Problem (solve in a separate paper please to be submitted in class with your NAM

Question

Problem (solve in a separate paper please to be submitted in class with your NAME on t)! Units MarginalUnits Marginal of X Utility, X ofY Utility,Y 20 16 12 16 14 12 10 Refer to the above data. Assume that the prices of X and Y are $4 and $2 respectively and that the consumer's income is $18. what is the combination of X and Y that maximizes his utility within his budget limits? What level of total utility is realized from the equilibrium combination of X and Y? Show ALL your DETAILED work please.

Explanation / Answer

We have price of X = $4 and Price of Y =$2 .

and total consumer income = $18.

The consumer is in equilbruim , where marginal utility per price of both goods is equal.

that is, equilbruim condition = ( Marginal utility of good 1 / price of good 1) = ( Marginal utility of good 2 / price of good 2) and subject to constraint that the consumer does not exceed his budget.

now we can compare that MUx/Px = MUy/Py = 5

but at this , consumer are not exhausting all his budget. because if he buy only 1 units of good X which cost him $4 and 4 units of good Y ,which costs him $8 . so , 8 +4 = $12 which is less than consumer budget. 12 < 18.

now, compare the utility MUx/Px = MUy/Py = 4

at this, if he buy 2 units of good X and cost him $ 8 ( 4*2 = 8) and he buys 5 units of good Y and whcih cost him $10 ( 5*2 = 10 ) . so , $8 + $10 = $18. which is equal to consumer income.

so the consumer is in equilbruim when he purchase 2 units of good X and 5 units of Good Y .

combination of X and Y = 2 units of X and 5 units of Y .

UNits of X MU of X MUx /Px Units of Y MU of Y MUy/Py 1 20 5 1 16 8 2 16 4 2 14 7 3 12 3 3 12 6 4 8 2 4 10 5 5 6 1.5 5 8 4 6 4 1 6 6 3

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