Ted has the following utility function U(x 1 , x 2 ) 20x 1 (x 1 ) 2 2(x 2 ) The price of good 2 is p 2 1 Let p 1 denote the price of good 1 and m denote Ted's income (a) Assume that m and p 1 are such that Ted consumes positive amounts of both goods Derive Ted's ordinary demand for good 1 (quantity of good 1 demanded as a function of the price of good 1 p 1 ) (b) Briefly motivate why the quantity of good 1 demanded does not vary with Ted's income m (so long as Ted consumes positive amounts of both goods) How does Ted respond to an increase in income m (c) What conditions for the price p1 and income m must be satisfied to ensure that Ted consumes positive amounts of both goods

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Question: Ted has the following utility function: U(x 1 , x 2 ) = 20x 1 (x 1 )^2 + 2(x 2 ). The price of

Ted has the following utility function: U(x₁, x₂) = 20x₁ (x₁)^2 + 2(x₂). The price of good 2 is p₂ = 1. Let p₁ denote the price of good 1 and m denote Ted's income.

(a) Assume that m and p₁ are such that Ted consumes positive amounts of both goods. Derive Ted's ordinary demand for good 1 (quantity of good 1 demanded as a function of the price of good 1 p₁).

(b) Briefly motivate why the quantity of good 1 demanded does not vary with Ted's income m (so long as Ted consumes positive amounts of both goods). How does Ted respond to an increase in income m?

(c) What conditions for the price p1 and income m must be satisfied to ensure that Ted consumes positive amounts of both goods?

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