Production and cost

Production and cost objectives Students should be able to Write a production function and distinguish between returns to scale and returns to a factor Use isocosts and isoquants to illustrate production trade-offs Employ short- and long-run cost curves to describe firm characteristics

Production functions A production function specifies maximum output from given inputs:

Empirical production functions Cubic Q=a0+a1XY+a2X2Y+a3XY2+a4X3Y+a5XY3 Cobb-Douglas Q = aXbYc log Q = log a + b log X + c log Y

Returns to scale Defined: The relation between output and a proportional variation of all inputs together Increasing returns to scale: Q=KL Decreasing returns to scale: Q=K1/3L1/3 Constant returns to scale: Q=K1/2L1/2

Returns to a factor Returns to a factor refer to the relation between output and variation in only one input Total product Average product Q/L Marginal product Q/L

Returns to a factor a common case

Illustrating production choices with isoquants Isoquants portray technical combination of inputs to produce a given level of output Shape of isoquants indicates substitutability between inputs

Optimal input combination isoquants

Differing input substitutability isoquants

Isocost lines Isocosts portray combinations of inputs that entail the same cost Isocosts change as input prices change

Isocost lines

Isocost lines changes in input prices

Cost minimization

Optimal input mix input price changes

Cost concepts Total cost Marginal cost Average cost Opportunity cost relation between total cost and output Marginal cost change in total cost when output rises one unit Average cost total cost divided by total output Opportunity cost value of best alternative resource use

Cost curves

Short run versus long run at least one input is fixed cost curves are operating curves Long run all inputs are variable cost curves are planning curves Fixed costs--incurred even if firm produces nothing Variable costs--change with the level of output

Short-run cost curves

Long-run average cost envelope of short-run average cost curves

Long-run average and marginal cost curves

Additional cost concepts Minimum efficient scale plant size at which long-run average cost first reaches its minimum point (Q*) Economies of scope cost of producing a joint set of products is less than cost of producing separately in separate firms Learning curves costs decline with production experience

Learning curve

Economies of scale versus learning effects

Profit maximization A firm should increase output as long as marginal revenue exceeds marginal cost A firm should not increase output if marginal cost exceeds marginal revenue At the profit-maximizing level of output, MR=MC

Optimal output and changes in marginal cost

Factor demand Efficient production requires that MPi/Pi= MPj/Pj The reciprocals represent marginal cost Pi/MPi=Pj/MPj=MC At the optimum output level Pi/MPi=MR From which we derive the demand curve for input i Pi=MRMPi

Factor demand curve