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Suppose that the total benefit and total cost from a continuous activity are, respectively, given by the following equations:
B(Q) = 100 + 36Q – 4Q^2 and C(Q) =80 + 12Q.
(Note: MB(Q) = 36 – 8Q and MC(Q) = 12.)
Use a negative sign (-) where appropriate.
a. Write out the equation for the net benefits.
b. What are the net benefits when Q = 1? Q = 5?
c. Write out the equation for the marginal net benefits.

Respuesta :

Answer:

a.  20 + 24Q - 4Q^2

b. 40 ; 40

c. 24 - 8Q

Explanation:

The equations are as follows:

a. The net benefit is

= Total benefits - Total costs

where,

Total benefits = B(Q) = 100 + 36Q – 4Q^2

Total costs = 80 + 12Q.

So, the net benefit is

=  100 + 36Q - 4Q^2 - 80 - 12Q

= 20 + 24Q - 4Q^2

b. When Q = 1,

N(Q) = 20 + 24 ×1  - 4×1^2

       = 40

When Q = 5,

N(Q) = 20 + 24 × 5  - 4×5^2

       = 40

c. MNB(Q) = dN(Q) ÷ dQ

                 = 24 - 8Q

We use the derivatives

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