Answer:
option (C) 16
Explanation:
Data provided in the question:
Utility function is [tex]=U(x, y, z)=x+z^{1/2} f(y)[/tex]
Number of tapes[tex]=z[/tex]
Number of tape recorders [tex]=y[/tex]
Amount of money [tex]=x[/tex]
Left to spend
[tex]f(y)=0 \quad \text { if }(y<1)[/tex]
[tex]f(y)=8,\quad y[/tex] is 1 or greater.
The price of tapes is $1
The question states that she has one tape recorder. i.e.,
[tex]y=1[/tex]
which means that [tex]f(y)=8[/tex] (since [tex]y=0[/tex] then [tex]u(x, y=1, z)[/tex]
[tex]=x+8 \sqrt{2}[/tex]
and
[tex]P_{x}=1[/tex]
we take [tex]P_{x}=1[/tex]
condition for utility maximizing is.
[tex]\frac{U x}{U_{z}}=\frac{P_{x}}{P_{z}}=[/tex]
[tex]\Rightarrow \frac{1}{\frac{8}{2 \sqrt{z}}}=1[/tex]
[tex]\Rightarrow \frac{\sqrt{z}}{4}=1[/tex]
[tex]\rightarrow \sqrt{z}=4[/tex]
[tex]z=16[/tex]
Hence, answer is option (C) 16
