Question #73266

An individual lives in a world where there are only two goods X and Y his utility function is U=50x-0.5x^2+100y-y^2.The price of x is 4 and his income per period is 672.
Derive his demand function for y

Expert's answer

U=50x-0.5x^2+100y-y^2.

MUx = 50 – x

MUy = 100 – 2*y

(50 – x)/( 100 – 2*y) = 4/Py

Py = 4*(100 – 2*y)/(50 – x )

4*x + (4*(100 – 2*y)/(50 – x )) = 672

4*x + (400 – 8*y)/(50-x) = 672

400 – 8*y = (672 - 4*x)* (50-x)

50 – y = 420 – 109x – 0.5x^2

y = 0.5x^2 + 109x – 370 is demand function for y

MUx = 50 – x

MUy = 100 – 2*y

(50 – x)/( 100 – 2*y) = 4/Py

Py = 4*(100 – 2*y)/(50 – x )

4*x + (4*(100 – 2*y)/(50 – x )) = 672

4*x + (400 – 8*y)/(50-x) = 672

400 – 8*y = (672 - 4*x)* (50-x)

50 – y = 420 – 109x – 0.5x^2

y = 0.5x^2 + 109x – 370 is demand function for y

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