# cost minimization & profit maximization

I guess that I am lost in some concepts…

As we learned from CFA, Economics –

(1) For a firm with N productive inputs, cost minimization requires that: MP(1)/P(1)=MP(2)/P(2)=… MP(n)/P(n). This equation tells us that, to minimize cost, the additional output per dollar spent to employ one additional unit of each input must be the same.

(2) For cost minimization and profit maximization , a firm must employ inputs in quantities such that: MRP(1)/P(1)=MRP(2)/P(2)=…=MRP(n)/P(n)=1. MRP is short for marginal revenue product, which equals to “MR*MC”.

My questions are –

1. When we say “cost minimization” in #(1), we are referring to “ average cost minimization”, aren’t we?
2. We also learned from Economics –
• a. The average cost is minimized when ATC=MC
• b. For any kind of market (expect for Oligopoly, which is a little bit complicated), the profit maximization is achieved when MR=MC
• How are we supposed to link these different pieces of knowledge together (#(1), #(2), #a, #b) to have a better understanding?

Yes, cost minimization refers to the lowest point of the average total cost curve (the same place where MC intersects ATC)

Cost minimization and profit maximization can occur at different quantities.

Minimizing costs does not imply maximizing profit.

Profit maximization is always always always at the quantity level where MC=MR

Under pure competition and monopolistic competition, profit will be maximized when average total cost is minimized (because the low barriers to entry allow new competitors to enter when ecomomic profits are being earned, and those new competitors will drive the price down to the level of minimum average total cost).

Under oligopoly and monopoly (without pure price discrimination), profit will be maximized when marginal cost equals marginal revenue, which isn’t necessarily (and, likely, isn’t at all) where average total cost is minimized.

I still have some difficulty in telling the differences and links between different concepts… Please find some follow-up questions below, as I really want to understand them clearly.

(1) We learned that the total consumer surplus and producer surplus can only be maximized at the equilibrium point (where MR = MC), but the rule does not necessarily apply to producer surplus (in isolation) or consumer surplus (in isolation). http://www.analystforum.com/forums/cfa-forums/cfa-level-i-forum/91319796 Please confirm.

(2) All the markets produce the equilibrium quantities when MR=MC. However, the equilibrium point is not necessarily the point where the suppliers’ profit (TR-TC) can be maximized, and it’s just the point where the whole market’s efficiency can be maximized. Am I right?

(3) Per the CFA Economics Textbook Reading #15, “for a firm with N productive inputs, cost minimization (not profit maximization) requires that: MP(1)/P(1)=MP(2)/P(2)=… MP(n)/P(n). “ We also learned that average cost is minimized when ATC=MC. In this way, can we say that for any markets, when the average costs are minimized, we will have both ATC=MC and MP(1)/P(1)=MP(2)/P(2)=… MP(n)/P(n)? If not, what are the differences between these two conditions?

(4) My original thought is totally with you - cost minimization and profit maximization can occur at different quantities, and minimizing costs does not imply maximizing profit. However, per the CFA Economics Textbook Reading #15, “for cost minimization and profit maximization , a firm must employ inputs in quantities such that: MRP(1)/P(1)=MRP(2)/P(2)=…=MRP(n)/P(n)=1.” It seems like employing inputs in quantities such that MRP(1)/P(1)=MRP(2)/P(2)=…=MRP(n)/P(n)=1 can help the individual firm to achieve both cost minimization and profit maximization at the same time? How are we supposed to understand the CFA textbook’s statement?

sorry I think I confused MB with MR.

Doubts are cleared now