Economics of Output Substitution: Product-Product Relationship PDF

Economics of Output Substitution: Product—Product relationship Chapter 7 1 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP...

Economics of Output Substitution: Product—Product relationship Chapter 7 1 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Topics of Discussion ▪ Production possibilities frontier (PPF) ▪ Profit maximizing combination of products 2 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Production Possibilities The goal is to find a combination of products that maximizes revenue for the maximum technical efficiency on the production possibilities frontier. 3 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Shows the substitution between two products given the most efficient use of firm’s resources 4 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Slope of the PPF The slope of the production possibilities curve is referred to as the Marginal Rate of Product Transformation, or MRPT. The value of the MRPT in our example is given by: MRPT =  Y (canned fruit) ÷  X (canned vegetables) 5 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Drops from Slope over range 108 to 95 between D and E is –1.30, or: -1310 Increases from 30 to 40 6 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Table 9.1:Production Possibilities for Sunspot Canning 95,000 40,000 - 108,000 ÷ - 30,000 = - 1.30 -13,000 10,000 7 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Level of output unattainable with with firm’s existing resources Efficiency is attained Technically Inefficient along the PPF use of firm’s resources 8 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Accounting for Product Prices Plotting the Iso-Revenue Line ISRL different combinations of two goods that a consumer can purchase at a constant level of income and different prices Canned fruit 30,000 cases of canned fruit 30,000 required at a price of $33.33/case to achieve A TARGET revenue of $1 million Role of input price We cannot determine the optimal combination of two products to produce without knowing the price of these two products. Canned 40,000 vegetables 9 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Plotting the Iso-Revenue Line 30,000 cases of canned fruit Canned fruit required at price of $33.33/case to achieve revenue of $1 million 30,000 40,000 cases of canned vegetables required at price of $25.00/case to achieve revenue of $1 million Canned 40,000 vegetables 10 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Original iso-revenue line Changes in income or both prices Line AB is the original iso-revenue line, indicating the number of cases needed to reach a specific sales target. Change in price of fruit Change in price of vegetables 11 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 The iso-revenue line would Original iso-revenue line Changes in income or both prices shift out to line EF if the revenue target doubled (or prices fell in half) while the line would shift in to line CD if revenue targets fell in half or prices doubled. Change in price of fruit Change in price of vegetables 12 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Original iso-revenue line Changes in income or both prices The iso-revenue line would Change in price of fruit Change in price of vegetables shift out to line BC is the price of fruit fell in half but shift in to line BD if the price of fruit doubled 13 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Original iso-revenue line Changes in income or both prices The iso-revenue line would Change in price of fruit Change in price of vegetables shift out to line AD if the price of vegetables fell in half but shift in to line AC is the price of fruit doubled. 14 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Profit Maximizing Combination of Products The profit maximizing combination of two products is found where the slope of the production possibilities frontier (PPF) is equal to the slope of the iso-revenue Curve, or where: Canned fruit Price of vegetables = – Canned vegetables Price of fruit Slope of an Slope of iso- PPF curve revenue line 15 25-Jul-24  Assume Line AB represents revenue for $1 million. 16 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  We want to find the profit-maximizing combination given the current prices of canned fruit and vegetables. 17 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Canned fruit Price of vegetables = – Canned vegetables Price of fruit Shifting line AB out in a parallel fashion holds both prices constant at their current level 18 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Table 9.2:Production Possibilities for Sunspot Canning 125,000 18,000 MRPT cases of cases of equals fruit vegetables -0.75 19 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Price ratio = -($25.00 ÷ $33.33) = - 0.75 125,000 18,000 MRPT cases of cases of equals fruit vegetables -0.75 20 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Price ratio = -($25.00 ÷ $33.33) = - 0.75 125,000 18,000 MRPT cases of cases of equals fruit vegetables -0.75 Canned fruit Price of vegetables = – Canned vegetables Price of fruit 21 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Canned fruit Price of vegetables = – Canned vegetables Price of fruit Shifting line AB out in a parallel fashion holds both prices constant at their current level 22 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Doing the Math Let’s assume the price of a case of canned fruit is $33.33 while the price of a case of canned vegetables is $25.00. If point M represents 125,000 cases of fruit and 18,000 cases of vegetables, then total revenue at point M is: Revenue = 125,000 × $33.33 + 18,000 × $25.00 = $4,166,250 + $450,000 = $4,616,250 23 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Doing the Math At these same prices, if we instead produce 108,000 cases of fruit and and 30,000 cases of vegetables, then total revenue would fall to: Revenue = 108,000 × $33.33 + 30,000 × $25.00 = $3,599,640 + $750,000 = $4,349,640 which is $266,610 less than the $4,616,250 earned at point M. 24 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Effects of a Change in the Price of One Product If the price of canned fruit fell in half, the firm must sell twice as many cases of canned fruit to earn $1 million if it focused solely on fruit production. 25 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Effects of a Change in the Price of One Product This gives us a new iso- revenue curve… line CB. 26 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Effects of a Change in the Price of One Product To see the effects of this price change, we can shift the new iso-revenue curve out to the point of tangency with the PPF curve…. 27 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Effects of a Change in the Price of One Product Shifting the new iso- revenue curve in a parallel fashion out to a point of tangency with the PPF curve, we get a new combination of products required to maximize profit. 28 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24 Effects of a Change in the Price of One Product The firm would shift from point M on the PPF to point N as a result of the decline in the price of fruit. That is, to maximize profit, the firm would cut back its production of canned fruit and produce more canned vegetables. 29 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24  Summary ▪ Concepts of iso-revenue line and the production possibilities frontier ▪ Marginal rate of product transformation (MRPT) ▪ Concept of profit maximizing combination of products ▪ Effects of change in product price ▪ Key decision rule – maximize profits where MRPT equals the ratio of the product prices 30 CAMS 2003: ECONOMIC OF OUTPUT SUBSTITUTION: PRODUCT--PRODUCT RELATIONSHIP 25-Jul-24