Im having trouble with filling in a table for MC TC and AC given a cost funchtion
The cost functon is C(q)= 50+.5q
im given q 1 through 7
Ive aready calculated TC for q=1 TC=50.5 for q=2 TC=51 and so on
MC is where im having Trouble.
i know MC = dC(q)/dq or change in cost over change in q.
my teacher is telling me that the MC for q=2 IS 51/2=25.5 But wouldnt MC= .5/1 ( 51-50.5)/(2-1) I cant get him to respond to my emails and im panicing
Thanks
It would help if you told us what MC, TC and AC mean. Marginal, total and average cost? It looks like your C(q) is already a total cost.
The marginal cost is the cost of making one more. That is clearly 0.5 here.
I understand your confusion and frustration. Let me explain the steps to calculate the Marginal Cost (MC) in this scenario and address your concern.
The Marginal Cost (MC) represents the additional cost incurred by producing one more unit of output. To calculate the MC, you need to differentiate the cost function, C(q), with respect to q.
In your case, the cost function is C(q) = 50 + 0.5q.
To find the MC for q=2, you can calculate it using the derivative of the cost function. Let's go through the steps:
Step 1: Differentiate the cost function, C(q), with respect to q:
dC(q)/dq = 0 + 0.5 = 0.5
Step 2: Plug in the value of q=2 into the derivative:
MC (q=2) = dC(q)/dq = 0.5
The result, MC (q=2) = 0.5, indicates that producing the second unit of output incurs an additional cost of 0.5 units of currency.
Now, let's address your concern regarding the calculation your teacher provided, MC (q=2) = 51/2 = 25.5.
It seems there might be a misunderstanding or mistake in the calculation your teacher provided. Since the cost function does not change between q=2 and q=1 (as the cost function is linear), the MC should be constant for any value of q.
Therefore, MC = 0.5 (as calculated in the previous steps) is correct. The MC should not vary based on the specific value of q. Your calculation, MC = (51-50.5)/(2-1) = 0.5/1 = 0.5, is also correct.
If you are still uncertain or would like further clarification, I recommend reaching out to your teacher for clarification or seeking assistance from classmates or other resources available to you.
Remember, it's crucial to properly understand the concepts and formulas involved, so don't hesitate to seek further help when needed.