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Econ 10A: Problem Set 3 (1) Ted's utility function over goods X1 and X2 is given by U(x1, x2) = 4√x1/2 * √x2/4. What are Ted's demands for goods 1 and 2 if the price of good 1 is 1, the price of good 2 is 2, and Ted has $18 to spend?

          Econ 10A: Problem Set 3 

(1) Ted's utility function over goods X1 and X2 is given by U(x1, x2) = 4√x1/2 * √x2/4. What are Ted's demands for goods 1 and 2 if the price of good 1 is 1, the price of good 2 is 2, and Ted has $18 to spend?
        
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Principles of Economics
Principles of Economics
Gregory Mankiw 8th Edition
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Econ 10A: Problem Set 3 (1) Ted's utility function over goods X1 and X2 is given by U(x1, x2) = 4√x1/2 * √x2/4. What are Ted's demands for goods 1 and 2 if the price of good 1 is 1, the price of good 2 is 2, and Ted has $18 to spend?
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Transcript

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00:01 To maximize the charlotte's utility.
00:04 We need to determine the optimal allocation of goods x 1 and x 2.
00:08 So to determine the optimal allocation of goods x 1 and x 2 we can do this by setting up a an optimization problem.
00:31 The first is to find the optimal allocation of good x 1.
00:34 We need to solve the following problem to maximize x 2 x 1 plus x 2 subject to the budget constraint be 1 into 1 plus b 2 into 2 equals to 1 e 1 is the price of good 1 and the price of good e 2 is the price of the good 2 i is the income dollar 40 so subject to the budget constraint.
01:20 So p 1 is the price of the good one that is all the two and price of the good to is dollar 20 and income is dollar 40.
01:42 So it's 2 into 1 plus 20 into 2 is equals to 40 to solve for x 1 x 2 we need the utility function to derive the marginal utilities of x 1 and x 2 and set them equal to each other.
01:58 So getting the marginal utility equal to each other simplifying the equation yet squaring the both side x 1 plus 2 or substituting the value of x 1 into the budget constraint.
02:57 It's substituting budget constraint...
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