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Unformatted text preview: century, technological progress has dramatically altered
the production of food in most countries, including many developing countries, so that the marginal product of labor has increased. These improvement include new high-yielding and disease-resistant strains of
seeds, better fertilizers, and better harvesting equipment. Food production overall throughout the world
has outpaced population growth more or less continually since the end of World War 2.
4 Hunger remains a severe problem in some areas in part because of the low productivity of labor force.
Although other countries can export agricultural products to these areas, mass hunger still occurs because
of the difﬁculty of redistributing foods to remote places and because of the low incomes of those less productive regions. 3.4 Marginal Rate of Technical Substitution Firms using more than two inputs for production needs to consider the best combinations of these inputs
to maximize proﬁts. Skilled workers (say university graduates) and less skilled workers may be quite
substitutable for providing simple services, for example those in Tim Hortons or in MacDonald. In contrast,
they may not be so substitutable in a workplace which requires advanced analytical skills. The marginal
rate of technical substitution is the key concept to describe the ”substitutability” of production inputs.
Suppose that we are operating with some input combination ( x1 , x2 ) and that we consider giving up a
little bit of factor 1 and using just enough more of factor 2 to produce the same amount of output y. How
much extra of factor 2, D x2 , do we need if we are going to give up a little bit of factor 1, D x1 ? This is just the
negative of the slope of the isoquant D x2 , which is commonly referred to as the marginal rate of technical
substitution, and denoted by MRTS12 :
MRTS12 = D x2
D x1 output is held constant (2) The marginal rate of technical substitution measures the tradeoff between two inputs in production. It
measures the rate at which the ﬁrm will have to substitute one input for another in order to keep output
To relate the formula for the MRTS to marginal products, we can use the same idea that we used to
determine the slope of the indifference curve. Consider a change in our use of factors 1 and 2 that keeps
output xed. Then we have
Dy = 0 = MP1 D x1 + MP2 D x2
which we can solve to get
MRTS12 = 3.5 D x2
D x1 =
D y =0 M P1
MP2 D y =0 (4) Returns to Scale Now let’s consider a different kind of experiment. Instead of increasing the amount of one input while
holding the other input ﬁxed, let’s increase the amount of all inputs to the production function. In other
words, let’s scale the amount of all inputs up by some constant factor: for example, use twice as much of
both factor 1 and factor 2. If we use twice as much of each input, how much output will we get? The most
likely outcome is that we will get twice as much output. This is called the case of constant return...
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- Summer '13