Use the following to answer question:
-(Table: Consumer Equilibrium)Use Table: Consumer Equilibrium.Assume that the price of good X is $2 per unit,that the price of good Y is $1 per unit,and that you have $10 to spend on both goods.To maximize utility,you would consume _____ units of X and _____ units of Y.
A)3;4
B)2;3
C)2;6
D)5;0

Question

Use the following to answer question: 
-(Table: Consumer Equilibrium)Use Table: Consumer Equilibrium.Assume that the price of good X is $2 per unit,that the price of good Y is $1 per unit,and that you have $10 to spend on both goods.To maximize utility,you would consume _____ units of X and _____ units of Y.
A)3;4 
B)2;3 
C)2;6 
D)5;0

Quizplus · Accepted Answer

The consumer's budget constraint is:2X + 1Y = 10Solving for Y, we get:Y = 10 - 2XThe consumer's utility function is:U = X^a * Y^bwhere a and b are positive constants.Substituting the budget constraint into the utility function, we get:U = X^a * (10 - 2X)^bTaking the derivative of U with respect to X, we get:dU/dX = aX^(a-1) * (10 - 2X)^b - 2bX^a * (10 - 2X)^(b-1)Setting dU/dX = 0, we get:aX^(a-1) * (10 - 2X)^b = 2bX^a * (10 - 2X)^(b-1)Dividing both sides by X^(a-1) * (10 - 2X)^(b-1), we get:a/2b = X/10 - 2XSolving for X, we get:X = 10a/2b + 4a/bSubstituting X back into the budget constraint, we get:Y = 10 - 2(10a/2b + 4a/b)Y = 10 - 10a/b - 8a/bY = 10 - 18a/bTherefore, the consumer would consume 10a/2b + 4a/b units of X and 10 - 18a/b units of Y to maximize utility.

Use the Following to Answer Question