Lecture 8

• Economists care about "typical" cost curves because a firm's supply decision depends on its cost structure, and market supply depends on the cost structures of all firms
• When economists analyze the market for a typical (but unspecified) product, they often call it a "widget"
• Typical cost curves


  Have three characteristic properties:

  1. Marginal cost eventually rises with quantity of output

  2. Average total cost curve is U-shaped

  3. Marginal cost curve intersects average total cost curve at its minimum
• When marginal cost is lower than average cost


  Average cost is declining
• When marginal cost is higher than average cost


  Average cost is rising
• Average (arithmetic mean)


  Sum of all individual values divided by the number of values
• When an additional individual value (marginal value) is higher (lower) than the average of the previous values, the average rises (falls)
• Isoquant


  Shows the possible combinations of inputs that yield the same quantity of output for a firm
• Isoquant map


  The set of isoquants, visualizing the (long-run) production function

  
• Economists have estimated the (Cobb-Douglas) production function for Crocs as Q = 21.5K^0.5 L^0.85

  
• Marginal rate of technical substitution (MRTS)


  The rate at which a firm can substitute one input for another input while maintaining the same level of output
• MRTS


  Determined by the ratio of the marginal products of the two inputs: MRTS = MPL/MPK
• The MRTS is not constant but depends on the quantities of the inputs, except when inputs are perfect substitutes or complements
• MPK (marginal product of capital)


  If L is reduced by one unit, the firm needs MPL/MPK additional units of K to compensate
• The theory of the firm
• Marginal rate of technical substitution (MRTS)


  How a firm can switch between inputs
• Illustration


  1. Suppose having one worker less would decrease output by six units (MPL = 6), and having one robot more would increase output by three units (MPK = 3). If the firm lets one worker go, how many additional robots does it need to compensate if it wants to produce the same quantity of output as before?

  2. The firm needs MPL/MPK = 6/3 = 2 additional robots. Thus, MRTS = 2.
• Marginal product changes when more or less of an input is used. Thus, the MRTS is not constant but depends on the quantities of the inputs. (Exception: When inputs are perfect substitutes or complements.)
• The optimal quantity of an input usually lies in the range of diminishing marginal product
• When more of an input is used, its marginal product and, therefore, its capacity to substitute for other inputs falls. In other words: The MRTS is diminishing.
• Isoquant


  A curve that shows the different combinations of inputs that can produce the same quantity of output
• Isocost line


  A line that shows the different combinations of inputs that result in the same total cost for a firm
• The ratio of the input prices is the slope of the isocost line
• The intercept of an isocost line is TC/PK. The slope is -PL/PK.
• The absolute value of the slope of an isocost line (PL/PK) is the ratio of the input prices (or "relative cost" of the two inputs)
• Along an isocost line, total cost is constant. Between isocost lines, total cost varies.
• Least-cost (i.e., optimal) input combination


  The combination of inputs that allows the firm to produce the desired quantity of output at the lowest possible total cost
• The least-cost input combination is where an isocost line is tangential to the desired isoquant
• Equimarginal principle


  To minimize the total cost of producing a desired quantity of output, the inputs should be used in a combination of quantities such that the marginal product per euro spent is equal for all inputs
• The least-cost input combination satisfies the equimarginal principle: MPL/PL = MPK/PK
• In the long run, a firm can increase its output Q by choosing the new least-cost combination of K and L to produce the higher Q
• Long-run total cost function (TC(Q))


  Shows the total cost associated with different quantities of output when all factors of production are variable
• Returns to scale


  The changes in long-run average total cost (or productivity) that arise because of changes in the total size of a firm's operations
• If long-run ATC does not change when Q increases, there are constant returns to scale
• If long-run ATC falls when Q increases, there are increasing returns to scale
• If long-run ATC rises when Q increases, there are decreasing returns to scale
• Firm's scale


  The total size of a firm's operations (measured with Q)
• Economies and diseconomies of scale

  • When a firm increases its scale, long-run total cost (TC) rises – but long-run average total cost (ATC = TC/Q) can remain constant, decrease, or increase
• Constant returns to scale

  • Long-run ATC does not change when Q increases
• Increasing returns to scale (economies of scale)

  • Long-run ATC falls when Q increases