I did mean Q
Suppose you are the manager of a small chemical company operating in a competitive market. Your cost of production can be expressed as C = 100 + Q2, where Q is the level of output and C is total cost.
a. Is this a short-run cost function?
b. What is the marginal cost function?
c. What is the level of total fixed cost?
d. If the price of chemicals is $60, what quantity of chemicals should be produced to maximize profit?
e. What will be the level of profits?
Economics/Math - economyst, Wednesday, November 4, 2009 at 9:15am
Take a shot, what do you think?
query. By Q2, do you really mean Q^2?
2 answers
I did mean Q^2. Again, my issue is that I don't know how to calculate the output to maximize profits. I appreciate any help. Thank you.
a) could be short run, could be long run. Not enough information to tell.
b) MC is the first derivitive of the Total Cost. So, MC = 2*Q
c) Fixed cost are cost that the firm incurs, regardless of the level of production. In your problem, FC=100.
d) maximize where MC=MR. Here 2*Q=60. Solve for Q. (I get Q=30)
e) profit is total revenue minus total costs. TR=30*60 = 1800. TC=100+(30)^2 = 1000. Ergo, total profit is $800.
b) MC is the first derivitive of the Total Cost. So, MC = 2*Q
c) Fixed cost are cost that the firm incurs, regardless of the level of production. In your problem, FC=100.
d) maximize where MC=MR. Here 2*Q=60. Solve for Q. (I get Q=30)
e) profit is total revenue minus total costs. TR=30*60 = 1800. TC=100+(30)^2 = 1000. Ergo, total profit is $800.
1 answer