Unit 2 Technology and incentives

2.6 Modelling a dynamic economy: Innovation and profit

A change in the relative prices of labour and energy will change the slope of the firm’s isocost lines. Looking at the positions of the three technologies in Figure 2.9, we can imagine that if the isocost line becomes steep enough (w/p rises, so coal becomes relatively cheaper), B will no longer be the least-cost technology: the firm will switch to A. This is what happened in England in the eighteenth century.

Suppose that the price of coal falls to £5, while the wage remains at £10.

From the table in Figure 2.9, with the new prices technology A allows the firm to produce 100 metres of cloth at least cost. Cheaper coal makes each method of production cheaper, but the energy-intensive technology is now cheapest.

In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). There are three points: A at (1, 6), B at (4, 2), and E at (10, 1). A downward-sloping line passing through point A and connecting the points F at (0, 4) and G at (8, 0) represents the isocost for £40.
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Technology Number of workers Coal required (tons) Total cost (£)
Wage £10, cost of coal £5 per ton
A 1 6 40
B 4 2 50
E 10 1 105

Figure 2.9 The cost of using different technologies to produce 100 metres of cloth: high relative cost of labour.

Technology A costs least when coal is relatively cheap: In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10 7. Coordinates are (number of workers, tons of coal). There are three points: A at (1, 6), B at (4, 2), and E at (10, 1).
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Technology Number of workers Coal required (tons) Total cost (£)
Wage £10, cost of coal £5 per ton
A 1 6 40
B 4 2 50
E 10 1 105

Technology A costs least when coal is relatively cheap

When the wage is £10 and the price of coal is £5, the table shows that technology A, which is more energy-intensive, produces 100 metres of cloth at a lower cost than B or E.

The £40 isocost curve: In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). There are three points: A at (1, 6), B at (4, 2), and E at (10, 1). A downward-sloping line passing through point A and connecting the points F at (0, 4) and G at (8, 0) represents the isocost for £40.
Fullscreen
Technology Number of workers Coal required (tons) Total cost (£)
A 1 6 40
B 4 2 50
E 10 1 105
Wage £10, cost of coal £5 per ton

The £40 isocost curve

Technology A is on the isocost line FG. At any point on this line, the total cost of inputs is £40. Technologies B and E are above this line, with higher costs.

The slope of the isocost line: In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). There are three points: A at (1, 6), B at (4, 2), and E at (10, 1). A downward-sloping line passing through point A and connecting the points F at (0, 4) and G at (8, 0) represents the isocost for £40.
Fullscreen
Technology Number of workers Coal required (tons) Total cost (£)
A 1 6 40
B 4 2 50
E 10 1 105
Wage £10, cost of coal £5 per ton

The slope of the isocost line

The slope of the isocost line is equal to the relative price of labour: –w/p = −10/5 = −2. If you spent £10 more on labour by hiring an extra worker, you could reduce coal by two tons and keep the total cost at £40.

Remember that to draw the isocost line through any point, such as A, we calculate the cost at A (£40) then find another point with the same cost. The easiest way is to find one of the end points, F or G. For example, if no coal was used, four workers could be hired for £40. This is point F.

Figure 2.9 shows that with the new relative price, technology A lies on the £40 isocost line, and the other two available technologies lie above it. They will not be chosen if technology A is available.

How does a cost-reducing innovation raise profits?

Now we can calculate the gains to the first firm to adopt the least-cost technology (A) when the relative price of labour to coal rises. Like its competitors, the firm is initially using technology B and minimizing its costs: this is shown in Figure 2.10 by the dashed isocost line through B (with end points H and J).

Once the relative price changes, the new isocost line through technology B is steeper and the cost of production is £50. Switching to the energy-intensive technology A reduces costs to £40 for 100 metres of cloth. Follow the steps in Figure 2.10 to understand how isocost lines change with the new relative prices.

In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). A downward-sloping, straight line representing a cost of £80 passes through points J (0, 4), B (4, 2) and H (8, 0). Another downward-sloping straight line passes through points G (0, 8), A (1, 6) and F (4, 0). Another downard-sloping straight line representing a cost of £50 passes through points  N (0, 10), B (4, 2) and M (5, 0). This line is parallel to the line passing through G, A and F.
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Technology Number of workers Coal required (tons) Total cost (£)
Wage £10, cost of coal £20 per ton
B 4 2 80
Wage £10, cost of coal £5 per ton
B 4 2 50
A 1 6 40

Figure 2.10 The cost of using different technologies to produce 100 metres of cloth.

At the original relative price, B is the lower-cost technology: In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). A downward-sloping, straight line representing a cost of £80 passes through points J (0, 4), B (4, 2) and H (8, 0).
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Technology Number of workers Coal required (tons) Total cost (£)
Wage £10, cost of coal £20 per ton
B 4 2 80

At the original relative price, B is the lower-cost technology

When the wage is £10 and the price of coal is relatively high at £20, the cost of producing 100 metres of cloth using technology B is £80: choosing technology B puts the firm on the HJ isocost line.

The price of coal falls to £5: In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). A downward-sloping, straight line representing a cost of £80 passes through points J (0, 4), B (4, 2) and H (8, 0). Another downward-sloping straight line passes through points G (0, 8), A (1, 6) and F (4, 0).
Fullscreen
Technology Number of workers Coal required (tons) Total cost (£)
Wage £10, cost of coal £20 per ton
B 4 2 80
Wage £10, cost of coal £5 per ton
B 4 2 50
A 1 6 40

The price of coal falls to £5

If the price of coal falls relative to the wage as shown by isocost line FG, then using technology A, which is more energy-intensive than B, costs £40. The table shows that with these relative prices, A is now the least-cost technology.

B now costs more than A: In this diagram, the horizontal axis shows the number of workers, ranging from 1 to 10, and the vertical axis shows tons of coal, ranging from 1 to 10. Coordinates are (number of workers, tons of coal). A downward-sloping, straight line representing a cost of £80 passes through points J (0, 4), B (4, 2) and H (8, 0). Another downward-sloping straight line passes through points G (0, 8), A (1, 6) and F (4, 0). Another downard-sloping straight line representing a cost of £50 passes through points  N (0, 10), B (4, 2) and M (5, 0). This line is parallel to the line passing through G, A and F.
Fullscreen
Technology Number of workers Coal required (tons) Total cost (£)
Wage £10, cost of coal £20 per ton
B 4 2 80
Wage £10, cost of coal £5 per ton
B 4 2 50
A 1 6 40

B now costs more than A

At the new relative prices, technology B is on isocost line MN, where the cost is £50. Switching to technology A will be cheaper.

The firm’s profits are equal to the revenue it gets from selling output, minus its costs.

Whether the newer, less labour-intensive technology or the older one is used, cloth is sold at the same price, and the same prices have to be paid for labour and coal. The change in profit is therefore equal to the fall in costs associated with adopting the new technology, and profits rise by £10 per 100 metres of cloth:

\[\begin{align*} \text{profit} &= \text{revenue} - \text{costs} \\ \text{change in profit from} \\ \text{switching from B to A} &= \text{change in revenue — change in costs} \\ &= 0-(40-50) \\ &= 10 \end{align*}\]

In this case, the economic rent for a firm switching from B to A is £10 per 100 metres of cloth, which is the cost reduction made possible by the new technology. The decision rule (remember, if the economic rent is positive, do it!) tells the firm to innovate.

entrepreneur
A person who creates or is an early adopter of new technologies, organizational forms, and other opportunities.

In our example, technology A was available, but not in use until a first-adopter firm responded to the incentive created by the increase in the relative price of labour. The first adopter is called an entrepreneur. When we describe a person or firm as entrepreneurial, it refers to a willingness to try out new technologies and to start new businesses.

The economist Joseph Schumpeter (discussed in the ‘Great economists’ box later in this section) made the adoption of technological improvements by entrepreneurs a key part of his explanation for the dynamism of capitalism. For this reason, innovation rents are often called Schumpeterian rents.

Innovation rents do not last forever. Other firms, noticing that entrepreneurs are making economic rents, will eventually adopt the new technology—and thereby reduce their costs and increase their profits.

To explore Joseph Schumpeter’s life and ideas in more detail, watch this video by Lynne Kiesling, a historian of economic thought.

creative destruction
Joseph Schumpeter’s name for the process by which old technologies and the firms that do not adapt are swept away by the new, because they cannot compete in the market. In his view, the failure of unprofitable firms is creative because it releases labour and capital goods for use in new combinations.

Then, with higher profits per 100 metres of cloth, the lower-cost firms will thrive. They will increase their output of cloth. As more firms introduce the new technology, the supply of cloth to the market increases. With more cloth available for sale, the price will start to fall. This process will continue until everyone is using the new technology. Once cloth prices have declined to the point where no one is earning innovation rents, firms that stuck to the old technology B will be unable to cover their costs, and they will go bankrupt. Joseph Schumpeter called this creative destruction.

Exercise 2.6 Suit-making technologies

Section 2.1 discussed how new suit-making technologies substantially cut the labour time and expertise required to custom-make a suit, compared to conventional tailoring methods used by skilled tailors. As a result, the new suit-making technologies became more profitable than conventional methods and were adopted by many firms.

Draw a diagram (or series of diagrams, like Figure 2.10) with non-tailor-skilled labour on the horizontal axis and tailor-skilled labour on the vertical axis to illustrate the effect of the new suit-making technology on tailoring firms. (Hints: Assume that each technology uses a particular type of labour (either tailor-skilled or non-tailor-skilled) more intensively. You do not need to use specific numbers in your answer.)

Question 2.6 Choose the correct answer(s)

Figure 2.6 shows different technologies for producing 100 metres of cloth.

Based on this information, what can we conclude?

  • Technology D is more energy-intensive than technology C.
  • Technology B dominates technology D.
  • Technology A is the cost-minimizing technology at all prices of coal and wages.
  • Technology C can sometimes be a cheaper technology than A.
  • Technology D uses more workers and less coal, and therefore is more labour-intensive than C.
  • Technology B uses fewer workers and fewer tons of coal than technology D to produce the same amount of cloth, so it dominates D.
  • Technology A would be costlier than B, D, or E if the price of coal were much higher than the wage level.
  • Technology C is dominated by A, as it uses both more workers and more coal than A. Therefore it can never be a cheaper technology than A.

Question 2.7 Choose the correct answer(s)

Based on the information in Figure 2.10, what can we conclude?

  • When the wage is £10 and the price of coal is £5, the combination of inputs at point N is more costly than the inputs at point B.
  • Isocosts MN and FG represent the same price ratio (wage/price of coal) but different total costs of production.
  • Isocost HJ represents a higher (wage/price of coal) ratio than isocost FG.
  • Isocost HJ represents all the points that can produce 100 metres of cloth at a particular price ratio.
  • At these prices, N and B are on the same isocost line. These two combinations of inputs cost the same.
  • The price ratio is equal to the slope of an isocost; since isocosts MN and FG have the same slope, we can infer that they represent the same price ratio. MN is higher than FG, and so represents higher total costs.
  • Isocost FG has a slope of −2 (replacing two tons of coal with one worker leaves the total cost of production the same), while isocost HJ has slope −0.5 (replacing one ton of coal with two workers leaves the total cost the same). This means that labour is relatively cheaper along HJ, or isocost HJ has a lower wage/price of coal ratio.
  • An isocost represents all combinations of workers and tons of coal for which the total cost of production is the same. Along isocost HJ, we know that at point B (four workers and two tons of coal) the technology can produce 100 metres of cloth. If a technology were available to produce at another point on the line, it would not necessarily produce 100 metres of cloth.

Great economists Joseph Schumpeter

Portrait of Joseph Schumpeter

Joseph Schumpeter (1883–1950) developed one of the most important concepts of modern economics: creative destruction.

Schumpeter brought to economics the idea of the entrepreneur as the central actor in the capitalist economic system. The entrepreneur is the agent of change who introduces new products and new methods of production, and opens up new markets. Imitators follow, and the innovation is diffused through the economy. A new entrepreneur and innovation launch the next upswing.

For Schumpeter, creative destruction was the essential fact about capitalism: old technologies and the firms that do not adapt are swept away by the new, because they cannot compete in the market by selling goods at a price that covers the cost of production. The failure of unprofitable firms releases labour and capital goods for use in new combinations.

evolutionary economics
An approach that studies the process of economic change, which includes technological innovation, the diffusion of new social norms, and the development of novel institutions.

This decentralized process generates a continued improvement in productivity, which leads to growth, so Schumpeter argued it is virtuous.1 Both the destruction of old firms and the creation of new ones take time. The slowness of this process creates upswings and downswings in the economy. The branch of economic thought known as evolutionary economics (you can read articles on the subject in the Journal of Evolutionary Economics) can clearly trace its origins to Schumpeter’s work, as well as most modern economic modelling that deals with entrepreneurship and innovation. Read Schumpeter’s ideas and opinions in his own words.2 3

Schumpeter was born in Moravia, which at the time was in the Austro-Hungarian Empire (and is now in the Czech Republic). He migrated to the US after the Nazis won the election in 1932 that led to the formation of the Third Reich in 1933. He also experienced the First World War and the Great Depression of the 1930s, and died while writing an essay called ‘The march into socialism’, which recorded his concerns about the increasing role of government in the economy and the resulting ‘migration of people’s economic affairs from the private into the public sphere’. As a young professor in Austria, he fought and won a duel with the university librarian to ensure that students had access to books. He also claimed that as a young man he had three ambitions in life: to become the greatest economist in the world, the greatest horseman in Austria, and the best lover in Vienna. He added that only the decline of the cavalry had stopped him from succeeding in all three.

Question 2.8 Choose the correct answer(s)

Read the following statements about Schumpeter’s ideas, and choose the correct option(s).

  • Entrepreneurs are crucial for capitalist economic systems.
  • According to the idea of creative destruction, unprofitable firms are those that imitate the entrepreneur’s original innovation.
  • Schumpeter believed that creative destruction was a virtuous cycle.
  • Creative destruction contributes to fluctuations in economic output because it is a slow process.
  • Schumpeter thought that the entrepreneur had an important role: introducing new products and new methods of production, and opening up new markets.
  • Unprofitable firms are those that do not adapt to (or fail to imitate) the new technologies and therefore cannot compete in the market.
  • Schumpeter argued that creative destruction was a positive process because it generates a continued improvement in productivity, which leads to growth.
  • It takes time for the labour and capital goods from failed firms to be used in new combinations, which contributes to upswings and downswings in the economy.
  1. Joseph A. Schumpeter. 1949. ‘Science and Ideology’. The American Economic Review 39 (March): pp. 345–59. 

  2. Joseph A. Schumpeter. 1997. Ten Great Economists. London: Routledge. 

  3. Joseph A. Schumpeter. 1962. Capitalism, Socialism, and Democracy. New York: Harper & Brothers.