(Solved): 4. (20 POINTS) Afirm has the following cost function TC=4q2+4q+1600 1 (a) Find the average cost, AC ...

4. (20 POINTS) Afirm has the following cost function $$TC=4q^2+4q+1600$$ 1 (a) Find the average cost, $$AC$$. (b) Find the first order condition to minimize $$AC$$ and solve it to find the output value that minimizes AC. (c) Find the second order condition. Use the second order condition to show that you have a minimum. (d) Find the marginal cost, $$MC$$. (e) Show that $$MC=AC$$ when $$AC$$ is at its minimum value.. 5. (20 POINTS)The demand function for a good is: $$p=?q^2?3q+2697$$ (a) Find the total revenue function and the marginal revenue function (b) Find the first order condition for total revenue maximization and solve it for the stationary values. (c) Find the second order condition. Use the second order condition to examine each of the stationary values, Find the value of $$q$$ that maximizes $$TR$$. 6. (20 POINTS ) A monopolist has the following cost function: $$TC=\frac{1}{3}{q}^3?30q^2+600q+50$$ and faces the following demand curve for her product: $$p=60?0.5q$$ (a) Write the firm's total revenue, $$TR$$ in term of $$q$$ (b) Knowing that profit $$I$$ is the difference between $$TR$$ and $$TC$$, that is, $$\mathrm{II}=TR?TC$$ write profit in terms of $$q$$. (c) Calculate the first order condition for profit maximization and solve it for the stationary values. (d) Find the second order condition. Use the second order condition to examine each of the stationary values. Find the value of $$q$$ that maximizs the monopolist's profit.