Question

Daisy received a tape recorder as a birthday gift and is not able to return it. Her utility function is U(x, y, z) = x + z 1/2 f(y), where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend. f(y) = 0 if y < 1 and f(y) = 24 if y is 1 or greater. The price of tapes is $4 and she can easily afford to buy dozens of tapes. How many tapes will she buy?a. 18 b. 14 C 16 d. 20

Answer 1

Answer:

option (C) 16

Explanation:

Data provided in the question:

Utility function is $=U(x, y, z)=x+z^{1/2} f(y)$

Number of tapes$=z$

Number of tape recorders $=y$

Amount of money  $=x$

Left to spend

$f(y)=0 \quad \text { if }(y$

$f(y)=8,\quad y$ is 1 or greater.

The price of tapes is $1

The question states that she has one  tape recorder. i.e.,

$y=1$

which means that $f(y)=8$ (since $y=0$ then $u(x, y=1, z)$

$=x+8 \sqrt{2}$

and

$P_{x}=1$

we take $P_{x}=1$

condition for utility maximizing  is.

$\frac{U x}{U_{z}}=\frac{P_{x}}{P_{z}}=$

$\Rightarrow \frac{1}{\frac{8}{2 \sqrt{z}}}=1$

$\Rightarrow \frac{\sqrt{z}}{4}=1$

$\rightarrow \sqrt{z}=4$

$z=16$

Hence, answer is option (C) 16