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Homework answers / question archive / Consider a consumer who purchases two goods ,x and y
Consider a consumer who purchases two goods ,x and y .The consumers utility function is U(x,y )is xy with Mux is y and MUy is x .In addition the demand curve for y is given by y is 1/2p where I is income .Assume initially that the consumers income is$160 the price of x is Px is $8 ,and the price of y is Py is $1.
a) From the given information determine
1.) The utility maximizing amount of x,
2)The utility maximizing amount of y,
3)The total utility at the utility maximizing bundle.
b) Now assume the price of y increases to $2. Recompute the values from part a) at the new price
Solution:
Given :
A consumer purchases two goods X and Y.
U(x,y) = xy
MUx = y
MUy = x
y = I/2p
PX = $8
PY = $1
a) To find the Utility maximizing amount of x and y
y= I/2Py
y= 160/2(1)
y= 80
Each unit of y costs $1, the consumer will spend $1(80) $80 = on y . This leaves $80 to spend on x .
Since x costs $8, the utility maximizing amount of x is therefore 10 units. At this bundle, total utility is U xy = 10(80)= 800.
b) Now assume the price of y increases to $2.
Y= I/2PY
= 160/2(2) = 40
Since each unit of y costs $2, the consumer will spend $2(40) $80 = on y . This leaves $80 to spend on x .
Since x costs $8, the utility maximizing amount of x is therefore 10 units.
At this bundle, total utility is U xy = 10(40) 400 .
