The Minimization of Total Costs of Production

• Invisible hand property 1: in a competitive industry, the total industry costs of production are minimized

• A firm in a competitive industry increases output until P = MC

  • Every firm in the same industry faces the same prices

• In a competitive market with N firms:

  • P = MC1 = MC2 = … = MCN

    • MC1 is the marginal cost of firm 1, MC2 is the marginal cost of firm 2, and so on

• Example:

  • You own two farms that you grow corn on

    • Farm 1 is on a hilly region where it is costly to seed and plow

    • Farm 2 is on ideal land for growing corn

  • You want to grow 200 bushels

    • The lowest-cost way to produce that amount is to produce all 200 bushels on Farm 2

    • The marginal costs of production on Farm 2 are lower than on Farm 1 for any level of output

    • What if you produced all 200 bushels on Farm 2 and no bushels on Farm 1?

    • How do you lower your total costs of production?

    • Instead of producing all 200 bushels on Farm 2, produce 197 on Farm 2 and 3 on Farm 1

    • When your produce on Farm 2, your costs of production decrease (this is the marginal cost of producing those last few bushels on Farm 1

• You should continue producing fewer bushels on Farm 2 and more on Farm 1 if the marginal costs of production of Farm 2 exceed those on Farm 1

  • produce less on Farm 2 and more on Farm 1 if MC2 > MC1

• You should switch production to from Farm 1 to Farm 2 if MC1 > MC2

• The way to minimize the total costs of production is to produce just so much on each farm so that the marginal costs of production are equalized (MC1 = MC2)

• If you own both farms, you can allocate production across the two farms so that the marginal costs of production are equal and so the total costs of production are minimized

• Another situation:

  • Farm 1 is in North Carolina and owned by Sandy and Farm 2 is in Iowa and owned by Pat

  • Sandy and Pat will never meet

  • Sandy and Pat sell their corn in the same market so each of them sees the same price of corn

  • How will they each maximize their profits?

    • Sandy will set P = MC1 and Pat will set P = MC2

    • This means that MC1 = MC2

    • If P = MC1 = MC2, then total costs of production are minimized

    • This means that a free market can mimic an ideal central planner

  • If Sandy and Pat only know their own market then they can still choose the output levels that minimize their own total costs

    • A central planner can’t allocate production correctly if it doesn’t know one of the other markets