Production and Cost in the Long Run Overheads

The long run In the long run, there are no fixed inputs or fixed costs; all inputs and all costs are variable The firm must decide what combination of inputs to use in producing any level of output

Cost minimization assumption For any given level of output, the firm will choose the input combination with the lowest cost

The cost minimization problem Pick y; observe w 1, w 2, etc; choose the least cost x’s Why not just pick 0 for all the x’s?

For any output level, there are are usually several different input combinations that can be used Each combination will have a different cost

Consider the hay problem x 1 x 2 TPPAPP A MPPMPPTFCTVCTCAFCAVCATCAMCMC

There are many ways to produce 2,000 bales of hay per hour WorkersTractor-WagonsTotal CostAverage Cost

Long run total cost By minimizing total cost of production for various output levels with all inputs variable, the firm determines the long run total cost of production

OutputWorkersTractor-WagonsCost Average Cost , , , , , , , , , , , , , , , , , , , , , , ,

Long run average cost of production LRATC

Examples y = 2000 y =

Graphically we can plot LRATC (LAC) as Long Run Average Cost Output - y Cost LAC

Long run costs are less than or equal to short run costs for any given output level Why? If we are free to vary all inputs in the long run, we can match any short run least cost combination

Consider the following data where the short run costs hold wagons fixed at the long run least cost level OutputLACAC AC AC , , , , , , , , , , , , , , , , ,

Consider long and short run average cost when wagons are at the 50,000 bale minimum cost Long And Short Run Average Cost Output - y Cost LAC AC

Consider long and short run average cost when wagons are at the 5,000 bale minimum cost Long and Short Run Average Cost Output - y Cost LAC AC

Consider long and short run average cost when wagons are at the 1,000 bale minimum cost Long and Short Run Average Cost Output - y Cost AC LAC

Because non-integer values for wagons are not typically feasible, we might consider alternative wagon levels instead Output - y Cost AC 2 Wagons

Consider 1, 2 and 3 wagons Output - y Cost LAC AC 1 Wagon AC 2 Wagons AC 3 Wagons

Consider 1, 2, 3 and 5 wagons LAC AC 1 Wagon AC 2 Wagons AC 5 Wagons Output - y Cost AC 3 Wagons

Now add 10 wagons LAC AC 1 Wagon AC 2 Wagons AC 5 Wagons Output - y Cost AC 3 Wagons AC 10 Wagons

Output per period $ Long-run average cost ATC 1 ATC 2 ATC 3 The long run average total cost curve (LRATC) is an envelope curve that touches all the short run average total cost curves (SRATC) from below.

Another Example

Plant size and economies of scale Economists often refer to the collection of fixed inputs at a firm’s disposal as its plant Restaurant Corn farmer Dentist building fixtures kitchen items land machinery breeding stock office drill

Choosing the optimal plant size For different output levels, different plants are appropriate Short Run Average Cost Output - y Cost AC 1 Wagon AC 2 Wagons

Consider plant sizes of 1, 2 and 3 wagons Short Run Average Cost Output - y Cost AC 1 Wagon AC 2 Wagons AC 3 Wagons

We can add 5, 6 and 7 wagons Short Run Average Cost Output - y Cost AC 1 Wagon AC 2 Wagons AC 3 Wagons AC 5 Wagons AC 6 WagonsAC 7 Wagons

AC 1 Wagon AC 2 Wagons AC 5 Wagons AC 7 Wagons AC 10 Wagons AC 15 Wagons Or 1, 2, 3, 5, 7, 10 and 15 wagons Short Run Average Cost Output - y Cost AC 3 Wagons

AC 2 Wagons AC 3 Wagons AC 10 Wagons AC 15 Wagons AC 20 Wagons And all the way up to 40 wagons Output - y Cost AC 1 Wagon AC 7 Wagons AC 40 Wagons AC 5 Wagons

7 Wagons 10 Wagons 20 Wagons Long and Short Run Average Costs Output - y Cost 5 Wagons 15 Wagons 40 Wagons LAC 40 wagons is only efficient at over 200,000 bales

Economies of size and the shape of LRATC We measure the relationship between average cost and output by the elasticity of scale (size)

If AC > MC, then the cost curve is downward sloping and  S > 1 If MC > AC, then the cost curve is upward sloping and  S < 1

MC Long Run Average & Marginal Cost Curves LRAC AC > MC   S > 1 y LRAC is downward sloping

MC Long Run Average & Marginal Cost Curves LRAC AC < MC   S < 1 y LRAC is upward sloping

Economies of scale (size) When average cost is falling as output rises, we say the firm experiences economies of scale or increasing returns to size When long run total cost rises proportionately less than output, production is characterized by economies of scale and the LRATC curve slopes downward

MC Long Run Average & Marginal Cost Curves LRAC AC > MC   S > 1 y Economies of Size/Scale

Why do economies of scale occur? Gains from specialization More efficient use of lumpy inputs blast furnace combine X-ray machine receptionist

Diseconomies of scale (size) When average cost rises as output rises, we say the firm experiences diseconomies of scale or decreasing returns to size When long run total cost rises more than in proportion to output, production is characterized by diseconomies of scale and the LRATC curve slopes upward

MC Long Run Average & Marginal Cost Curves LRAC AC > MC   S > 1 y Diseconomies of Size

Why do diseconomies of scale occur? Changes in the quality of inputs Supervision and motivation problems Externalities or congestion in production

Constant returns to scale (size) When average cost does not change as output rises, we say the firm experiences constant returns to size or scale When both output and long run total cost rise by the same proportion, production is characterized by constant returns to scale and the LRATC is flat

Why do constant returns to scale occur? Duplication of processes Fixed production proportions and replication Economies and diseconomies balance out

General shape of the LRAC curve Output - y Cost LRAC

The End

LAC AC 1 Wagon AC 2 Wagons AC 5 Wagons Output - y Cost AC 3 Wagons AC 10 Wagons