This is the formula of the production function Q is quantity of output produced, L labour used and K is capital employed. Because there are three variables I would have to use the three- dimension graph, but there is an economic trade-off which reduces complex of three dimension graph to two dimensions. We will use an isoquant curve which originally represents combination of labour and capital that can produce a given level of output (Besanko, 2005). Capital is usually defined as machines, robots and computers. I suppose it is easier to understand general model of production function where we have labour and capital. But short after I introduce production function where labour and capital will be changed two variables - high tech and low tech labour.
Chart 1 Isoquant for the Production Function
(Adopted from Besanko D. & Breautigam, 2005 pg. 196)
Firm produces at level Q1. The isoquant Q1 combines two inputs; capital on vertical axis and labour on horizontal. We can change combination of inputs from point A (c;a) on Q1 curve to point B (d;b) on the same curve. As I said the combination of inputs had changed but the output did not vary. Theses substitutions are possible whenever both inputs have positive marginal products. When firms increase both inputs the output raises from Q1 to Q2.
Positive marginal product is the reason why isoquants are downward sloping and convex with the bend to the origin. There is a possibility of upward sloping backward bending isoquant but at those points production function is in the uneconomic region of production where marginal products are negative. But the cost minimizing firm would never produce in that region (Besanko, 2005).
Production function, Marginal product of labour and capital, isoquant have very important role in this discussion about high tech and low tech workers. The other very important issue is Marginal Rate of Technical Substitution of labour for capital. The MRTS is derived from steepness of isquant and it tells us the rate at which quantity of capital can be increased for every one unit increase in the quantity of labour, holding the output constant. I could further use example of production function where labour and capital are substituted, but according to the topic of assignment I will introduce high tech and low tech worker into this assignment. Obviously we will have to hold capital at constant level. For sake of argument, the level of capital in this case computers should be quite high. Chart 2 represents the MRTS of high tech workers for low tech workers.
Chart 2 MRTS H, L
(Adopted from Besanko D. & Breautigam, 2005 pg. 199)
The MRTS H, L along the Q= 1200 for a particular production function. At point A, the slope of tangent line is -6. Thus, MRTS H, L at point A is 6. That means that we can substitute 1 high tech worker hour for 6 low tech worker hours. At point B, the slope of tangent line is -2/3 and MRTS H, L is 2/3. It represents that at this point 1 high tech worker hours is possible to substitute with 10 minute of low tech worker. As we go down along Q curve the MRTS H, L gets smaller. This phenomenon is known as diminishing marginal rate of technical substitution. When the MRTS H, L decreases along Q curve while L increases the isoquant is convex to the origin. According to Besanko there is precise connection between MRTS H, L and the marginal product of high tech (MPH) and low tech (MPL) worker. When there is a change in both working hour units of computer literate and illiterate the change in output would be:
This equation shows that Marginal Rate of Technical substitution of low tech workers for high tech worker is the ratio of marginal product of low tech workers to the marginal product of high tech workers. According to Besanko Frank Lichtenberg made a study using data on employment and computer usage in the workplace. He estimated marginal rate of technical substitution of high tech workers – computer abs information system personnel- for low tech labour- workers employed in activities other than information system and technology. He held typical U.S. firm’s capital fixed and also assumed that the stock of computer equipment remained fixed as well. He data showed that MRTS of high tech labour to low-skilled was about 6. Once the firm has determined its stock of computers the computer literate worker can be substituted for 6 computer illiterate employees. Lichtenberg claim that reason why MRTS of high tech labour was so large was due to technical progress and investment. After the company invested in acquisition of computer equipment the marginal product of high tech workers was much higher than low tech workers.
Other measurement which can ease the debate between high tech and low tech labour could be elasticity of substitution. Specifically, this elasticity of substitution represents how quickly marginal rate of technical substitution of high tech labour for low tech labour changes as we move along Q curve. As high tech are substituting low tech labour the ratio between high tech and low tech workers, H/L, must fall. The marginal rate of technical substitutions of high tech labour for low tech labour also falls.
Once again let’s take a look at chart 2. At point A MRTS H, L = 6 and high tech – low tech ratio is 6 while at point B MRTS H, L= 2/3 and H/L ratios is 2/3 due to it ∆MRTS H, L = MRTSB H, L – MRTSA H, L = -5,333(3) and Σ=(-5, 333(3)/6) (6/-5,33(3))= 1. Besanko claims if elasticity is closer to 0, there is little opportunity of substitution between inputs and obviously the larger the elasticity the more opportunity to substitute.
Chart 3 Isoquant for the CES production
(Adopted from Besanko D. & Breautigam, 2005 pg. 208)
Chart 3 represents three (the red curves) most common models of production function. The production under L shaped curve has no substitutions. Linear production function has ∞ elasticity and is perfectly substituting labour for capital. The other three curves elasticity are between 0< Σ <∞ and are isoquant shape. Definitely workers with high tech skills and low tech labour lay in this section. Obviously it depends on type of company is employing these workers. Because one type of company demand more low tech labour, but if would look at telecommunications companies or electronic companies high tech workers have higher MRTS and lower elasticity.
Graph 4 Cost minimising problem with respect to the price of high tech workers
I thought about the example I could give which shows how does wages of workers determine company to employ high tech or low tech workers. Let’s look at the graph 4. The company’s total cost is represented with the isocost line TC for instance the company’s total cost is TC. Money incomes play a big role in this discussion. Wage rate is also important. If five years ago wages of computer literate and illiterate workers was the same and now it changed. High tech employee earns twice as much as low tech employee but he is 6 times more efficient than low tech worker. The company is better off employing 1 high tech worker than 3 low techs. The total cost function will display it clearly. And it is clear in the graph 4. The wage rate for high tech workers increased from w2 to w1. Obviously company had to deduct wages from low tech labour to cover the expense of high skilled workers. Their wage rate fell from w3 to w4. The changes in wages caused a pivot in TC and new cost minimising trade off was set on at point A. The pivot of isocost line had influence on new increase of MRTS of high tech workers for low tech.
Also one of the issues which could influence high tech and low tech workers preference in the company is market structure. According Besanko monopoly firms do not need to invest that much as companies in perfect competitions. As well there is no need to replace many low tech workers with high tech labour. For one good reason, monopoly does not have any competition as their product has got a constant demand and monopoly has a power of setting price. Competitive markets tend to invest more and use more high tech workers. For instance, in electronic equipment market a Samsung company around 10 years ago used to be a of cheap knockoffs products, but they had risen the investment and developed newest technology which was obviously handled by high tech workers. Now Samsung is one of the leading manufacturers of mobile phones and white goods (Lev- Ram, 2007)
To conclude with, there is still no clear definition if the high tech labour already changed low tech labour. Probably in some sectors of industries such as ICT, banking high tech employees already changed low tech. But there are still industries which need low tech workers who can complete manual jobs and just don’t need high tech skills in their lives. However, the technical progress main change this high tech- low tech ratio even more significantly if more efficient equipment will be invented which could successfully substitute people.
Bibliography:
Besanko D. A and Braeutingam. R.R, (2005) Microeconomics 2nd edition, Hoboken, NJ: John Willey & Sons, USA
Eurostat statistics ‘percentage of households that have access to computers in the U.K.
[accessed on 5th of January, 2008]
Lev-Ram M, ( 2007 August) Samsung's Identity Crisis . San Francisco: Vol. 8, Iss. 7; p.p. 60
[accessed on 5th of January, 2008]