Law of Variable Proportions, MRTS, and Isoquants in Economics, Exercises of Development Economics

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Table of Contents

1. Law of Variable Proportions

2. MRTS

3. Isoquants

4. Economies & Diseconomies of Scale

5. Differences b/w Internal & External Economies of Scale

Law of Variable

Proportions

MRTS – Marginal

Rate of Technical

Substitutions

What Is the Marginal Rate of Technical Substitution – MRTS?

The marginal rate of technical substitution shows the rate at which you can

substitute one input, such as labor, for another input, such as capital, without

changing the level of resulting output.

same output level. The MRTS is represented by the absolute value of an isoquant's

slope at a chosen point.

A decline in MRTS along an isoquant for producing the same level of output is called

the diminishing marginal rate of substitution. The figure below shows that when a

firm moves down from point (a) to point (b) and it uses one additional unit of labor,

the firm can give up 4 units of capital (K) and yet remains on the same isoquant at

point (b). So the MRTS is 4. If the firm hires another unit of labor and moves from

point (b) to (c), the firm can reduce its use of capital (K) by 3 units but remains on

the same isoquant, and the MRTS is 3.

Isoquant

What Is an Isoquant?

An isoquant is a firm’s counterpart of the consumer’s indifference curve. An isoquant

is a curve that shows all the combinations of inputs that yield the same level of

Thus, an isoquant is a curve

showing all combinations of labor and capital that can be used to produce a given

quantity of output.

Isoquant Map

An isoquant map is a set of isoquants that shows the maximum attainable output from

any given combination inputs.

Properties of Isoquants

1. An isoquant lying above and to the right of another isoquant represents a higher level of output. This is because of the fact that on the higher isoquant, we have either more units of one factor of production or more units of both the factors. This has been illustrated in figure 3. In figure 3, points A and B lie on the isoquant IQ 1 and IQ 2 respectively. At point A we have = OX 1 units of Labor and OY 1 units of capital. At point B we have = OX 2 units of Labor and OY 1 units of capital. Though the amount of capital (OY 1 ) is the same at both the points, point B is having X 1 X 2 units of labor more. Therefore, it will yield a higher output.Hence, it is proved that a higher isoquant shows a higher level of output. 2. Two isoquants cannot cut each other Just as two indifference curves cannot cut each other, two isoquants also cannot cur each other. If they intersect each other, there would be a contradiction and we will get inconsistent results. This can be illustrated with the help of a diagram as in figure 4.

4. No isoquant can touch either axis If an isoquant touches the X-axis it would mean that the commodity can be produced with OL units of labor and without any unit of capital. Point K on the Y-axis implies that the commodity can be produced with OK units of capital and without any unit of labor. However, this is wrong because the firm cannot produce a commodity with one factor alone. 5. Isoquants are negatively sloped An isoquant slopes downwards from left to right. The logic behind this is the principle of diminishing marginal rate of technical substitution. In order to maintain a given output, a reduction in the use of one input must be offset by an increase in the use of another input.

Figure 8 shows that when the producer moves from point A to B, the amount of labor increases from OL to OL 1 , but the units of capital decreases from OK to OK 1 , to maintain the same level of output. The impossibility of horizontal, vertical or upward sloping isoquants can be shown with the help of the following diagrams. Consider figure 9(A) At point A, we have OL units of labor and OK units of capital and at B, we have OL 1 units of labor and OK units of capital. OL 1 + OK > OL + OK, and so combination B will yield a higher output than A. Therefore, points A and B on the IQ curve cannot represent an equal level of the product. Hence, the isoquant cannot be a horizontal straight line like AB. Consider figure 9(B) At point A, we have OL units of labor and OK units of capital. At point B, we have OL units of labor and OK 1 units of capital.

An important feature of an isoquant is that it enables the firm to identify the efficient range of production consider figure 11. Both the combinations Q and P produce the same level of total output. But the combination Q represents more of capital and labor than P. combinations Q must therefore be expensive and would not be chosen. The same argument can be made to rule out combination T or any other combination lying on a portion of the isoquant where the slope is positive. Positively sloped isoquants imply that an increase in the use of labor would require an increase in the use of capital to keep production constant. In general, for any input combination on the positively sloped portion of an isoquant, it is possible to find another input combination with less of both the inputs on the negatively convex portion that will produce the same level of output. Therefore, only the negatively sloped segment of isoquant is economically feasible.

In figure 12, the segment P 1 S 1 is the economically feasible portion of the isoquant for IQ. If we consider such feasible portions for all the isoquants, then the region comprising of these portions is called the economic region of production. A producer will operate in this region. It is shown in figure 12. The lines OP 1 P 2 and OS 1 S 2 are called ridge lines. Ridge lines may be defined as lines separating the downward sloping portions of a series of isoquants from the upward sloping portions. They give the boundary of the economic region of production.

When we talk about the scale of production of a firm, we often hear about the fact that

large-scale production, usually, helps in reducing the cost of production. Economies of

scale refer to these reduced costs per unit arising due to an increase in the total output.

Diseconomies of scale, on the other hand, occur when the output increases to such a

great extent that the cost per unit starts increasing. In this article, we will look at the

internal and external, diseconomies and economies of scale.

The difference between economies of scale and

diseconomies of scale

Economies of scale and diseconomies of scale are two related – but distinct

concepts. As explored further below, economies of scale arise from the cost of

production decreasing as the volumes increase. Diseconomies of scale are the

opposite – costs increasing as volumes increase.

Economies of scale: Savings that arise from increasing scale

Economies of scale arise from savings that are achieved as the volume of

production increases – the more you make of a product, the lower the cost per

item.

Common sales economies include:

o Purchasing materials at a better rate : There may be volume discounts

in the raw materials, arising from better bargaining power, savings on

delivery, or other cost savings relative to small or one-off purchases.

o Fixed costs are spread over a larger number of products : There are

likely fixed costs in operating, inured irrespective of the number of

products produced. These may include the rent on a facility, the cost of

machinery, or the cost of developing the product. When you manufacture

a larger volume of products, these costs are spread over a much larger

number of products, in turn pulling the fixed cost allocated to each

product lower.

o Labor cost per unit declines : Beyond costs that are entirely fixed, there

are certain variable costs that may decline the greater volume that you

produce. Greater volumes may allow more efficient routines to be

implemented, potentially reducing the labor component of each product

produced.

Diseconomies of scale: Additional costs that arise from increasing scale

Diseconomies of scale arise from savings that are achieved as the volume of

production increases – the more you make of a product, the lower the cost per

item.

Common sales economies include:

o Coordination difficulties : A key cause of diseconomies of scale is

associated with coordination difficulties as the firm grows. While it is easy

to manage a small organization, a large organization has a lot of moving

parts – each potentially pulling in different directions, with different

perceptions of what the firm is, and what it should be doing.

o Extra layers of management : Beyond the coordination difficulties that

can occur in large organizations, the extra layers of management add in

additional costs. There may be additional layers of management requires

to supervise operations, each with associated overhead expenses.

o Lack of focus on small improvements : Another possible source of

diseconomy of scale arises because particularly large firms may not be

interested in making minor incremental improvements. In part because of

coordination difficulties, and in part because of monitoring issues, there

may not be the incentives in place to drive managers to pursue small

efficiency improvements. Small changes may be thought not big enough

to move the needle, with a danger that waste and inefficiencies gradually

start to seep in.

The relation between economies of scale and diseconomies of scale

Economies of scale and diseconomies of scale are at odds with one another.

Initially, the size of the economies of scale may outweigh any diseconomies,

with the net effect being that costs decline as volume increases. However,

there comes a point where these effects start to plateau off – savings that

come from increasing production volumes may start to decline past a certain

point. For example, if you are making 1 million of a particular item, there may

only be relatively negligible better bargaining power with suppliers to increase

that to 10 million.

This can create a U-shaped relationship between production volumes and

costs – initially costs decline as economies of scale outweigh diseconomies,

but then past a certain point (the minimum efficient scale), the diseconomies of