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CHAPTER • The Cost of Production 251 From the chosen isocost line, determine the minimum cost of producing the output level that has been selected Graph the output-cost combination in Figure 7.6 (b) Suppose we begin with an output of 100 units The point of tangency of the 100-unit isoquant with an isocost line is given by point A in Figure 7.6 (a) Because A lies on the $1000 isocost line, we know that the minimum cost of producing an output of 100 units in the long run is $1000 We graph this combination of 100 units of output and $1000 cost as point D in Figure 7.6 (b) Point D thus represents the $1000 cost of producing 100 units of output Similarly, point E represents the $2000 cost of producing 200 units which corresponds to point B on the expansion path Finally, point F represents the $3000 cost of 300 units corresponding to point C Repeating these steps for every level of output gives the long-run total cost curve in Figure 7.6 (b)—i.e., the minimum long-run cost of producing each level of output In this particular example, the long-run total cost curve is a straight line Why? Because there are constant returns to scale in production: As inputs increase proportionately, so outputs As we will see in the next section, the shape of the expansion path provides information about how costs change with the scale of the firm’s operation EX AMPLE REDUCING THE USE OF ENERGY Policy makers around the world have been concerned with finding ways to reduce the use of energy In part, this reflects environmental concerns—most energy consumption uses fossil fuels and thus contributes to the emission of greenhouse gases and global warming But energy, whether in the form of oil, natural gas, coal or nuclear, is also expensive, so if companies can find ways to reduce their energy use, they can lower their costs There are essentially two ways that companies can reduce the amount of energy they use The first is to substitute other factors of production for energy For example, some machines might be more costly but also use less energy, so if energy prices rise, firms could respond by buying and using those energy-efficient machines, effectively substituting capital for energy This is exactly what has happened as energy prices rose in recent years: firms bought and installed expensive but more energy-efficient heating and cooling systems, industrial processing equipment, trucks, cars, and other vehicles The second way to reduce energy use is through technological change As time passes, research and development lead to innovations that make it possible to produce the same output using fewer inputs—less labor, less capital, and less energy Thus even if the relative prices of energy and capital stay the same, firms will use less energy (and less capital) to produce the same output Advances in robotics during the past two decades are an example of this; cars and trucks are now produced with less capital and energy (as well as less labor) These two ways of reducing energy use are illustrated in Figures 7.7(a) and (b), which show how capital and energy are combined to produce output.8 The isoquants in each figure represent the various combinations of capital and energy that can be used to generate the same level of output The figures illustrate how reductions in energy use can be achieved in two ways First, firms can substitute more capital for energy, perhaps in response to a government subsidy for investment in energysaving equipment and/or an increase in the cost of electricity This is shown as a movement along isoquant q1 from point A to point B in Figure 7.7(a), with capital increasing from K1 to K2 and energy decreasing from E2 to E1 in response to a shift in the isocost curve from C0 to C1 Second, technological This example was inspired by Kenneth Gillingham, Richard G Newell, and Karen Palmer, “Energy Efficiency Economics and Policy,” Annual Review of Resource Economics, 2009, Vol 1: 597–619
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