Understanding Consumer Demand and Utility in Economics
Theoretical Support # 4
Exercise Class
Consumer Demand Theory of Utility
Economics and Industrial Organization I
Total and Marginal Utility
The demand for a product arises from the satisfaction (utility) that consumers derive from consuming it. Initially, as a person consumes more units of a product over time, their total utility increases. However, with increasing consumption, we observe that marginal utility (the additional satisfaction gained from consuming one more unit) decreases. Eventually, a point is reached where total utility is maximized, and marginal utility becomes zero, known as the saturation point. Beyond this point, marginal utility becomes negative, leading to a decline in total utility as consumption continues. This decline may occur due to factors such as overconsumption, storage issues, changes in taste, or health risks, resulting in consumer dissatisfaction.
Marginal utility is defined as the change in total utility resulting from the consumption of an additional unit. Each value corresponds to the marginal utility (UMgx) at the midpoint between two levels of consumption.
This theory employs the term “utils” to measure levels of utility achieved, serving as a fictional unit to express and differentiate between levels of satisfaction.
Example 1:
Suppose the following table shows the amounts consumed (Qx), total utility (UTx), and marginal utility (UMgx) that a person experiences while consuming good X over a period of time.
Qx | UTx | UMgx
0 | 0 | 0
1 | 1 | 1
2 | 10 | 8
3 | 18 | 6
4 | 32 | 4
5 | 44 | 2
6 | 52 | 0
7 | 30 | -2
As consumption increases, total utility (UTx) rises until the fifth and sixth units, where it plateaus, then declines from the seventh unit onward. Marginal utility (UMgx) decreases with increased consumption until the sixth unit, where no satisfaction is experienced, leading to a rejection of the product starting from the seventh unit.
Example 2:
If we plot the above table for total utility and marginal utility, we obtain the corresponding curves of UTx and UMgx (with Qx on the horizontal axis and utilities on the vertical axis).
2. Consumer Equilibrium
In economics, it is assumed that the objective of a rational consumer is to maximize total utility or satisfaction derived from spending their income. A consumer achieves equilibrium when they spend all their income, and the utility or satisfaction from the last dollar spent on each product is equal. Mathematically, this can be expressed as:
UMgx / Pn = UMgy / Pz = UMgz / Px = …
Under the condition that all income is spent, we have:
PxQx + PyQy + PzQz + … + PnQn = Y (where Y is the individual’s income)
The following table shows UMgx and UMgy for different levels of consumption:
Q | UMgx | UMgy
1 | 6 | 11
2 | 12 | 14
3 | 10 | 31
4 | 29 | 41
5 | 8 | 57
6 | 6 | 74
7 | 5 | 82
Assuming product X and product Y are the only goods available, with prices Px = $2 and Py = $1, and an income (Y) of $12 per analysis period, the consumer spends all their income.
Since marginal utilities decrease with increased consumption, total utility can be maximized by ensuring maximum utility for every dollar spent. Thus, the consumer should spend their first $2 on product Y, as buying two units yields 21 utils (11 + 10) compared to 16 utils from spending the same amount on X. The consumer should continue to allocate their spending based on the highest utility until their income is exhausted, as shown in the table below:
Y | X | Utils Spent | Utils | Decision
1 | 2 | $2 | 16 | Buy Y
2 | 2 | $2 | 17 | Buy Y
3 | 1 | $2 | 16 | Buy X
4 | 1 | $2 | 13 | Buy X
5 | 1 | $2 | 12 | Buy X
Total Income | $12 | Total Units Bought | 36 | Total Utility Obtained | 425
This demonstrates the maximum utility achievable by spending all available income under the levels of consumer satisfaction assigned to each product. If the consumer spends their income differently, total utility would be lower.
The conditions for utility maximization are satisfied with Qx = 3 and Qy = 6:
UMgx / UMgy = 12 / 6 = 6 / 6
Px / Py = $2 / $1
Under the condition that all income is spent:
PxQx + PyQy + PzQz + … + PnQn = Y (where Y is individual income)
2×3 + 1×6 = $12
Thus, the marginal utility of the last dollar spent on X (6 utils) equals the marginal utility of the last dollar spent on Y (6 utils), and the total spent on X ($6) plus the total spent on Y ($6) equals the total income of the individual.
The same conditions must be met for more than two products in a consumer’s basket.
3. Exchange
Opportunities for exchange between consumers at equilibrium exist to the extent that both consumers can increase their utility through price changes. For two individuals to engage in a voluntary exchange, it is necessary that both benefit; if one person gains nothing or loses, they will refuse to negotiate.
Assuming there are only two individuals (A and B) and two products (X and Y), mutually beneficial exchange opportunities arise if the UMgx / UMgy for person A differs from UMgx / UMgy for person B.
As the amounts exchanged increase, the two ratios converge in value. If they become identical, there will be no opportunity for beneficial exchange, and negotiation will cease.
4. Derivation of the Demand Curve of an Individual
Based on the theory of diminishing marginal utility and the concept of consumer equilibrium, we can derive an individual’s demand curve for a specific product. We start by assuming a consumer’s equilibrium condition, from which we obtain a point on the demand curve for the product in question. Then, we analyze different price situations (alternatives to equilibrium), adjusting consumption levels to reach a new equilibrium condition, thus obtaining another point on the demand curve. Repeating this process with various prices will identify new equilibrium points for the consumer, and connecting these points will yield the individual demand curve.
Example 4:
Suppose we want to derive the demand curve for product X, using the same data from Example 3. For the consumer in Example 3, who maximizes total utility by spending all their income, we found that they had to buy 3 units of X when the price of X was Px = $2 (with PY = $1). This gives us a point on the demand curve for consumer equilibrium under the indicated conditions. If the price of X falls to Px = $1, the original balance is disrupted, as the last dollar spent on X (to buy the third unit) now yields 12 utils, while the last dollar spent on Y yields only 6 utils (to buy the sixth unit). To achieve a new balance, the consumer must buy more units of X, leading to a decrease in UMgx, which occurs when they purchase 6 units of X.
UMgx / UMgy = 12 / 6 = 6 / 6
Px / Py = $2 / $1
Under the condition that all income is spent:
PxQx + PYQy + PzQz + … + PnQn = Y (where Y is the individual’s income)
1×6 + 1×6 = $12
Thus, we obtain a second point on the demand curve for product X, and so on. By analyzing various prices, we can find new equilibrium points that will provide additional points for the individual demand curve. Assuming a straight line connecting the two points, we can reflect this consumer behavior.
5. What Happens to the Other Product? Cross Effects
When the price of product X decreases:
– If the demand for X (Dx) is unitary elastic, the quantity of Y (Qy) will not change.
– If the demand for X (Dx) is elastic, the quantity of Y (Qy) will decrease.
– If the demand for X (Dx) is inelastic, the quantity of Y (Qy) will increase.
Example 5:
In the previous example, we analyzed the same amount of money spent on product X ($6 per time period). When the price of X decreased from $2 to $1, we determined that the demand curve for X was necessarily unitary elastic.
ΔQ / ΔP = (Qf + Qg) / (Pf + Pg) = 1
The amount of money spent was the same for both products ($6), and with the price of Y ($1) unchanged, the quantity purchased remained at 6 units before and after the price change of X. We can conclude that when Dx is unitary elastic (within the range of price change), a change in Px leaves the quantity demanded of Y unchanged. However, the situation will differ for cases where elasticity is elastic or inelastic.
6. Substitution Effect and Income Effect
The transition from one consumer equilibrium point to another can be analyzed in relation to two effects: substitution effect and income effect.
Substitution Effect: When the price of a product decreases, consumers tend to replace it with other products that have remained unchanged, leading to an increase in the quantity demanded of the product whose price has fallen.
Income Effect: This occurs when the price of a product decreases (ceteris paribus = all else being equal), resulting in an increase in the purchasing power of consumers’ money income, effectively increasing their real income. Consequently, consumers tend to buy more units of the product whose price has decreased if it is a normal good, and fewer units if it is an inferior good.