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17 March, 07:33

Max has utility function u (x1, x2) = x1 (x2 + 1). The price of x1 is $2 and the price of x2 is $1. Income is $10. How much x1 does Max demand? How much x2? If his income doubles and prices stay unchanged, will Max's demand for both goods double?

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  1. 17 March, 11:12
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    1. x2=9/2, x1=11/4

    2. If his income doubles and prices stay unchanged, his demand for both goods does not double

    Explanation:

    Max has utility function u (x1, x2) = x1 (x2 + 1). The price of x1 is $2 and the price of x2 is $1. Income is $10. How much x1 does Max demand? How much x2? If his income doubles and prices stay unchanged, will Max's demand for both goods double

    for ease lets designate x1 as x and x2 as y

    max sets (y+1) / x=2

    and His budget constraint is 2x + y = 10

    solving the the two equations simultaneously

    y+1=2x ...

    2x+y=10

    rearrange y-2x=-1

    y+2x=10

    2y = 9

    y=9/2

    from equation 2, substitute the value of y into equation 2

    y+2x=10

    9/2+2x=10

    2x=10-9/2

    x=11/4

    If his income doubles and prices stay unchanged, his demand for both goods does not double
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