# The Theory of Consumer Behavior – the Theory of Utility

9 September 2016

Utility Maximisation (optimization) •Occurs at the point where: •MU per dollar of Product X = MU per dollar of Product Y •The equilibrium MU per dollar is 8 •The consumer would purchase 2 units of product X and 3 units of product Y to maximise total utility •At the equilibrium the consumer would realise 2920 utils •An income of \$170 is required to realise utility maximisation Example 2: Prices of Product Y increases (\$40 to \$100) •When the price of Product Y increases consumers realise less MU per dollar from the consumption of this product. Consumers will switch from Product Y to Product X in order to maximise TU. •To restore equilibrium consumers will now purchase less of product Y and more of product X •The new equilibrium occurs at the MU per dollar of 4

•Consumers will maximise TU by consuming 3 units of Product X and 2 units of Product Y. Example 3: The marginal utility per dollar and the level of income. Income = \$120 •The point of utility maximisation is where the marginal utility per dollar for each product is 10 •The consumer would purchase 2 units of product X and 2 units of product Y. This would require expenditure of \$120 •This combination of consumption would yield 2000 utils An increase in income to \$160 •Assuming that savings are zero the consumer would allocate all income to purchase the combination of products that yields the highest total utility. •An increase in income of \$40 allows the consumer to purchase one additional unit of Product Y or 2 additional units of Product X. •The consumer would allocate marginal income to the product which yields the next highest MU per dollar •In this example the consumer would purchase one dditional unit of Product Y as the MU per dollar of this product (8) is higher than the MU per dollar of consuming additional units of Product X ( 5, 2. 5 ) •When income increases from \$120 to \$160 the combination of products that yields the highest total utility is : • 3 units of Product Y and 2 units of Product X •The consumer will attain 2320 utils of total utility.

## The Theory of Consumer Behavior – the Theory of Utility Essay Example

The Budget Constraint •The limited amount of income available to consumers to spend on goods and services. •The budget constraint and prices of products will determine the consumer’s level of utility. Remembering that MU per dollar of Product X = MU per dollar of Product Y to achieve consumer equilibrium or optimisation •Example: Two products are used in this example – pizza and coke The price of pizza is \$2 per slice The price of coke is \$1 In this example 3 consumption combinations satisfy optimisation: 1 pizza and 3 coke ( MU per \$ = 10) 3 pizza and 4 coke ( MU per \$ = 5) 4 pizza and 5 coke ( MU per \$ = 3) Optimisation continued •A consumer with a budget constraint of \$13 will maximise utility with 4 slices of pizza and 5 cups of coke. TU = 105 utils) •A consumer with a budget constraint of \$5 will maximise utility with one slice of pizza and 3 cups of coke (TU = 65 utils) Deriving the demand curve from utility analysis •The demand curve may be derived from the principles of utility – maximisation and consumer equilibrium. •Law of demand: As the price of a product decreases the quantity demanded increases. •Total utility, marginal utility and the budget constraint can all be linked and be used to explain the law of demand. •The following example demonstrates how the demand curve for Product B is derived. Product A = \$4

Qty Tu MU MU per \$ 0 0 – – 1 600 600 150 2 800 200 50 3 960 160 40 4 1040 120 30 Product B P= \$2 TU MU MU per \$ 0 – – 700 700 350 900 200 100 1000 100 50 1040 40 20 P = \$5 MU per \$ – 140 40 20 8 •When PA = \$4 and PB = \$2 consumer equilibrium is achieved when the consumer consumes 2 units of A and 3 units of B. When PB increases to \$5, consumer equilibrium is achieved when the consumer consumes 3 units of A and 2 units of B. The demand schedule for PB PB QDB \$2 3 \$52 Utility and consumer decision making In summary, the two conditions for maximising utility are: 1. 2. Spending on Product A + Spending on Product B = Amount available to be spent. The marginal rate of substitution •Marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility. The formula is:

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