Question

Suppose the total benefit derived from a given decision, q, is b(q) = 20q – 2q2 and the corresponding total cost is c(q) = 4 + 2q2, so that mb(q) = 20 – 4q and mc(q) = 4q. instruction: use a negative sign (-) where appropriate.
a. what is total benefit when q = 2? q = 10? when q = 2: 32 when q = 10: 150
b. what is marginal benefit when q = 2? q = 10? when q = 2: 12 when q = 10:
c. what level of q maximizes total benefit? 5
d. what is total cost when q = 2? q = 10? when q = 2: 12 when q = 10:
e. what is marginal cost when q = 2? q = 10? when q = 2: 8 when q = 10: f. what level of q minimizes total cost? 0 g. what level of q maximizes net benefits? 2.5 check my work

Answer 1

Answer:

$[tex]Total benefit = b(q) = 20q – 2q^{2} Total cost is c(q) = 4 + 2q^{2} , Marginal benefit = mb(q) = 20 – 4q Marginal Cost = mc(q) = 4q.$

a. $when q = 2 Total Benefit = 20q – 2q^{2} = 20(2) – 2(2)^{2} = 40 – 8 =32 When q = 10 Total Benefit = 20q – 2q^{2} = 20(10) – 2(10)^{2} = 200 – 200 = 0$  b. When q = 2 Marginal Benefit = 20 – 4q = 20 - 4(2) = 20 – 8 = 12  When q = 10 Marginal benefit = 20 – 4q = 20 – 4(10) = 20 – 40 = -20[/tex]

c. Total Benefits are maximised when MB=0

$MB(q)= 20 - 4q = 0 = 20 = 4q = q= 5$

Therefore, q=5 maximizes total benefits.

d. Total cost is given by $c(q) = 4 + 2q^{2}$

When q=2,

$TC =c(q) = 4 + 2q^{2} = 4 + 2 (2)^{2} = 4 + 8 =12$

When q= 10

$TC =c(q) = 4 + 2q^{2} = 4 + 2 (10)^{2} = 4 + 200=204$

e. $Marginal cost = MC(q) = 4q At q=4 MC(q) = 4(4) = 16 At q= 10 MC(q) = 4(10)=40$

f. Total cost is minimized at Q=0.  At any other level Total cost is increasing for every value of Q.

g. Net benefits are maximized when $NMB(Q) = MB(Q)-MC(Q) = 0 = 20 – 4Q – 4Q = 0 = 20 - 8Q =0 =20=8Q =Q=2.5$

So, q=2.5 maximizes net benefits.