value is 64.

(b) Given: . Differentiating we get:

As the second derivative is negative, maximum occurs at Q=2, and maximum value is 12.

(c) Given: . Differentiating we get:

As the second derivative is negative, maximum occurs at L=A²/64, and maximum value is A²/16.

(d) Given: . Differentiating we get:

If , then the second derivative is negative, and maximum occurs at , and maximum value is

.

However, if , then the second derivative is positive, and minimum occurs at , and minimum value is

Colby Messinger answered 3 years ago

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