A consumer’s utility function is U = logx + logy2 , where and y are two...

A consumer’s utility function is U = logx + logy2 , where and y are two consumption goods. The price of x is $2.00 per unit and the price of y $5.00 per unit. Her budget is $1000. Solve her utility maximization problem and find her optimal consumption of x and y. Will your answers change if the consumer’s utility function is U = logxy2 instead – why or why not?

Expert Solution

When U= logx + logy2, using solver in excel where, setting utility to be maximised, changing quantities and keeping the Budget constraint to $1000 we get,

Price	goods	Quantities	Budget	Utility
2	x	92.16	184.33
5	y	163.13	815.67	6.86
			1000

When U= logxy2, using solver in excel where, setting utility to be maximised, changing quantities and keeping the Budget constraint to $1000 we get,

Price	goods	Quantities	Budget	Utility
2	x	166.67	333.33
5	y	133.33	666.67	6.47
			1000

Yes the quantities change as both equations are of different forms

Rahul Sunny answered 2 years ago

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