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## Use of indifference curves in practice in solving society’s problems

In microeconomic theory, an indifference curve is a graph showing different bundles of goods, each measured to quantity, as to which the consumer is indifferent. That is at each point on the curve, the consumer has no preference for one bundle over another. In other words, they are all equally preferred. One can refer equivalently to each point on the curve as rendering the same level of utility (satisfaction) for the consumer. Indifferent curves can be applicable in various situations by analyzing demands and preferences of consumers towards different combinations of products. This analysis can the be applied in different circumstances including;

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It can be used in determining allocation of resources to production or social services. Firms and Government can employ indifference curves of different consumers to analyze what consumers prefer if faced with choice and limited resources. This can be measured by the marginal rate of substitution which indicates how much of one product or service is willing to give up to gain one unit of another. Those products with low marginal rate of substitution seem to be preferred by consumers and hence government and/or firms should produce more of such products.

i) ii)

A

A

B B

In the above illustration, if there are limited resources, indifference curve (i) indicates that the consumer prefers product A to B since he is willing to give up more of B to gain a unit of A. The opposite is true in Figure (ii). This indicates that if resources are limited, production of the preferred good should be allocated more resources than the other good.

Indifference curves can also be applied by firms to decide what attributes in a product consumers value most. By knowing what attributes consumers prefer most, companies are able to make decisions relating to what improvements in products are important to customers. Companies will therefore employ resources in improvements that add value to customers thus being effective and efficient in satisfying consumer wants.

i) ii)

A

A

B B

In figure (i), if A and B are attributes in a product, then consumers in figure (i) will be preferring attribute A to B and hence companies are better of improving attribute a to get more customers and to satisfy them. The opposite is true in figure (ii).

iii) Indifference curves can also be used by government in its fiscal policies. The slope of indifference curves can be used to evaluate those goods that customers value more and are unwilling to give up. In such a case, when prices of such goods go up, the government can subsidize such products so that consumers can continue to afford them. The same policy can also be applied in taxation where those products that are producing externalities are taxed more to discourage their use.

A i ii

B

In the above figure, customers value product B to A since they give up more units of A to get fewer units of A. In case of a subsidy on the product that consumers value, the consumer moves from the lower indifference curve and goes to a higher indifference curve thus increasing value to consumers. The consumer in the process lowers the consumption of the less preferred product.

iv) Indifference curves can also be used by firms and producers to evaluate the effect of change in income and price of goods on consumption patterns. Substitution and income effects which can be analyzed through indifference curves shows how consumption of a good will change with changes in income, price of the good or prices of other goods. A drop in the price of one good without any compensating change in income or other prices produces both a substitution effect and an income effect. The substitution effect always increases the consumption of the good whose price has fallen; the income effect may increase or decrease it depending on the type of good.

The above diagram indicates what would happen to consumption of tea and turnips if there was taxation on tea or the price of tea was increased from 2.5 to 4. This would lead to less tea being consumed and more turnips being consumed. A firm before it decides to increase prices can benefit from such analysis.

v) Indifference curves can also be applied in determining wages for different individuals to give up their leisure for work.

i) ii)

W

W

L L

In figure i, the individual values leisure more than work while in figure ii, the individual values work more than leisure. This indicates that an organization will have to pay individual i, more money to make him give up his leisure than they are required to pay individual ii. Individual I can therefore cost more and work less hours than individual ii.

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## Question two

The laws of returns to scale States that as a firm in the long run increases the quantities of all factors employed, other things being equal, the output may rise initially at a more rapid rate than the rate of increase in inputs, then output may increase in the same proportion of input, and ultimately, output increases less proportionately.

## Q=aLbCc

Where Q stands for output, L for labor, and C for capital. The parameters a, b, and c (the latter two being the exponents) are estimated from empirical data. This model indicates that as you change labour and capital, output is bound to change.

## Assumptions:

Technique of production is unchanged.

All units of factors are homogeneous.

Returns are measured in physical terms.

There are three phases of returns in the long run; the law of increasing returns, the law of constant returns, the law of diminishing returns.

The law of Increasing Returns describes increasing returns to scale. There are increasing returns to scale when a given percentage increase in input will lead to a greater relative percentage increase in output; where proportionate change in output is greater than proportionate change in inputs (factors). In the long run, Production Function Coefficient (PFC) is measured by the ratio of proportionate change in output to proportionate change in input. âˆ†Q/Q = âˆ†Q x F.

## A Cobb Douglass Production function

The process of increasing returns cannot go on for ever. It is followed by constant returns to scale. While expanding its scale of production, the firm gradually exhausts the economies responsible for increasing returns. Thereafter, constant returns occur when PFC coefficient is = 1, it will be constant returns to scale.

As expansion is continued, growing diseconomies of factors are encountered. When powerful diseconomies are met by feeble economies of certain factors, decreasing returns to scale results. This happens when PFC (production function coefficient) < 1. causes of decreasing returns may be;

Though all physical factors are increased proportionately, organization and management as a factor cannot be increased in equal proportion.

Business risk increases more than proportionately when scale of production is enhanced. Entrepreneurial efficiency also has its limitations.

Growing diseconomies of large-scale production set in when scale of production increases beyond a limit.

Problem of supervision and coordination becomes complex and intractable in a large scale operation and becomes unwieldy to manage

This law of returns to scale can be applied in production and allocation of resources in different sectors. When a business is expanding all factors of production, the law applies and if expansion goes on and on, decreasing returns to scale will result. This gives the firm the ultimate position to produce in where more increase in factors will not result in increase in output.

The technological physical relationship between inputs and outputs per unit of time, is referred to as production function. The relationship between the inputs to the production process and the resulting output is described by a production function. The production function is the name given to the relationship between rates of input of productive services and the rate of output of the product. It is the economist’s summary of technical knowledge. The level of production depends on technical conditions. If there is improvement in the technique of production, increased output can be obtained even with the same (fixed) quantity of factors. However, at a given point of time, there is only one maximum level of output that can be obtained with a given combination of factors of production. This technical law which expresses the relationship between factor inputs and output is termed as production function. This is applied by firms to determine the best combination of factors of production so as to result in optimum returns.

Returns to scale are important for determining how many firms will populate an industry. When increasing returns to scale exist, one large firm will produce more cheaply than two small firms. Small firms will thus have a tendency to merge to increase profits, and those that do not merge will eventually fail. On the other hand, if an industry has decreasing returns to scale, a merger of two small firms to create a large firm will cut output, raise average costs, and lower profits. In such industries, many small firms should exist rather than a few large firms.

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