Production, Inputs, and Cost: Building Blocks for Supply Analysis, Part 1

Production, Inputs, and Cost: Building Blocks for Supply Analysis 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 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. TABLE 1. TPP, MPP, and APP for Flo’s Chicken Farm Corn in bags TPP in lbs. MPP in lbs. APP in lbs. 0 0.0 ----- ----- 1 14.0 14.0 14.0 2 36.0 22.0 18.0 3 66.0 30.0 22.0 4 100.0 34.0 25.0 5 130.0 30.0 26.0 6 156.0 26.0 26.0 7 175.0 19.0 25.0 8 184.0 9.0 23.0 9 185.4 1.4 20.6 10 180.0 -5.4 18.0 11 165.0 -15.0 15.0 12 144.0 -21.0 12.0 FIGURE 1. TPP with Different Quantities of Corn Total Output of Poultry Meat Total Physical Product (TPP) in lbs. 200 180 160 140 120 100 80 60 40 20 0 6 8 7 9 10 11 12 5 4 3 2 0 0 1 2 4 6 8 10 Quantity of Corn (bags per week) 12 14 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. 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. FIGURE 2. Flo’s MPP Curve MPP Rising 34 Falling Negative 14 0 0 -21 MPP 0 4 9 12 Bags of corn 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. 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? 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 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. Table 2. Flo’s TPP, MPP, and MRP Schedules Bags of Corn TPP MPP TR (P*TPP) MRP (P*MPP) P corn Profit 0 0.0 ----- $0.00 ----- $10.00 $0.00 1 14.0 14.0 10.50 $10.50 10.00 0.50 2 36.0 22.0 27.00 16.50 10.00 7.00 3 66.0 30.0 49.50 22.50 10.00 19.50 4 100.0 34.0 75.00 25.50 10.00 35.00 5 130.0 30.0 97.50 22.50 10.00 47.50 6 156.0 26.0 117.00 19.50 10.00 57.00 7 175.0 19.0 131.25 14.25 10.00 61.25 8 184.0 9.0 138.00 6.75 10.00 58.00 9 185.4 1.4 139.05 1.05 10.00 49.05 10 180.0 -5.4 135.00 -4.05 10.00 35.00 11 165.0 -15.0 123.75 -11.25 10.00 13.75 12 144.0 -21.0 108.00 -15.75 10.00 -12.00 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. 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. 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. 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. Marginal Rule for Optimal Input Proportions Price corn = $10 per 40 lb. bag MPP bag corn = 30 lbs. meat Price soy = $20 per 40 lb. bag MPP bag soy = 50 lbs. meat 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 ↓output by 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. 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. 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. 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.