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

option (C) 16

Step-by-step 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<1)`

`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 √(2)`

and

`P_(x)=1`

we take
`P_(x)=1`

condition for utility maximizing is.

`(U x)/(U_(z))=(P_(x))/(P_(z))=`

`\Rightarrow (1)/((8)/(2 √(z)))=1`

`\Rightarrow (√(z))/(4)=1`

`\rightarrow √(z)=4`

`z=16`

Hence, answer is option (C) 16