Optimization Problems Assignment | Homework For You

Solve each of the following optimization problems.

a. (4 pts.) A drug company sells an over-the-counter medication in a perfectly competitive market, where the price is p = 24. For each of the following cost functions, write down the company’s profit-maximization problem, and then find q*.

i. C(q) = 20

ii. C(q) = 304 +7

iii. C(q) = 104

iv. C(q) = 249

b. (4 pts.)

A firm chooses q to solve the profit-maximization problem below! max (q) = (10 – 9)- 24

i. Use the first-order condition to find a “candidate solution q*

ii. Use the second-order condition to verify that q* is the optimal choice.

iii. Find (9)

c. (4 pts.) A restaurant sells a mixture of sit-down meals (91) and take-out meals (92).

The market for each meal type is perfectly competitive, with prices P1 = 18 and P2 = 8, respectively, and the restaurant’s cost function is C (91.42) = 341 +42 The restaurant’s profit maximization problem is therefore max (91,92) = 1891 +892 – 34 – 4

i. Find 91, 92, and profits (91-99).

ii. Now suppose that a loud construction project reduces demand for sit-down meals in the area, so that p goes down. Assuming that p2 remains unchanged, what happens to the restaurant’s optimal quantity of take-out meals (92)? Get Economics homework help today