Bill gets utility (satisfaction) from two goods, x and y, according to the utili

Question

Bill gets utility (satisfaction) from two goods, x and y, according to the utility function u(x,y) = ln(x) +ln(y). While Bill would like to consume as much as possible he is limited by his income, which is 100 dollars. Good x costs $2 per unit and good y costs $4 per unit, so his budget constraint is 100 = 2x + 4ymaximize Bill Bill gets utility (satisfaction) from two goods, x and y, according to the utility function u(x,y) = ln(x) +ln(y). While Bill would like to consume as much as possible he is limited by his income, which is 100 dollars. Good x costs $2 per unit and good y costs $4 per unit, so his budget constraint is 100 = 2x + 4ymaximize Bill

Explanation / Answer

lafrangian equation = P = lnx+lny+ m(100-2x-4y)

dp/dx = 1/x - 2m = 0

so x = 1/2m

dp/dy = 1/y -4m = 0

so y = 1/4m

now 2x+4y = 100

so

2/2m + 4/4m = 100

=>2/m = 100

=> m = 1/50

so x = 25 y = 12.5

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