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A consumer has preferences = x₁¹/² x₂ ¹/²and demand functions x₁ = 2p₁ ; x₂ = 2p₂ Income is $100.

How many units of each good does the consumer buy if the price of each good is $1? What is the consumer’s utility?

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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.

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