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Free AIOU Solved Assignment Code 801 Spring 2023
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Course: Introduction to Macroeconomics (801)
Semester: Spring, 2023
ASSIGNMENT No. 1
Q.1 What are the main criteria’s for classifying firms into industries. In your opinion which criteria serve the better?
Two criteria are commonly used for the definition of an industry, the product being produced (market criterion), and the methods of production (technological criterion).
According to the first criterion firms are grouped in an industry if their products are close substitutes. According to the second criterion firms are grouped in an industry on the basis of similarity of processes and/or of raw materials being used.
Which classification is more meaningful depends on the market structure and on the purpose for which the classification is chosen. For example, if the government wants to impose excise taxes on some industries the most meaningful classification of firms would be the one based on the product they produce. If, on the other hand, the government wants to restrict the imports of some raw material (e.g. leather), the classification of firms according to similarity of processes might be more relevant.
1. Market Criterion: Similarity of Products:
Using this criterion we include in an industry those firms whose products are sufficiently similar so as to be close substitutes in the eyes of the buyer.
The degree of similarity is measured by the cross-elasticity of demand, which we defined as:
ec = dqj / dpi. pi / qj
Where qj = quantity produced by the jth firm
Pi = price charged by the ith firm.
What is the required value of the cross-elasticity in order to classify the ith and jth firms in the same industry? The answer to this question cannot be based on a priori theoretical grounds if the products are differentiated. In this event the degree of closeness or similarity is defined on an empirical basis, depending on the purpose of the study in each particular case. For some purposes a broad definition of products is more appropriate, while for other purposes a narrower definition based not only on the technical substitutability but also on the economic substitutability (in the sense of similar price ranges) of commodities, may be more desirable.
For example, the motor-car industry would include all types of motor-cars, from the cheapest Mini to the most expensive Rolls- Royce and the specialized sports cars. This classification is used by the tax authorities in Britain where car taxation is uniform for all types of cars. However, this classification is not appropriate if one wants to analyze the pricing decisions of the car manufacturers. For this purpose one should use a narrower definition of an industry, for example the ‘popular’ models, the ‘luxury’ models and the ‘sports’ models. In each such ‘group’ the products are both technical and economic substitutes.
It is useful to examine the concept of an industry as applied in the different traditional market structures, so as to illustrate the importance of substitutability. In pure competition the application of the product criterion for the definition of an industry is straightforward. In this market structure the product is assumed to be homogeneous and the number of sellers is large. Under these conditions the cross- elasticity of demand for the product of each firm is infinite. There is perfect substitutability between the products of the various firms and this leads to a unique price in the market, since no buyer would be prepared to pay a higher price for a product technically identical with that of other firms.
In monopolistic competition products are differentiated by design, quality, services associated with its supply, trademarks, etc. Thus the products are not perfect substitutes in the eyes of the buyer, and the question arises of how close substitutes the commodities must be if they are to be grouped in the same ‘industry’. Both Chamberlin and Joan Robinson recognized that with differentiated products each firm has its own market, and hence some degree of monopoly power in setting its own price.
However, they both recognized the necessity of retaining the concept of an industry in order to give their theory the required degree of generality, and develop it within the partial- equilibrium framework. Joan Robinson defined the product as ‘a consumable good, arbitrarily demarcated from other kinds of goods, but which may be regarded for practical purposes as homogeneous within itself’.
Thus, she views products as forming a chain of substitutes, the continuity of which is broken by gaps between successive products along the chain. Products thus isolated by such gaps can be classified in an industry despite their minor differences. Basically this definition of the industry uses the measure of price cross-elasticity.
An industry includes the firms whose demand curves exhibit high price cross-elasticity. She brushed aside the problem of how high this cross- elasticity should be by assuming that there would be gaps in the values of cross-elasticity and these gaps would demarcate the industrial groups.
A similar definition was adopted by Kaldor. He views products as occupying a given position on a scale, with products on either side being more close substitutes as compared with products further away on this scale
Each ‘product’ can be conceived as occupying a certain position on a ‘scale’; the scale being so constructed that those products are neighbouring each other between which the consumer’s elasticity of substitution is the greatest (a ‘product’ itself can be defined as a collection of objects between which the elasticity of substitution of all relevant consumers is infinite). Each producer then is faced on each side with his nearest rivals; the demand for his own product will be most sensitive with respect to the prices of these; less and less sensitive as one moves further away from him.
Chamberlin, in his original formulation of the Theory of Monopolistic Competition (Harvard University Press, 1933) defined his large ‘group’ as comprising firms which produce very similar although differentiated commodities:’… The difference between (the varieties of products) are not such as to give rise to differences in cost. This might be approximately true where say similar products are differentiated by trade marks’. The conceptual and empirical difficulties implied in the above definition of an industry lead Triffin to preach the abandonment of the concept of the industry as being inconsistent with the notion of ‘product differentiation’ and the unique character of each firm’s product.
The monopolistic competition writers resorted to the limping device of keeping intact, for the purpose of analysis, that concept of an industry, which their study of differentiation showed to be untenable. Triffin argued that all goods are to some degree substitutable for one another in that they compete for a part of the income of the consumer. Every firm competes with all the other firms in the economy, but with different degrees of closeness. Thus, he concluded, the concept of an industry is irrelevant as a tool of analysis. The best way for analyzing the economic relationships of firms is to adopt a general equilibrium approach. This view was later adopted by Chamberlin.
Andrews has severely criticized the abandonment of the concept of an industry. He argued that the rejection of the concept of the industry is both unnecessary and undesirable. The concept is of great importance both in economic analysis and in real- world situations. Andrews advocated the classification of industries on the basis of similarity of processes, arguing that this classification is more relevant for analyzing the pricing decisions of the firm (see below).
Edwards in dealing with oligopolistic markets, has attempted to retain the definition of an industry in terms of the product. He argues that the retention of the concept of an industry as a tool of analysis is essential to the economist as well as to the businessman and the government. He says that product differentiation does not necessitate the abandonment of the concept of an industry. He accepts Chamberlin’s view that a ‘group’ or ‘industry’ is not a definite economic entity (with definite edges) like the Marshallian concept of an industry, but an analytical tool which should be used with all degrees of generality.
In a broad definition an industry includes all the range of products which are technical substitutes in that they satisfy the same need (for example the motor-car industry includes all firms which produce all types of cars). Within this broad group of products there are definite subgroups (popular models, luxury models, sports cars) which tend to have very similar technical characteristics.
Thus, for each subgroup there will be a unique price in the long run (because the products are technically identical or very similar and there will be no cost differences), but consumers’ preferences create a separate market for each firm. For the broad group of products there will be a cluster of prices in the long term reflecting the differences in the technical characteristics and therefore the differences in costs of the different varieties.
Edwards argues that there is a tendency in British manufacturing for the pattern of production within an industry (in the broad definition) to stabilize (in normal conditions) into a conventional product-pattern with a corresponding conventional price-pattern (Edwards, Monopoly and Competition in the British Soap Industry).
If the price-quality pattern is strictly stable then the various subgroups of products can be treated as one for demand purposes. Edwards recognizes that in the real world the price-quality pattern does not in fact remain strictly stable. However, he argues that the degree of stability is sufficient to justify the assumption that the price-quality is approximately constant and can be treated as such for all practical purposes.
2. The Technological Criterion: Similarity of Processes:
According to this criterion, an industry is defined so as to include firms which use similar processes of production. The similarity may lie in the methods of production, the raw materials used, or the channels of distribution. Chamberlin, before Triffin’s attack on his ‘large group’ model, attempted the extension of the concept of the industry to cover the supply aspects of a market. He said that the ‘group’ need not necessarily be defined on the basis of the substitutability between products. Industry classifications based upon technological criteria rather than upon the possibility of market substitution were perfectly legitimate for all purposes.
Andrews also advocated the definition of an industry on the basis of similarity of processes. Joan Robinson in her later writings recognized that her original definition of the industry was not adequate for oligopolistic market structures and suggested a redefinition of the industry based on the technological criterion of similarity of processes
The concept of an industry, though amorphous and impossible to demarcate sharply at the edges, is of importance for the theory of competition. It represents the area within which a firm finds it relatively easy to expand as it grows. There are often certain basic processes required for the production of the most diverse commodities (tennis balls, motor tyres and mattresses) and economies in the utilization of by-products under one roof.
The know-how and trade connections established for one range of products make it easier to add different commodities of the same technical nature to a firm’s output than it is to add mutually commodities made of different materials, or made or marketed by radically different methods. It should be noted that the technological criterion of similarity of processes suffers from the same defects as the product-substitutability criterion. How similar should the processes employed by various firms be in order to group them in the same industry? The advocates of the technological criterion do not discuss such problems.
In conclusion we can say that in markets where the product is differentiated the ‘industry’ concept cannot be as definite as in markets where the product is homogeneous. The definition of the borderlines between industries will be to some extent arbitrary, irrespective of the criterion used for the classification of firms into industries.
Regarding the two criteria traditionally used for industrial classifications, no general conclusion can be drawn as to which is better. The choice depends on the purpose of the classification. It seems, however, that the integration of the two criteria (substitutability of products and technological similarity of processes) is most desirable in analyzing the behaviour of the firm in oligopolistic market structures which are typical of the modern business world.
It is generally accepted that entry considerations are important in explaining the observed behaviour of firms. Entry cannot be satisfactorily analysed unless both the demand substitutability and the supply conditions are simultaneously considered. It is via substitutability of the products that the entry of additional firms can affect the demand of established firms. Thus the effects of entry cannot be analysed on the basis of technological similarity alone.
In general all decisions of firms (pricing, level of output, changes in style, selling activities, financial policies, investment decisions) are taken in the light of actual as well as of potential competition by new entrants. This suggests that product considerations as well as technological similarities of processes should be integrated in analyzing the behaviour of firms.
AIOU Solved Assignment Code 801 Spring 2023
Q.2 Using necessary and sufficient conditions, explain consumer’s equilibrium diagrammatically as well as mathematically.
A consumer is said to be in equilibrium when he feels that he “cannot change his condition either by earning more or by spending more or by changing the quantities of thing he buys”. A rational consumer will purchase a commodity up to the point where price of the commodity is equal to the marginal utility obtained from the thing.
If this condition is not fulfilled the consumer will either purchase more or less. If he purchases more, MU will go on falling and a situation will develop where price paid will exceed MU. In order to avoid negative utility, i.e., dissatisfaction, he will reduce consumption and MU will go on increasing till P = MU.
On the other hand, if MU is greater than the price paid, the consumer will enjoy surplus satisfaction from the units he has already consumed. This will induce him to buy more and more units of the commodity leading to successive fall in MU till it is equated to its price. Thus, by a process of trial and error — by buying more or less units, a consumer will ultimately settle at the point where P = MU. Here, his is total utility is maximum.
However, P = MU is a necessary but not a sufficient condition for a consumer’s equilibrium. In Fig. 4, we find that the MU curve is intersecting the price curve PP at two different points M and N. So far M is concerned, although by having OA quantity the consumer is reaching the point where P – MU but it is not equilibrium.
For by purchasing extra units above OA he can enjoy surplus satisfaction. Why then will he stop at OA? He will continue using the thing till he reaches OB. If he goes beyond this point, for every extra unit P is greater than MU and he shall have to suffer dissatisfaction. Thus, the sufficient condition of consumer equilibrium is that the MU curve must cut the price curve at its downward segment and not at its rising segment.
The objective of a rational consumer is to maximise utility (welfare) subject to:
(1) A fixed level of money income
(2) A fixed set of commodity prices.
Now, what is fundamental equilibrium condition that has to be satisfied if a consumer is spending his income on different goods so as to make himself truly best off in terms of utility or satisfaction?
Certainly he would not expect that the last egg he is buying brings him exactly the same marginal utility as the last cake he is buying. One cake costs much more than an egg. One may guess that he should go on buying a good which costs twice as much per unit as another until he ends up in his equilibrium bringing him just twice as much in marginal utility.
Thus, if the consumer has arranged his consumption so that every single good brings him marginal utility just exactly proportional to its price, then he could not gain extra utility and thus improve his position by departing from such an equilibrium.
This fundamental condition can now be stated:
A consumer with a fixed money income and facing a fixed set of market prices of goods can reach equilibrium or the level of maximum satisfaction or utility only when he acts thus;
Law of equal marginal utilities per rupee:
Each good — such as egg — is demanded up to the point where the marginal utility per rupee spent on it is exactly the same as the marginal utility of a rupee spend on any other good—such as cake.
Why does this law hold? If any one good gave more marginal utility per rupee the consumer would gain by taking money away from other goods and spending more on that good — up to the point where the law of diminishing marginal utility brought its marginal utility per rupee down to equality. If any good gave less marginal utility per rupee than the common level, the consumer would buy less of it’s until the marginal utility of the last rupee spent on it had risen back to the common level.
The Law of Equi-marginal Utility (or the Principle of Substitution) follows from the Law of Diminishing Marginal Utility. According to the latter, a person goes on buying the units of a commodity one after another till its marginal utility becomes equal to its price. In the case of more than one commodity, he examines the marginal utility of the last unit of money spent on the different commodities.
More precisely, for the maximisation of satisfaction, income must be allocated in such a way that the marginal utility of an unit of money’s worth (for example, one rupee’s worth) is the same for every commodity. If it is found that the marginal utility of the last unit of money spent on say, X commodity is greater than that derived from another commodity, say, Y commodity, he substitutes X for Y. Such a process of substitution goes on till the marginal utility of the last unit of money spent on X and on Y becomes equal to each other.
Beyond this point, further substitution will not be beneficial to him, for that would involve a decrease in his total utility. This is known as the Law of Equi-marginal Utility. Marshall puts the Law in the following words: “If a person has a thing which he can put to several uses, he will distribute it between these uses in such a way that it has the same marginal utility in all”. If he has a greater utility in one use than in another, he would gain by taking away some of it from the second use and applying it to the first.
Proof of the Law:
The Law of Equi-marginal Utility can be proved as follows- Let us suppose that a person has Rs. 5 to spend on X and Y commodities during a particular period of time, say a day, and he gets marginal utility from each of these two commodities as shown in the following table:
The table shows that a person can either spend all the five rupees on X or Y or divide these between the two. If he spends all the five rupees on X, the last rupee spent on X would give 10 units utility, but if that rupee is spent on Y (i.e., four rupees for X and one rupee for Y) he will get a greater amount of utility. So, he will substitute Y for X.
This process continues till the marginal utility of the last rupee spent on X and on Y will give him the same marginal utility, and he will attain this stage when he spends Rs. 3 on X and Rs. 2 on Y. At this stage, his total utility from his spending will become (25 + 20 + 16 = 61 units from X and 23 + 16 = 37 units from Y) 98 units and this will be the maximum amount of total utility that he can get from his spending. Thus, if a person equalises the marginal utility from each of his purchases, he gets the maximum amount of satisfaction. So, the doctrine of maximum satisfaction can be deduced from this law.
This law can also be explained in another way to show the optimum purchase of the consumer or the consumer’s equilibrium. A consumer buys a commodity up to that amount at which its price is equal to its marginal utility. In the case of purchase of many commodities, maximum satisfaction requires the allocation of income in such a way that the marginal utilities of units of various goods bought are proportional to their prices.
In other words, if apples cost twice as much per kg. as potatoes, the consumer must adjust his purchases of these two goods until the marginal utility of a kg. of apple is twice as great as the marginal utility of a kg. of potatoes. So, in equilibrium, the marginal utilities of the different commodities purchased are proportional to their prices and these ratios of marginal utility to price must be equal to the common marginal utility of money.
If he distributes his expenditure rationally among commodities, X, Y, Z, etc., the following relationship will hold good in equilibrium:
MU of X/ Price of X = MU of Y/Price of Y = MU of Z/Price of Z = MUM
where MUM is the common marginal utility of money (i.e., marginal utility of a rupee).
The equi-marginal principle can be illustrated in Fig. 5 to show the maximum satisfaction.
Fig.1 illustrates quantity consumed of two commodities, X shown on the right side and Y on the left side. The marginal utility curves for each use are also shown. The curve X is farther from the vertical axis (OM) than the Y curve to indicate the relatively stronger desire for X.
Let us suppose that a consumer has Rs. 5 to spend and PX = PY = Re.1. Given the MU curves for X and Y the best allocation of his income is 3 units of X and 2 units of Y, because with these quantities the marginal utilities are equal. Any other allocations will lower the total satisfaction (the entire shaded area in the diagram).
Let us show it by devoting 4 units in X and 1 unit in Y. In such a case, the area between 3 and 4 under M U curve of X would be a gain, but there would be a loss of the area between 2 and 1 under the MU curve of Y. Clearly the loss is greater than the gain. Any other allocations excepting 3 units in X and 2 units in Y would give the consumer a lower total utility.
AIOU Solved Assignment 1 Code 801 Spring 2023
Q.3 Derive consumer and market demand curves from indifference curves.
A demand curve shows how much quantity of a good will be purchased or demanded at various prices, assuming that tastes and preferences of a consumer, his income, prices of all related goods remain constant.
This demand curve showing explicit relationship between price and quantity demanded can be derived from price consumption curve of indifference curve analysis.
In Marshallian utility analysis, demand curve was derived on the assumptions that utility was cardinally measurable and marginal utility of money remained constant with the change in price of the good. In the indifference curve analysis, demand curve is derived without making these dubious assumptions.
As price of good X falls from Rs. 15 to Rs. 10, the budget line shifts to PL2. Budget line PL2 shows that price of good X is Rs. 10. With a further fall in price to Rs. 7.5 the budget line takes the position PL3. Thus PL3 shows that price of good X is Rs. 7.5. When price of good X falls to Rs. 6, PL4 is the relevant budget line.
The various budget lines obtained are shown in the column 2 of the Table 8.3. Tangency points between the various budget lines and indifference curves, which when joined together by a line constitute the price consumption curve shows the amounts of good X purchased or demanded at various prices.
With the budget line PL1 the consumer is in equilibrium at point Q1 on the price consumption curve PCC at which the budget line PL1 is tangent to indifference curve IC1. In his equilibrium position at Q1 the consumer is buying OA units of the good X. In other words, it means that the consumer demands OA units of good X at price Rs. 15.
When price falls to Rs. 10 and thereby the budget line shifts to PL2, the consumer comes to be in equilibrium at point Q2 the price-consumption curve PCC where the budget line PL2 is tangent to indifference curve IC2. At Q2, the consumer is buying OB units of good X.
In other words, the consumer demands OB units of the good X at price Rs. 10. Likewise, with budget lines PL3 and PL4, the consumer is in equilibrium at points Q3 and Q4 of price consumption curve and is demanding OC units and OD units of good X at price Rs. 7.5 and Rs. 6 respectively. It is thus clear that from the price consumption curve we can get information which is required to draw the demand curve showing directly the amounts demanded of the good X against various prices.
The above demand schedule which has been derived from the indifference curve diagram can be easily converted into a demand curve with price shown on the V-axis and quantity demanded on the X-axis. It is easier to understand the derivation of demand curve if it is drawn rightly below the indifference curve diagram.
In the diagram at the bottom, where on the X-axis the quantity demanded is shown as in indifference curves diagram in the top pannel, but on the Y- axis in the diagram in the bottom panel price per unit of the good X is shown instead of total money. In order to obtain the demand curve, various points K, L, S and T representing the demand schedule of the above table are plotted. By joining the points K, L, Sand T we get the required demand curve DD.
In most cases the demand curve of individuals will slope downward to the right, because as the price of a good falls both the substitution effect and income effect pull together in increasing the quantity demanded of the good. Even when the income effect is negative, the demanded curve will slope downward to the right if the substitution effect is strong enough to overwhelm the negative income effect. Only when the negative income effect is powerful enough to outweigh the substitution effect can the demand curve slope upward to the right instead of sloping downward to the left.
The demand curve slopes downward because of two forces, namely, income effect and substitution effect. Both the income effect and substitution effect usually work towards increasing the quantity demanded of the good when its price falls and this makes the demand curve slope downward. But in case of Giffen good,the demand curve slopes upward from left to right.
This is because in case of a Giffen good income effect, which is negative and works in opposite direction to the substitution effect, outweighs the substitution effect. This results in the fall in quantity demanded of the Giffen good when its price falls and therefore the demand curve of a Giffen good slopes upward from left to right. Price consumption curve of a Giffen good slopes backward. In order to simplify the discussion in this figure we have avoided the numerical values of prices and have instead used symbols such as, P1, P2, P3 and P4 for various levels of the price of good X.
With the fall in price from P1 to P2 and shifting of budget line from PL1 to PL2, the consumer goes to the equilibrium position Q3 at which he buys OM2 amount of the good. OM2 is less than OM1. Thus with the fall in price from P1 to P2 the quantity demanded of the good falls. Likewise, the consumer is in equilibrium at Q3 with price line PL3 and is purchasing OM3 at price P3.
To sum up, in most cases (that is, in case of normal goods) the demand curve of individuals will slope downward to the right, because as the price of a good falls both the substitution effect and income effect pull together in increasing the quantity demanded of the good. Even in case of inferior goods for which the income effect is negative, the demand curve will slope downward to the right if the substitution effect is strong enough to overwhelm the negative income effect. Only in case of Giffen goods for which the negative income effect is powerful enough to outweigh the substitution effect, the demand curve slopes upward to the right intend of sloping downward to the left.
AIOU Solved Assignment 2 Code 801 Spring 2023
Q.4 a) Explain “law of variable proportions” in the light of classical production function.
Law of Variable Proportions occupies an important place in economic theory. This law is also known as Law of Proportionality.
Keeping other factors fixed, the law explains the production function with one factor variable. In the short run when output of a commodity is sought to be increased, the law of variable proportions comes into operation.
Therefore, when the number of one factor is increased or decreased, while other factors are constant, the proportion between the factors is altered. For instance, there are two factors of production viz., land and labour.
Land is a fixed factor whereas labour is a variable factor. Now, suppose we have a land measuring 5 hectares. We grow wheat on it with the help of variable factor i.e., labour. Accordingly, the proportion between land and labour will be 1: 5. If the number of laborers is increased to 2, the new proportion between labour and land will be 2: 5. Due to change in the proportion of factors there will also emerge a change in total output at different rates. This tendency in the theory of production called the Law of Variable Proportion.
“As the proportion of the factor in a combination of factors is increased after a point, first the marginal and then the average product of that factor will diminish.” Benham
“An increase in some inputs relative to other fixed inputs will in a given state of technology cause output to increase, but after a point the extra output resulting from the same additions of extra inputs will become less and less.” Samuelson
“The law of variable proportion states that if the inputs of one resource is increased by equal increment per unit of time while the inputs of other resources are held constant, total output will increase, but beyond some point the resulting output increases will become smaller and smaller.” Leftwitch
Law of variable proportions is based on following assumptions:
(i) Constant Technology:
The state of technology is assumed to be given and constant. If there is an improvement in technology the production function will move upward.
(ii) Factor Proportions are Variable:
The law assumes that factor proportions are variable. If factors of production are to be combined in a fixed proportion, the law has no validity.
(iii) Homogeneous Factor Units:
The units of variable factor are homogeneous. Each unit is identical in quality and amount with every other unit.
The law operates in the short-run when it is not possible to vary all factor inputs.
In order to understand the law of variable proportions we take the example of agriculture. Suppose land and labour are the only two factors of production.
By keeping land as a fixed factor, the production of variable factor i.e., labour can be shown with the help of the following table:
From the table 1 it is clear that there are three stages of the law of variable proportion. In the first stage average production increases as there are more and more doses of labour and capital employed with fixed factors (land). We see that total product, average product, and marginal product increases but average product and marginal product increases up to 40 units. Later on, both start decreasing because proportion of workers to land was sufficient and land is not properly used. This is the end of the first stage.
The second stage starts from where the first stage ends or where AP=MP. In this stage, average product and marginal product start falling. We should note that marginal product falls at a faster rate than the average product. Here, total product increases at a diminishing rate. It is also maximum at 70 units of labour where marginal product becomes zero while average product is never zero or negative.
The third stage begins where second stage ends. This starts from 8th unit. Here, marginal product is negative and total product falls but average product is still positive. At this stage, any additional dose leads to positive nuisance because additional dose leads to negative marginal product.
In fig. 1, on OX axis, we have measured number of labourers while quantity of product is shown on OY axis. TP is total product curve. Up to point ‘E’, total product is increasing at increasing rate. Between points E and G it is increasing at the decreasing rate. Here marginal product has started falling. At point ‘G’ i.e., when 7 units of labourers are employed, total product is maximum while, marginal product is zero. Thereafter, it begins to diminish corresponding to negative marginal product. In the lower part of the figure MP is marginal product curve.
Up to point ‘H’ marginal product increases. At point ‘H’, i.e., when 3 units of labourers are employed, it is maximum. After that, marginal product begins to decrease. Before point ‘I’ marginal product becomes zero at point C and it turns negative. AP curve represents average product. Before point ‘I’, average product is less than marginal product. At point ‘I’ average product is maximum. Up to point T, average product increases but after that it starts to diminish.
Three Stages of the Law:
1. First Stage:
First stage starts from point ‘O’ and ends up to point F. At point F average product is maximum and is equal to marginal product. In this stage, total product increases initially at increasing rate up to point E. between ‘E’ and ‘F’ it increases at diminishing rate. Similarly marginal product also increases initially and reaches its maximum at point ‘H’. Later on, it begins to diminish and becomes equal to average product at point T. In this stage, marginal product exceeds average product (MP > AP).
2. Second Stage:
It begins from the point F. In this stage, total product increases at diminishing rate and is at its maximum at point ‘G’ correspondingly marginal product diminishes rapidly and becomes ‘zero’ at point ‘C’. Average product is maximum at point ‘I’ and thereafter it begins to decrease. In this stage, marginal product is less than average product (MP < AP).
3. Third Stage:
This stage begins beyond point ‘G’. Here total product starts diminishing. Average product also declines. Marginal product turns negative. Law of diminishing returns firmly manifests itself. In this stage, no firm will produce anything. This happens because marginal product of the labour becomes negative. The employer will suffer losses by employing more units of labourers. However, of the three stages, a firm will like to produce up to any given point in the second stage only.
- b) Optimize the following Cobb-Douglas production function subject to the given constraints by
- i) Forming Lagrange function ii) Finding the critical values.
Subject to 2K + 6L = 380
Lagrange function (ζ) = 2K + 6L + λ (380 – K^0.3 L^0.3)
d ζ / dL = 6 – λ (0.3) K^0.3 L^-0.7 = 0…………………1
d ζ / dK = 2 – λ (0.3) K^-0.7 L^0.3 = 0………………….2
d ζ / d λ = 380 – K^0.3 L^0.3…………………………….3
λ = 6 / 0.3 (L^0.7 / K^0.3)
λ = 20 (L^0.7 / K^0.3)…………..4
λ = 2 / 0.3 (K^0.7 / L^0.3)……….5
From 4 and 5
λ = λ
3 (L^0.7 / K^0.3) = (K^0.7 / L^0.3)
3 (L^0.7 * L^0.3) = K^0.7 K^0.3
q = (3L)^0.3 L^0.3
q = 3^0.3 L^ 0.6
380 = 3^0.3 L^0.6
380 / 1.390 = L^0.6
273.304 = L^0.6
L = 11467.063
L = 11467
K = 3(11467)
K = 34401
L = 11467 and K = 34401 required result.
AIOU Solved Assignment Code 801 Autumn 2023
Q.5 Derive long run total cost curves from expansion path.
On an infinitely dense map of isoquant curves, consider the different equilibrium isocost lines. In this way, uniting the different production methods that are technically and economically efficient, we would obtain the «expansion path of production. Through the data acquired from this path, we could in the right panel represent the production levels associated with the different total costs. In this way, joining these points, the long-run total cost curve is attained.
In the case of such an expansion path, the cost incurred by the firm for the two inputs, i.e., the cost as entered in the equation of the ICL, would be the firm’s total variable cost (TVC), and if we add the firm’s total fixed cost (TFC) to this TYC, we would obtain the firm’s short-run total cost (STC).
On the other hand, if we assume that the firm uses two variable inputs, X and Y, and no fixed inputs, then it should be understood that we are discussing the long run. In that case, the same expansion path, viz., OK, would be the firm’s long-run expansion path. In the case of such an expansion path, the level of cost that is entered in the equation of the ICL should be taken as the long-run total cost (LTC) of the firm.
Again, of the two inputs, X and Y, that are used by the firm, one, say X, is a variable input and the other, Y, is a fixed input, then also the expansion path derived from the production function would be a short-run expansion path.
E1 is the cost-minimising point subject to q = q1, because at any other point on IQ1, say, at F1 to the northwest of E1, the required quantity of Y would be more than y̅, which is unavailable, or, at a point like J1 to the southeast of E1, the required quantity of Y would be less than y and that of X more than x1.
Consequently, at J1 the cost of output q1 would be higher than that at the point E1, because here the expenditure on Y being fixed at p1y̅, the expenditure on X would be larger than that at E (pXx* > pXx1).
Similarly, if the firm decides to expand and produce a higher q at q2 on IQ2, it would have to produce at the point E2(x2, y̅). For at E2, the cost would be minimum possible, since given
y = y, x = x2 is the minimum amount of X that would be required to produce q = q2.
In the same way, if the firm’s output is to be q3 on IQ3 (q3 > q2), then the firm would be in equilibrium at the point E3(x3, y).
If we now join the points E1, E2, E3, etc. by a curve, we would get the short-run expansion path of the firm in the one variable and one fixed input case. This expansion path would be a horizontal straight line like GH in Fig. 8.15, since y is constant (= y̅) along the path. The equation of this expansion path is
y = y̅