The Firm’s Production and Selling Decisions

1. 4 The Firm’s Production and Selling Decisions

2. Outline • Production and Input Choice, with One Variable Input • Multiple Input Decisions: The Choice of Optimal Input Combinations • Cost and Its Dependence on Output • Economies of Scale

3. Outline • Price and Quantity: One Decision, Not Two • Total Profit: Keep your Eye on the Goal • Marginal Analysis and Maximization of Total Profit • Generalization: The Logic of Marginal Analysis and Maximization

4. Production and Input Choice, with 1 Variable Input • Arkansas chicken farmer named Florence, who owns a small poultry business. • She knows Q corn she feeds her chickens will impact Q meat. • She could also buy more T, growth hormones, and L to ↑Q meat. But for now, let’s focus on the relationship between poultry meat and corn.

5. TABLE 1. TPP, MPP, and APP for Flo’s Chicken Farm

6. FIGURE 1. TPP with Different Quantities of Corn

7. Production and Input Choice, with 1 Variable Input • Total Physical Product (TPP) = amount of output that can be produced as 1 input changes, with all other inputs held constant. • Table 1 shows TPP or how much chicken Flo can produce with different Q corn, holding all other inputs fixed. • If Q corn = 0 → Q meat = 0. Each add. bag of corn yields more poultry. 4 bags → 100 lbs. After 9 bags, ↑corn → ↓output –chickens are so overfed they become ill.

8. Production and Input Choice, with 1 Variable Input • Average Physical Product (APP) = TPP/(Q of input) = measures output per unit of input. • E.g., 4 bags corn → 100 lbs meat, so APP = 25. • Marginal Physical Product (MPP) = additional output resulting from a 1 unit increase in the input, holding all other inputs constant. • E.g., ↑corn from 4 to 5 bags, the 5th bag yields an add. 30 lbs of meat.

9. FIGURE 2. Flo’s MPP Curve

10. Graph of MPP • Marginal returns to an input typically rise and then fall. • Area of ↑MPP (1 to 4 bags) → each add. bag of corn adds more to TPP than previous bag. ↑TPP rapidly. • Area of ↓MPP (between 4 and 9 bags) → each add. bag of corn adds less to TPP than previous bag. ↑TPP at a dim. rate. • Area of (-)MPP (beyond 9 bags) → each add. bag of corn reduces TPP by more than previous bag. ↓TPP.

11. The “Law” of Diminishing Marginal Returns • ↑ Q of any one input, holding Q of all other inputs constant, leads to lower marginal returns to the expanding input. • E.g., Flo feeds chickens more and more, without giving them extra water, cleaning up after them more, or buying add. chickens. Eventually overfed and become sick. • Law of dim. marginal returns should hold for most activities. Can you think of one?

12. Optimal Purchase Rule for a Single Input • How does a firm decide on the quantity of an input? • Assume P corn = $10/40-lb bag and P chicken = $0.75/lb. Consider purchasing just 1 bag of corn. Does this max profits? • 1 bag produces 14 lbs of chicken. TR: $0.75 x 14 = $10.50 TC: $10 x 1 = $10.00 Profit: = $0.50 • Shouldn't stop at 1 bag because 2 bags yield more profit. TR: $0.75 x 36 = $27.00 TC: $10 x 2 = $20.00 Profit: = $7.00

13. Optimal Purchase Rule for a Single Input • Easier way to proceed. Until 9 bags, each add. bag of corn ↑Q chicken. So each bag (1-9) raises TR, but also costs $10. To max profit, Flo should compare revenue that each bag generates against the cost of each bag. • Marginal Revenue Product (MRP) = MPP x Price of output. • MRP = add. revenue generated from ↑input by 1 unit.

14. Table 2. Flo’s TPP, MPP, and MRP Schedules

15. Optimal Purchase Rule for a Single Input • Rule: If MRP > P of an input → use more of the input. If MRP < P of an input → use less of the input. • Purchase an input where MRP = P of the input. • E.g., Flo should purchase 7 bags of corn. Can you explain why she should not buy the 8th bag? • Note: ↓MPP (bag 4 to 9) → ↓MRP. At 7 bags, Flo is producing where dim. MPP sets in. Flo should stop ↑corn purchases when MRP falls to = P of corn.

16. Multiple Input Decisions • Firms seek the method of production that is least costly. • Consider the choice between L and K in prod. Compared with Mexico, in U.S., L is expensive and K is cheap. So (K/L) U.S. > (K/L) Mexico • One input can often be substituted for another in production. • E.g., shoes produced in Mexico are manufactured using more L and less K than shoes in U.S.

17. Multiple Input Decisions • A firm can produce same amount of a good with less of one input (say L) as long as it’s willing to use more of another input (like K). • Actual combos of inputs (such as K and L) depend on relative P of inputs. Firms strive to produce a good using the least expensive method.

18. Marginal Rule for Optimal Input Proportions • E.g., Flo can feed chickens soymeal or cornmeal –they are substitutes in production. • Not perfect substitutes. Soymeal has more protein but fewer carbohydrates than corn. • Best to feed some combo of 2 meals. ↓Q poultry if Flo relies too much on 1 input. There are dim. returns to substitution among the inputs.

19. Marginal Rule for Optimal Input Proportions How much of each input should Flo purchase? • Feed ↑corn and ↓soy. Soy costs twice as much, but yields only 67% more meat. • If Flo ↓soy by 1 bag → saves $20. But ↓outputby 50 lbs. So buy 1.67 (or 50/30) bags of corn to make up for ↓output, cost = $16.70. She saves $3.30 while holding Q output fixed.

20. Marginal Rule for Optimal Input Proportions • Above: MPPsoy/Psoy < MPPcorn/Pcorn i.e., 50/$20 < 30/$10 • Soy yields 2.5 lbs. meat per $1 while corn yields 3 lbs. per $1. More output from corn rather than soy at the margin. • MPP of an input/P of an input = add. output from spending $1 on the input. • By substituting input with lower output per $1 for input with higher output per $1; firm can reduce costs while holding Q output fixed.

21. Marginal Rule for Optimal Input Proportions • Rule: if MPPb/Pb > MPPa/Pa→ spend less on input a and more on input b. • Optimally, MPPa/Pa = MPPb/Pb • Above: MPPcorn/Pcorn > MPPsoy/Psoy • These ratios will equalize at an optimum because of dim. MPP. As Flo uses ↑corn and ↓soy →↓MPP corn and ↑MPP soy, until two ratios are equal.

22. Marginal Rule for Optimal Input Proportions • Changes in Input Prices and Input Proportions: • Optimally, MPPcorn/Pcorn = MPPsoy/Psoy • What if ↑P corn? • Then ↑MPP corn to match ↑P corn. How? Flo will use ↓corn and ↑soy until ratios are equal. • As ↑P input → firms switch to cheaper inputs.

23. Cost Curves and Input Quantities • 3 different cost curves –Total Cost (TC), Average Cost (AC), and Marginal Cost (MC). • Flo’s costs depend on Q of inputs and on P of those inputs. • To calculate costs, assume: • P corn is beyond Flo's control. • Q of all other inputs (except corn) are fixed. • P corn = $10 per 40 lb. bag

24. TABLE 3. TPP, TC, and AC for Flo’s Chicken Farm

25. Cost Curves and Input Quantities • TPP → Q output firm can produce given Q inputs. Q inputs and P inputs → firm can determine TC of producing any Q output. • TC = P inputs x Q inputs • AC = TC/Q output • E.g., TC 100 lbs = $40 → AC = $40/100 = $0.40 • MC = TC when output increases by 1 unit • E.g., if TC 100 lbs. = $40.00 TC 99 lbs. = $39.70 MC 100th lb. = $0.30 • Note: table above doesn’t show this because ↑output > 1.

26. FIGURE 3. Flo’s Total Cost Curve

27. FIGURE 4. Flo’s Average Cost and Marginal Cost Curves AC and MC typically ↓ and then ↑ as the ↑output level.

28. Fixed and Variable Costs • TC, AC, and MC can be divided into 2 parts –fixed costs and variable costs. • Fixed cost is the cost of an input whose Q does not ↑ when ↑output. Input that the firm requires to produce any output. Any other cost is a variable cost. • E.g., takes at least 1 taxi to run a cab co. and its cost is the same whether 1 or 60 people ride in it. But gas use rises as more people ride. Taxi is a fixed cost and gas is a variable cost. What are the fixed and variable costs where you work?

29. Fixed and Variable Costs • TC = TVC + TFC • AC = AVC + AFC • AC = TC/Q output • AVC = TVC/Q output • AFC = TFC/Q output

30. Table 4. Flo’s Total and Average Fixed Costs Flo pays rent of $5 per week for her chicken coop.

31. FIGURE 5. Graph of Flo’s Total Fixed Cost

32. FIGURE 6. Graph of Flo’s Average Fixed Cost If Flo produces 1 package, TFC is carried by 1. But if she produces 4, TFC gets divided between 4 packages. So ↓AFC as ↑output.

33. FIGURE 7. Flo’s Total Variable Cost Curve TVC has same shape as TC because ↑variable costs as ↑output.

34. Fixed and Variable Costs • Marginal Cost = Marginal Variable Cost (MVC) Why doesn't MC have a fixed component (i.e., MC = MVC + MFC)?

35. Shape of the Average Cost Curve • AC is generally U shaped –it initially declines and eventually rises with the level of output. • AC declines for 2 reasons: • Changing input proportions: at first, Flo feeds chickens more corn while holding all other inputs constant. Output rises rapidly when ↑MPP corn, which tends to ↓AC. • ↓Average fixed costs as ↑output.

36. Shape of the Average Cost Curve • AC eventually rises for 2 reasons: • Dim MPP: ↑output more slowly as ↓MPP corn, which tends to ↑AC. • Bureaucratic mess: as firms grow in size they lose personal touch of management and become increasingly bureaucratic, which drives up costs. • Point where ↑AC varies by industry. AC in auto industry begins ↑ after more units of output than farming. Huge K investment → AFC↓ dramatically.

37. Short-run versus Long-run Costs • Cost of changing a firm's output level depends on period of time under consideration. Many input choices are precommitted by past decisions. • Sunk cost = a cost to which a firm is precommitted for some limited period of time. • E.g., a 2-year-old machine with a 9-year economic life is a variable cost after 7 years because the machine would have to be replaced anyway.

38. Short-run versus Long-run Costs • SR = period of time when some of the firm's cost commitments end. • LR = period of time when all of the firm's cost commitments end. • There are no fixed costs in LR –all costs are variable. • E.g., if # of workers can be altered daily, and # of machines altered yearly, and size of plant every 10 years. Then 10 years is the LR.

39. Short-run versus Long-run Costs • Size of a firm may be fixed in SR because it has purchased or leased a particular plant, but firm can alter size of its plant in LR. • E.g., Flo has already built a chicken coop, which restricts her ability to ∆ output level in SR. In LR, Flo can build a new larger coop to produce more.

40. Average Cost Curve in the Short and Long Run • LR AC curve differs from SR AC curve because all inputs are variable in LR. • E.g., In SR, Flo can only chose how many chickens to squeeze into coop. In LR, she can chose among different coop sizes.

41. FIGURE 8. Flo’s SR and LR Average Cost Curves

42. Average Cost Curve in the Short and Long Run • If Flo expects to sell 40 → she buys a small coop with AC of SL. If Q = 40 → AC = $12 (pt U). • She is surprised by strong D and can sell 100 with AC = $12 (pt V). • Now she needs a bigger coop with AC of BG with its lower AC of $9 for Q = 100. • In SR, Flo is stuck with AC of SL. In LR, she can replace coop and the relevant AC is STG. • LR AC curve shows the lowest possible SR AC for each output level.

43. Economies of Scale • Returns to scale indicates how the output level changes when all the firm's inputs are doubled. • Increasing Returns to Scale (IRTS): Q output more than doubles. • IRTS gives a cost advantage to larger firms. Found in industries like telecommunications, electricity, automobiles, and aircraft. • Constant Returns to Scale (CRTS): Q output doubles. • Decreasing Returns to Scale (DRTS): Q output less than doubles. • Gives a cost advantage to smaller firms. Most U.S. industries have DRTS.

44. Economies of Scale • Returns to scale impacts the shape of the AC curve. • AC = TC/Q output = (P input x Q input)/Q output • E.g., if Q inputs doubles and Q output doubles, then AC is constant.

45. AC Increasing returns Constant returns Decreasing returns to scale to scale to scale AC AC FIGURE 9. 3 Possible Shapes for the AC Curve Long-Run Average Cost Long-Run Average Cost Long-Run Average Cost Quantity of Output Quantity of Output Quantity of Output (a) (b) (c)

46. Economies of Scale • Law of dim. marginal returns and IRTS may seem contradictory, but they are unrelated. • Dim. marginal returns refers to increasing a single input. Returns to scale refers to a doubling of all inputs. • A firm with dim. returns to a single input could have IRTS, CRTS, or DRTS.

47. Price and Quantity: One Decision, Not Two • Critical decision -when Apple decides how many ipods to produce and P it will charge. • P affects how consumers respond and Q affects K and L costs. • When firms chose P and Q to max profits → they can pick only one –P or Q. • Chose P → customers decide Q • Chose Q → market determines P at which this Q can be sold

48. FIGURE 10. Demand Curve for Flo’s Poultry Meat Flo faces a local D curve. If she picks P = $19 → Qd = 1. If she picks Q = 9 → P = $11 to find required # of customers. A $19 Price per package B $11 D 1 9 Quantity of Chicken (20 lb-packages per week)

49. Price and Quantity: One Decision, Not Two • Each pt on D curve corresponds to a (P,Q) pair. A firm can pick 1 pair, but it can never pick P from 1 pt on D and a different Q from another pt on D. • Economists assume that firms pick (P,Q) pair that maximizes profits.

50. Total Profit: Keep Your Eye on the Goal • Total profit (or economic profit) = TR – TC (including opportunity cost) • Opportunity costs include any K or L supplied by the firm’s owners. • Economic profit = Accounting profit – opportunity cost. • E.g., if a talented attorney, gives up her salary of $120,000 to start her own law firm and earns $150,000 after paying for all operating costs → accounting profit = $150,000 but economic profit = $30,000 • E.g., if you start a business and earn 6% on money you invested but could have earned 4% in T-Bills → economic profit = 2%.