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1 Ch. 6: What to Produce? Where we’ve been… How much to produce? (Ch. 4) “Factor-product” decision rules say increase production until the marginal cost from an extra unit of output equals the marginal benefit. How to produce? (Ch. 5) With a least cost combination of inputs. “Factor-factor” decision rules say maintain production, but replace one input for another until the cost of a replaced input equals the cost of adding another input.

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2 Ch. 6: What to Produce? NOT on Exam 1, but fair game for FINAL Where we’re going… Now we add additional types of outputs. Before:Now: milkmilk and cheese PB CupsReg. and Crunchy PB Cups sweet cornsweet corn and tomatoes Now there are competing “ends” for our limited resources. (Think opportunity costs.) Today’s Goals: Two new tools, and a decision rule

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3 Assumptions 1. The firm produces two outputs. (a complication) 2. The firm has a fixed set of resources. (a simplification) 3. The firm is a price taker (both in inputs and outputs).

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4 Production Possibilities Frontier (PPF) Ch. 6 Tool #1 The Production Possibilities Frontier (PPF) is a curve depicting all the combinations of two products than can be produced using a given level of inputs. Sometimes called the production possibilities curve (PPC).

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5 Deriving the Production Possibilities Frontier A Farmers Market Example : Before, we examined a farmer who was just growing and selling sweet corn. Now we want to expand operations to include tomatoes. Inputs: Fertilizer, equipment, seed, and other inputs – These are already purchased, so they’re fixed. Labor – I can hire additional labor, so labor is variable FOR NOW.

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6 Two separate production functions for corn (in dozens) and tomatoes (in bushels) Deriving the Production Possibilities Frontier What if we contracted for 4 units of labor. So consider X fixed at 4. How much corn and tomato production is possible?

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7 Production combinations for X = 4 Deriving the Production Possibilities Frontier What if we fixed labor at X = 8

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8 Deriving the Production Possibilities Frontier Production combinations for X = 8 Let’s graph the PPF when X = 4

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9 Deriving the Production Possibilities Frontier (Graphically) PPF: X = 4 Let’s add a PPF when X = 8

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10 Deriving the Production Possibilities Frontier (Graphically) PPF: X = 4 PPF: X = 8

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11 Marginal Rate of Product Substitution (MRPS) Ch. 6: Formula #1 The MRPS describes… the rate at which one output must be decreased as production of the other output is increased (given a fixed amount of inputs). The MRPS is the slope of the production possibilities frontier (PPF).

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12 Marginal Rate of Product Substitution (MRPS)

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13 Marginal Rate of Product Substitution (MRPS) Any mention of corn or tomato prices yet?

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14 Economic Relationships: Isorevenue Total Revenue: TR = (P Y1 x Y 1 ) + (P Y2 x Y 2 ) Ch.6: Tool #2 Isorevenue line: A line indicating all combinations of two products that will generate the same level of revenue. Don’t forget our latest economic “adage”: Buy low, sell high.

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15 Economic Relationships: Isorevenue Output combinations generating $150 Revenue, where Price of corn (P Y1 ) = $2.50/dozen Price of tomatoes (P X2 ) = $5.00/ bushel

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16 Economic Relationships: Isorevenue Output combinations generating $150 Revenue with Price of corn (P Y1 ) = $2.50 and Price of tomatoes (P X2 ) = $5.00 What happens to the Isorevenue line if we increase our revenue target? What happens to the line if the price of tomatoes increases? What happens if the price of tomatoes decreases? TR=150 TR=225

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17 Summary: Isorevenue line 1) The end points show what happens if all production and sales were devoted to a single output. 2) A change in the total revenue is a parallel shift in the isorevenue line. 3) A change in one output price causes the isorevenue line to rotate. 4) The slope of the isorevenue line is also called the “inverse price ratio” (IPR): Ch. 6: Formula #2 Slope of TR = IPR = -P Y2 /P Y1

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18 Putting PPF and isorevenue together PPF (X=4) PPF (X=8) TR = $150 Price of corn (P Y1 ) = $2.50 Price of tomatoes (P Y2 ) = $5.00 If labor is fixed at X=4, What is the most revenue you can by producing and selling corn and tomatoes?

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19 Putting PPF and isorevenue together PPF (X=4) PPF (X=8) TR = $150 If labor is fixed at X=8, Now what is the most revenue you earn by producing and selling corn and tomatoes? Price of corn (P Y1 ) = $2.50 Price of tomatoes (P Y2 ) = $5.00 Rev.= (Y 1 = 30 )x(P Y1 = $2.50) + (Y 2 = 48 )x(P Y2 = $5.00) = $75 + $240 = $315

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20 Putting PPF and isorevenue together PPF (X=4) PPF (X=8) TR = $150 Price of corn (P Y1 ) = $2.50 Price of tomatoes (P Y2 ) = $5.00 Rev.= (Y 1 = 75 )x(P Y1 = $2.50) + (Y 2 = 69 )x(P Y2 = $5.00) = $187.50 + $345 = $532.50

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21 The Decision Rule: PPF (X=4) PPF (X=8) TR = $150 Choose the outputs (Y 1 and Y 2 ) so that the slope of the Production Possibility Frontier (PPF) equals the slope of the Isorevenue Line.

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