Consider the profit maximisation problem from the previous problem set, and

continue to $$assume that

p$=16$r$=2$f$($K$,$L$)=$squareKL$$l$($w$)=$nw

where n$$is $$a positive constant.

$1.$Using a mathematical argument, show this critical point is $$not

a saddle point

$2.$using a mathematica argument, catgorise it$$as $$a local maximum or $$local minimum

$3.$using a mathematical argument, categorise it$$as $$a local maximum or l$$ocal minimum

now suppose the company must adhere to $$a fairness policy that aims to $$ensuer workers are paid adequately, the ratio of $$total factory rental payments againts total wage payments cannot exceed beta sign, where beta sgn$$is $$a positive constant. Everything else remains the same.

a$.$formally write the firm's constrained profit maximization problem

b$.$write the lagrangian and first order conditions

c$.$identifit the cases from complementary slackness, along with tehir associated equation and check

d$.$find the firm's wage offer curve as $$a function of $$the policy strictness beta sign

for the rest of $$the

e$.$does the offerered wage increase or $$decrease as $$the policy is $$lossened$?$ provide a mathematical argument

f$.$given your previous answer, is $$the policy effective?