Final answer:
The consumer will buy 2 units of each good when the price is $1 for each, with an income of $100, resulting in a utility of 2. Income, prices, and preferences determine consumer choices, subject to effects like substitution and income effects on purchasing power.
Step-by-step explanation:
When the price of each good, x₁ and x₂, is $1 and the consumer's income is $100, the consumer's demand functions can be used to determine how many units of each good the consumer will buy. Given the demand functions x₁ = 2p₁ and x₂ = 2p₂, and setting p₁ = p₂ = 1, the consumer will purchase x₁ = 2×1 = 2 units of good 1 and x₂ = 2×1 = 2 units of good 2. The consumer's utility, based on their preferences, x₁¹/₂ x₂¹/₂, can be calculated by substituting the quantities of x₁ and x₂ into the utility function, yielding a utility level of (2)¹/₂ × (2)¹/₂ = 2.
The concepts of income, prices, and preferences play a vital role in affecting consumer choices. A change in any of these factors can lead to a change in the consumption pattern due to the substitution effect and the income effect. The substitution effect occurs when a change in the price of a good causes a consumer to substitute one good for another, while the income effect occurs when a change in the price of a good affects the consumer's real income and hence their purchasing power.