Problem $2.$

Suppose the total benefit derived from a continuous decision, Q$,$ is B$($Q$)=20$Q $2$Q$2$ and the corresponding total cost is c$($Q$)=4+2$Q$2.$

a$)$ What is the marginal benefit function?

b$)$ What is the marginal cost function?

c$)$ What is the total benefit when Q $=2?$ Q $=10?$

d$)$ What is the marginal benefit when Q $=2?$ Q $=10?$

e$)$ What level of Q maximizes total benefit?

f$)$ What is the total cost when Q $=2?$ Q $=10?$

g$)$ What is the marginal cost when Q $=2?$ Q $=10?$

h$)$ What level of Q minimizes total cost?

i$)$ What level of Q maximizes net benefits?

j$)$ If marginal costs exceed marginal benefits, then

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$1.$ the firm ends up with a net loss.

$2.$ the firm's average costs exceed average benefits.

$3.$ the firm should decrease its production level.

$4.$ the firm should not change its production level.

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