Timmy consumes two commodities x and y. His utility function is min{x+ 2y, y + 2x}. He chooses to buy 10 units of good x and 20 units of good y. The price of good x is $1. What is Timmy’s income? Explain your answer.

Answer 1

To find Timmy's income, we need to evaluate the cost of the goods he purchased and their corresponding prices.

The cost of the 10 units of good x is given by:
10 units * $1/unit = $10

The cost of the 20 units of good y is not provided, but we can calculate it by comparing the prices of x and y using Timmy's utility function:
min{x + 2y, y + 2x}

By substituting the quantities purchased by Timmy into the utility function, we get:
min{10 + 2(20), 20 + 2(10)}
min{10 + 40, 20 + 20}
min{50, 40} = 40

Thus, the cost of the 20 units of good y is $40.

To find Timmy's income, we add up the costs of the goods he purchased:
$10 + $40 = $50

Therefore, Timmy's income is $50.