Income and Substitution Effects of a Price Change - Essay Example

Income and Substitution Effects of a Price Change Introduction The objects of the consumer choice is called consumption bundle. The objective of the consumer is to maximize the well being. They are well informed about the goods that they can purchase. They desire a variety of goods and services. There are two sets of consumption bundles (x1,x2) and (y1,y2). The consumer has the ability to rank them according to their affordability. When the consumer is just satiated consuming the bundle of x goods as compared to the satisfaction he would have earned consuming the other bundle of y goods, according to his own preferences, then it is said that the consumer is indifferent (Hussen, n.d.). Complete, reflexive and transitive are the axioms of consumer theory. The theory of consumer preferences can be formulated on the basis of the above axioms (Samuelson, 1956. p.3). (Varian, H., 2006.p. 37). The two axes represent a typical consumption of a consumer of goods 1 and 2. A consumption bundle (x1,x2) is taken along with the other consumption bundles that are preferred weakly to the selected bundle. This is what we mean by set that are weakly preferred. The indifference curve is formed by the bundles forming the boundary of the selected set i.e. the bundles that will provide the consumer as much satisfaction as the selected bundle. The indifference curve can be drawn through any consumption bundle. One of the disadvantages in using indifference curve analysis is that it shows only the consumption bundle perceived by the consumer being indifferent. It fails to capture the bundles which are better or worse. One of its characteristic is indifference curve that represents distinct preferential levels cannot cross. The rate at which the consumer likes to substitute goods is called the marginal rate of substitution. MRS is derived from the slope of the indifference curve (Varian, 2006, p. 48). The budget constraint of the consumer is p1x1+p2x2=m. The consumption of good 1 is taxed at a rate of t. The new budget constraint will be (p1+t)x1+p2x2=m. The effect of the change in price on the demand conditions is shown in the figure below. (Varian, 2006, p. 88). It is uncertain whether such tax will increase or decrease the consumption of good 1. The optimal choice of the consumer must satisfy the budget constraint. (p1+t)x1*+p2x2*=m, x1* and x2* are the optimal choices. (Varian, 2006, p. 74). The set of bundles that is preferred by a consumer to the optimal choice is above the indifference curve and the set of bundles that is against the affordability is above the indifference curve. Hence the optimal choice is the best bundle that can be chosen by the consumer. Now, an income tax is taken into consideration which raises the revenue by the same amount as the tax. The form of that budget constraint will be p1x1+p2x2=m-tx1*, where tx1* is the rise in revenue because of tax. (Varian, 2006, p. 88). The new budget constraint has the same slope as the original one and the budget line with income tax passes through the optimal choice of the consumer. This establishes the fact that (x1*,x2*) lies on the income tax budget line. But it is not the optimal choice of the consumer. There is some point on the budget line that is preferred to (x1*,x2*) as the budget line cuts the indifference curve t (x1*,x2*). There are two axioms of revealed preference theory, the strong axiom (SARP) and the weak axiom (WARP). The latter states that if a bundle of x-goods is directly revealed preferred to the y-bundle and the two bundles are distinct, then it will not be the case where q1y1+q2y2 is greater than or equal to q1x1+q2x2, (q1, q2) being the prices of the y-bundle consisting of two goods y1 and y2 (Barnett II, 2003, p. 42). Let us consider the table below: Observation p1 p2 x1 x2 1 1 2 1 2 2 2 1 2 1 3 1 1 2 2 Cost of each bundle at each set of prices: Bundles Prices The diagonal terms in the above table shows the required amount of spending of the consumer at each choice. It can be said whether any bundle is revealed preferred to the other. In the above case, bundle 3 was purchased when bundle 1 is affordable. This implies that bundle 3 is revealed preferred to bundle 1. This is shown with the star sign. This is a violation of WARP. It can be concluded that a consumer who has stable preferences cannot generate the data in the above tables as he always chooses the best affordable goods. SARP states that if x-bundle is directly or indirectly revealed preferred to y-bundle and the two bundles are distinct, then it will not be the case where the same y-bundle is directly or indirectly revealed preferred to x-bundle. Bundles Prices Bundle 1 is revealed preferred directly to bundle 2 and again bundle 2 is revealed preferred directly to bundle 3. This implies that bundle 1 is indirectly revealed preferred to 3. This is indicated by the star in the parenthesis. Income and Substitution effect The substitution effect is defined as the change in demand due to the change in the exchange rate between the two goods. The income effect is defined as the change in demand of a good due to an adjustment in purchasing power of the consumers (Money Terms, n.d.). The movement in prices is broken up into two steps. In the first case the relative prices changes and the income adjust accordingly keeping purchasing power as constant and in the second there are adjustments in the purchasing power keeping the relative prices as constant. (Varian, 2006, p. 138). The price of good 1 has decreased. The budget line will now be flatter. The pivoted budget line has the same slope as the original one and so the relative prices also remain the same. The income associated with the two budget lines is different and so the vertical intercept changes. The original consumption bundle (x1,x2) is just affordable. The purchasing power has not changed in the sense that the same consumption bundle is still affordable taking the pivoted line into consideration. The money income that will make the original consumption bundle just affordable be m1. It is also the income associated with the original budget line. Therefore, m1=p11x1+p2x2 and m= p1x1+p2x2, as (x1,x2) is affordable at (p1, p2, m) and (p11, p2, m1). So, m1-m= x1[p11- p1]. Thus a change in income is necessary to make the old bundle affordable at the new prices. If price goes down there will be negative adjustments in income. When price goes up, the purchasing power goes down and a positive change in income is necessary to keep the purchasing power constant. Although the original consumption bundle is still affordable it is not the optimal purchase at the pivoted budget line. (Varian, 2006, p. 140). The optimal budget line has been denoted by Y. This bundle of goods is the optimal bundle of goods when price changes and income adjusts to keep the old bundle affordable. The movement from X to Y is called the substitution effect (Hallam, n.d., p. 2). A parallel shift of the budget line is the movement that occurs when income changes and relative prices remain constant. The consumer’s income is changed from m1 to m, keeping the prices constant at (p11, p2). In the figure, there is movement from (y1,y2) to (z1,z2). The last movement can be called as income effect since it changes income while the prices are kept fixed at the new prices. More precisely, income effect, Δ x1n, is the change in demand for good 1 when there is a change in income from m1 to m, holding the price of good 1 at p11. Δ x1n= x1(p11,m)- x1(p11, m1). Conclusion The income effect can operate in either way. It will tend to increase or decrease the demand the demand for good1 depending on whether the good is normal or inferior (Miller, n.d. p. 2). If the good considered is normal, then decrease in income will lead to decrease in demand. If the good considered is inferior, then the decrease in income will lead to an increase in demand. In case of substitution effect, if the price of a good goes down then the change in demand for the good due to substitution effect must be non-negative. If p1> p11, then x1(p11, m1) is greater than equal to x1(p1,m), so that Δ x1s is greater than equal to zero. The substitution effect moves in opposite direction to the price effect (Bellas, n.d. p. 5). Since the change in demand due to substitution effect is opposite to the change in price it can be said that the substitution effect is negative. If the price increases, the demand for the good due to the substitution effect decreases. References Hussen, A. n.d. Indifference curve analysis. [pdf]. Available at: http://cc.kzoo.edu/~hussen/Eco305.handout3.doc.pdf. [Accessed:28th March, 2012]. Samuelson, P., 1956. Social Indifference curves. [pdf]. Available at: http://gatton.uky.edu/faculty/hoytw/751/articles/samuelsonsic.pdf. [Accessed:28th march, 2012]. Varian, H., 2006. Intermediate Microeconomics. 7th Edition. Affiliated East-West Press Private Limited. Barnett II, W. 2003. The Modern Theory of Consumer Behavior: Ordinal or Cardinal?. [pdf].Available at: http://mises.org/journals/qjae/pdf/qjae6_1_3.pdf. [Accessed:28th March, 2012]. Money Terms, n.d. Income Effect. [online]. Available at: http://moneyterms.co.uk/income-effect/. [Accessed:28th March, 2012]. Hallam, A. n.d. Income and Substitution Effects-A Summary. [pdf]. Available at: http://www2.econ.iastate.edu/classes/econ101/hallam/Income_Substitution.pdf. [Accessed:28th March, 2012]. Bellas, A. n.d. Income and Substitution Effects. [pdf]. Available at: http://faculty.metrostate.edu/BELLASAL/352/Lec05.pdf. [Accessed:28th March, 2012]. Miller, P. n.d. Income and substitution effects of a price change. [pdf]. Available at: http://krypton.mnsu.edu/~millep1/econ406/misc/Income%20and%20Substitution%20Effects%20Explained.pdf. [Accessed:28th March, 2012]. Read More