(Q1)

Giga Gadget (GG) is a monopoly in the market for gadgets. The demand function for gadgets is given by Q=12P/(square root A), where Q is the quantity of gadgets, P is the price of a gadget, and A is the advertising spending of GG. Production cost of GG is C(Q)=Q2 . Currently the advertising spending of GG is A=4 . Your job is to determine the optimal quantity of gadgets GG should produce. Write down the problem you need to solve, as an unconstrained optimization problem with only one variable, Q . (Assume that your job is only to find the optimal quantity, and you have no say in advertising decisions. That is, A is an exogenous variable for you.}

(Q2)

Write down the first order condition(s) of your problem.

(Q3)

Find the critical value of Q

(Q4)

Write down the Second Order Condition of your problem and check whether it is satisfied.

(Q5)

let's assume that once GG decided on quantity you calculated for Q3, it cannot be changed again.

Now suppose you are the head of the Advertising department. What is the optimal advertising spending of GG?

(Note: you will have to write down the problem, the FOC, find critical value, check SOC).