Assume that the prices of goods X and Y are fixed at $ 15 and $ 10 respectively and that the representative consumer has a monthly fixed income of $ 5000. Based on this information, determine the amounts of food and clothing within his restricted budget that maximize the consumer’s utility
U (x,y) = 20. x3. y5
(M) = $ 5000
Px = $ 15
Py = $ 10
so:
MaxU (x,y) = U(x,y)
MaxU (x,y) = 20. x3. y5
Y= M – Px . x
Py
Y = 5000 – 15 x
10
Y= 500 – 1,5 x
MaxU (x,y) = U(x,y)
MaxU (x,y) = 20x3 . (500 – 1,5x)5
Could you please help with this?
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