Homework Help Forum: Economics/Algebra

Posted by cb on Sunday, October 25, 2009 at 2:07pm.

Can someone help with the following: I know how to get the MC and AC; however I'm not sure on the algabraic part. Given the following short-run total cost function, answer the following questions. TC = 3q2 + 5q + 300 a. Find the marginal and average cost functions. b. Show that AC is at its minimum when q = 10 and that MC = AC at this output.

• Economics/Algebra - MathMate, Sunday, October 25, 2009 at 3:41pm

  A. Given: tc(q)= 3q²+5q+300 The marginal cost is what would cost an extra item (quantity) for a given quantity q. It is obtained by finding the derivative of tc(q) with respect to q: marginal cost, mc(q) = tc'(q) = d(tc(q))/dq = 6q+5 Average cost is the total cost of q items averaged over q, i.e. divided by q. average cost, ac(q) = tc(q)/q B. mc(10) = 6*10+5 = 65 ac(10) = (3*(10)² + 5*(10) + 300 )/10 = 65 Thus mc(10) = ac(10)

  
  

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