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Katie Kwasi’s utility function is U(x1, x2) = 2(ln x1) + x2. Given her current income and the current relative prices, she consumes 10 units of x1 and 15 units of x2. If her income doubles, while prices stay constant, how many units of x1 will she consume after the change in income?

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Answer:

Katie Kwasi's Utility Function

The units of x1 that she will consume after the change in income is:

= 40 units of x1

Explanation:

a) Data and Calculations:

Katie Kwasi’s utility function, U(x1, x2) = 2(ln x1) + x2

Current consumption = 10 units of x1 and 15 units of x2

When her income doubles, with prices staying constant, Katie will consume:

= 2(2 * 10 of x1) + 15 of x2

= 40 units of x1 + 15 units of x2

Therefore, she will consume 40 units of x1 and 15 units of x2

b) The above function expresses mathematically Katie's utility to be a function of the units of x1 and x2 that she can consume, given her income constraint.  If her income doubles, Katie will consume double units of x1 and the same units of x2 as she was consuming before the change in income.

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