Question 1
Consumer Surplus is the typical tool for measuring consumer welfare. It can also be defined as the area under the Marshallian demand curve but above the price (Willig, 1976). This is a representation of the total gain in welfare gained by the consumer from buying a good, as shown in figure 1. It is also defined as the difference between the maximum willingness to pay and the market price (Johansson, 1991). General theory dictates that a reduction in the price of a good leads to an increase in consumer surplus, and an increase real income and welfare because it allows the consumer to buy other goods. It can be calculated using the rule of half (formula 1) which only serves for linear demand functions where there are single price changes (Dekker, 2017). Using integration, consumer surplus can be derived with a more precise representation of welfare change (ibid). Formula 2 shows how consumer surplus is calculated using integration.
∆CS=(X_1+X_2)/2(p_1-p_2) (1)
∆CS=∫_(p_i2)^(p_i2 ) X(p,Y)dp_i (2)
FIGURE 1
However, in multiple price changes, the areas left to the demand curve cannot be used to estimate consumer surplus. Positive changes in consumer surplus may not be in the same direction as changes in welfare (measured by consumer’s utility function). This is because if some prices increase while others fall, the money measure may suggest that the consumer has gained yet the consumer deems that the change reduces his welfare (Johansson, 1991). This is called the path dependency problem. This can be corrected by observing and estimating the consumer’s utility function and therefore avoiding using the left of the demand curve as a measure of estimating changes in utility. If consumer utility functions are restricted to move in a symmetric direction one can easily observe and estimate consumer surplus. Two symmetric functions derived from this restriction are quasi-linear and homothetic utility functions. Quasi-linear utility functions assume that if income increases, all the extra income is spent on a single commodity (Johansson, 1991). This means the income effect from price changes on goods are not felt for all commodities except the one used as a numeraire (ibid). The Cobb-Douglas utility function is an example of the latter, which assumes that if income doubles, the demand for all goods consumed doubles as well. Because of these two assumptions, it is assumed that compensated consumer surplus is directly affected by price changes. These two concepts are reiterated by Hicks (1956), who states that for consumer surplus to be correctly estimated, the income effect should be small. An important assumption needed in computing Marshallian consumer surplus is that marginal utility of income is held constant (Marshal, 1961). This is because, the marginal utility of income is used to translate a monetary gain or loss of welfare from units of money to units of utility (Johansson, 1991).
Since individual utility functions are unobservable, indirect measures such as consumer surplus are used in reflecting changes in welfare (Johansson, 1991). Consumer surplus expresses unobserved gained utility in observable monetary terms which helps in judging alternative economic equilibria. Economists such as Harberger (1954, 1964) emphasised the use of compensating variation (CV) as a measure of welfare gain or Loss. Silberberg (1972) built on this by highlighting the use of CV as a tool for decision making in matters to do with public policy such employment. In public policies which aren’t just political, consumer surplus measures can be used to formulate means of payment and regulation of benefits. These measures are discussed below.
Question 2
As discussed above, if there is no path dependency problem, a unique measure of consumer surplus holds. Literature suggests different methods for measuring consumer surplus. The Hicksian demand functions are generally accepted as the simple methods. Hicks (1956) introduced measures of compensated demand functions. First, the Compensating variation (CV); defined as ‘the maximum (minimum) amount of money that can be taken from (must be given to) a household to leave it just as well off as it was before a fall (rise) in prices’ (Johansson, 1991 pp 49). Secondly, Equivalent variation (EV) is defined as the ‘minimum (maximum) amount of money that must be given to (taken from) a household to make it as well off as it would have been after a fall (rise) in prices’ (Johansson, 1991 pp 49). During single price changes, CV is less than EV. However, in multiple price changes, it is not certain that EV exceeds CV. The derivation of CV is shown in figure 2 where the price of good (a) is reduced while that for good (b) is fixed. Considering prices (p) and income (y); along the indifference curve U0, the optimal demand is at A. If the price of good (a) falls, the budget line rotates outward and the consumer moves to point B along the indifference curve U1. This is due to the substitution effect. Figure 2 also shows EV. If price did not fall, the amount of Y0 Y1 would have to be added to her income in order for him to reach the same level of utility I2 as with the lower price and initial income. The EV is the distance between the two budget lines ensuring the same level of utility U2 with the lower price and initial income, (but now at the old price p1, thus choosing point D instead of B (Johansson, 1991). Thirdly, compensating surplus(BE), which also represents Marshallian consumer surplus, is the excess of total expenditure which an individual is willing to pay (Y0Y3) rather than not have anything (go to point A rather than pay p1), over that which he has to pay (Y0Y2 at point B). According to Hicks (1943), compensating surplus doesn’t concentrate on rationing hence not important to welfare economics. After paying BE, the individual would be able to reach a higher indifference curve by purchasing less of good (b), therefore meaning a force is needed to move him to E and not out of his free will (Hicks, 1943). Fourthly, the equivalent surplus (AF) is the compensation one would be ready to accept in exchange for the price fall not happening if he was to buy the old quantity at the lower price. This would leave him at a higher indifference curve (I2). For the four Hickiasian measures, if there is a price increase, compensating measures become equivalent and vice versa. While Hicksian surplus measures the difference in attaining the initial utility level at the initial and subsequent prices, the Marshallian measures difference in price changes in order to buy the original quantity of goods. Marshall (1947), pp. 124. defines it as ‘The excess of the price which he would be willing to pay rather than go without the thing, over that which he actually does pay, is the economic measure of this surplus satisfaction. It may be called consumer’s surplus’. Unlike the Hicksian measures, it assumes utility is not fixed while income is fixed (Johansson, 1991). In a situation where there are quasi-linear utility functions, the Marshallian and Hicksian consumer surplus are the same (CV=S=EV).
FIGURE 2
A more direct approach to acquiring these measures may be to derive a robust form of the direct utility function and solve it for the associated demand equations to use in the approximation. By using the implied indirect utility or expenditure function, changes in welfare can be evaluated using Roy’s identity. The resulting equation can be used to estimate the relevant welfare measures. McKenzie and Pearce (1982) criticize the use of the mentioned approximations and propose direct calculation of the money approximation through a Taylor series. It involves using parameters, derived from integrated demand equations, in a Taylor series approximation. Since a Taylor series can be made arbitrarily accurate, McKenzie and Pearce (1982) argue that the use of Hickisan demand functions is not necessary. Vartia (1983) proposed another method for calculating willingness to pay measures. He tries to develop a method to measure change in prices while remaining on a given indifference curve. Since these two methods require complex methods of integrating demand equations, the Hicksian demand functions are preferred.
Question 3(a)
In a situation where a policy intervention for goods exhibiting high-income effect, the Hickisian consumer surplus would be appropriate. This is essential because, unlike the Marshallian consumer surplus, the income effect is compensated and not just felt. According to Silberberg (1972), during price changes, willingness to pay and actual compensation may not necessarily be similar despite holding the original and final prices constant. This means the Marshallian consumer surplus would be invalidated as the consumer’s gain. Also, according to Dekker 2017, in huge income effects, there will be measurement errors that will invalidate the Marshallian consumer surplus. Wilings approach can help in approximating Marshallian consumer surplus (provided the marginal utility of income is not large) that directly relates to CV and EV based on price and income elasticities.
Question 3(d)
A social welfare function (estimates social welfare) is a rule for generating a set of preferences for society for each set of individual preferences (Dekker, 2017). It attempts to provide a complete ranking of all possible social states. Social preferences need to be defined for any set of individual preferences. These individual preferences can be observed and compared through their utilities, which is estimated from their utility function. In deriving a utility function, individual preferences need to be reflexive, complete, transitive and non-satiated resulting in a continuity of preference ordering. These assumptions allow the individual utility to be measured and compared therefore exhibiting ordinality. With these assumptions, one can rank states and aggregate them and derive a social welfare function. Since utility is used to derive social welfare, both exhibit ordinal properties. Furthermore, cardinality cannot reveal utility intensities because we can know if an individual prefers one thing to another but not how much he prefers one to another. Moreover, social welfare functions convey a view on the distribution of social welfare and may derive the same weight to all households regardless of whether they are rich or poor (Johansson, 1991 pp 6). Consequently, negating the statement ‘Utility is cardinal’ and concurring with ‘social welfare is ordinal’.