Lecture 7

• Firms can have many objectives

  e.g., pay dividends, ensure job safety, have a positive impact on society
• If a firm goes bankrupt, it cannot achieve any objectives. Thus, firms need to make profits (or, at least, not incur losses – which is almost the same)
• Firms seek to maximize profit


  max π = TR - TC = P × Q - TC
• Many economists believe that firms' attempts to maximize profit are also in society's best interest, as long as external effects (e.g., pollution) are taken into account
• Production function


  Relationship between the quantities of the inputs used to produce a good and the quantity of output of that good
• The production function shows the relationship between the quantities of the inputs used to produce a good and the quantity of output of that good
• Short run


  Time frame in which there are fixed factors of production
• Long run


  Time frame in which all inputs can be adjusted and, thus, there are only variable factors of production
• In the analysis, capital is assumed to be a fixed factor of production in the short run
• Marginal product (syn. marginal return) of an input


  Change in output that arises when the quantity of a variable factor of production is increased by one unit
• Marginal product is the slope of the production function
• Marginal product follows a characteristic path when the quantity of the input rises: increasing, then diminishing, then potentially negative
• The optimal quantity of an input usually lies in the range of diminishing marginal product
• Q(K*, L)


  Production function
• Determining the optimal quantity of an input

  1. Identify if it is in the range of increasing, diminishing, or negative marginal product

  2. Marginal analysis: Compare additional revenue contribution and additional cost
• The optimal quantity of an input cannot lie in the range of negative marginal product
• In the range of increasing marginal product, the firm should use more of the input
• Value of the marginal product of labor


  P x MPL
• P x MPL > PL

  The firm should employ more workers
• Production function


  Inputs -> Technology -> Output
• Cost function


  Output -> Inputs -> Cost
• The cost of producing a certain quantity Q is given by the total cost function: TC(Q) = PK x K(Q) + PL x L(Q)
• Explicit costs


  Costs that represent an outlay of money by the firm
• Implicit costs


  Costs that do not represent an outlay of money by the firm
• Economic profit is total revenue minus total opportunity cost (explicit + implicit costs)
• Fixed costs (FC)


  Costs of fixed factors of production that do not depend on output
• Variable costs (VC)


  Costs of variable factors of production that do depend on output
• Total cost can be expressed as the sum of fixed and variable costs: TC(Q) = FC + VC(Q)
• Average fixed cost (AFC)


  Fixed cost per unit of output
• Marginal cost (MC)


  Increase in total cost from producing an additional unit of output
• Mathematically, marginal cost is the derivative of the total cost function: MC = dTC/dQ
• If the cost function is TC = 1500 + 5Q + 7Q^2, then FC = 1500, VC = 5Q + 7Q^2, AFC = 1500/Q, AVC = (5Q + 7Q^2)/Q
• Cost function


  TC = f(Q)
• Variable costs


  VC = 5Q + 7Q2. E.g., if Q = 10, VC is €750. If Q = 0, VC is €0.
• Average fixed cost


  AFC = 1500/Q. E.g., if Q = 10, AFC is €150.
• Average variable cost


  AVC = (5Q+7Q2)/Q = 5 + 7Q. E.g., if Q = 10, AVC is €75.
• Average total cost


  ATC = (1500+5Q+7Q2)/Q.
• Marginal cost


  MC = dTC/dQ = 5 + 14Q. E.g., if Q = 10, MC is €145.
• Sunk cost


  An expense that has already been committed and cannot be recovered. Since sunk costs cannot be recovered, they should be ignored in (rational) decision making.
• Fixed costs are sunk in the short run, because the firm cannot avoid them even if it temporarily shuts down (Q = 0). In the long run, fixed costs are not sunk, because the firm can avoid them by permanently exiting the market.