Production and Cost in the Long Run Nihal Hennayake

Production Isoquants In the long run, all inputs are variable & isoquants are used to study production decisions – An isoquant is a curve showing all possible input combinations capable of producing a given level of output – Isoquants are downward sloping; if greater amounts of labor are used, less capital is required to produce a given output

A Typical Isoquant Map

Marginal Rate of Technical Substitution The MRTS is the slope of an isoquant & measures the rate at which the two inputs can be substituted for one another while maintaining a constant level of output The minus sign is added to make MRTS a positive number since ∆K / ∆L, the slope of the isoquant, is negative

The MRTS can also be expressed as the ratio of two marginal products: Marginal Rate of Technical Substitution As labor is substituted for capital, MP L declines & MP K rises causing MRTS to diminish

Isocost Curves Show various combinations of inputs that may be purchased for given level of expenditure (C) at given input prices (w, r) Slope of an isocost curve is the negative of the input price ratio (-w/r) K-intercept is C / r Represents amount of capital that may be purchased if zero labor is purchased

Isocost Curves

Optimal Combination of Inputs – Two slopes are equal in equilibrium – Implies marginal product per dollar spent on last unit of each input is the same Minimize total cost of producing Q by choosing the input combination on the isoquant for which Q is just tangent to an isocost curve

Optimal Input Combination to Minimize Cost for Given Output

Output Maximization for Given Cost

Optimization & Cost Expansion path gives the efficient (least-cost) input combinations for every level of output – Derived for a specific set of input prices – Along expansion path, input-price ratio is constant & equal to the marginal rate of technical substitution

Expansion Path

Long-Run Costs Long-run total cost (LTC) for a given level of output is given by: LTC = wL * + rK * Where w & r are prices of labor & capital, respectively, & (L *, K * ) is the input combination on the expansion path that minimizes the total cost of producing that output

Long-Run Costs Long-run average cost (LAC) measures the cost per unit of output when production can be adjusted so that the optimal amount of each input is employed – LAC is U-shaped – Falling LAC indicates economies of scale – Rising LAC indicates diseconomies of scale

Long-Run Average & Marginal Cost Curves

Economies of Scale Larger-scale firms are able to take greater advantage of opportunities for specialization & division of labor Scale economies also arise when quasi-fixed costs are spread over more units of output causing LAC to fall Variety of technological factors can also contribute to falling LAC

Economies & Diseconomies of Scale

Purchasing Economies of Scale Purchasing economies of scale arise when large-scale purchasing of raw materials enables large buyers to obtain lower input prices through quantity discounts

Learning or Experience Economies “Learning by doing” or “Learning through experience” As total cumulative output increases, learning or experience economies cause long-run average cost to fall at every output level

Relations Between Short-Run & Long- Run Costs LMC intersects LAC when the latter is at its minimum point At each output where a particular ATC is tangent to LAC, the relevant SMC = LMC For all ATC curves, point of tangency with LAC is at an output less (greater) than the output of minimum ATC if the tangency is at an output less (greater) than that associated with minimum LAC

Long-Run Average Cost as the Planning Horizon