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George's income is $3,000 a year, and he spends his entire income on butter and guns,...

George's income is $3,000 a year, and he spends his entire income on butter and guns, the price of a gun is $100 and the price of one pound of butter is $5. when he maximizes his utility, the marginal utility of george's last gun purchase is 50. what is the marginal ultility of the last pound of butter he purchases when he maximizes his utility?

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Answer #1

Assume for simplicity , X stands for gun and Y stands for butter

Px = 100

Py = 5

I = 3000

MUx = 50

MRS = MUx/MUy  

= 50/MUy

At utility maximizing point or optimal point

MRS = Px/Py

MUx/MUy = 100/5

50/MUy = 20

50/20 = MUy  

MUy = 2.5

Thus, MU of the last pound of butter is 2.5 when George maximizes his utility  

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