4. A consumer’s utility function is U = x + z . If the budget constraint...

Question

Question

4. A consumer’s utility function is U = x + z . If the budget constraint has a slope ( − px / pz ) = -2, which statement is true?
a. z* >0,x* =0

b. z* = x* > 0
c. z* =0,x* >0
d. Not possible to say, given the information provided. e. None of the above.

Answer 1

Answer #1

Given

U=x+z

Marginal utility from x=dU/dx=1

Marginal utility from z=dU/dz=1

Marginal utility per dollar spent from x=1/px

Marginal utility per dollar spent from z=1/pz

Slope of budget line indicates that px is twice the price of z (pz).

It means that Marginal utility per dollar spent from x is half to that of z.

It implies that agent would consume z only to maximize utility.

So, for any positive budget,

Optimal consumption is z*>0 and x*=0

Correct option is

a. z* >0,x* =0

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Answer 2

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