Question

5. Jack Benny can get blood from a stone. If he has a stones, the number of pints of blood he can extract from them is f(1) = 2.. Stones cost Jack $w each. Jack can sell each pint of blood for $p. (a) How many stones does Jack need to extract y pints of blood? (b) What is the cost of extracting y pints of blood? (c) What is Jack's supply function when stones cost 8 each? When stones cost $w each? (d) If Jack has 19 relatives who can also get blood from a stone in the same way, what is the aggregate supply function for blood when stones cost $w each?

Answer 1

5. (a) The production function is
y= 2.1/3
, and the cost of production is . We have
y= 2.1/3
or
1/3=0.5
or
r* = 0.125
, which is the input demand. This is the amount of stones required to extract y pints.

(b) The cost function would be or
c= w(0.125)
or
c= 0.125wy
. This is the cost of extracting y pints.

(c) The supply function would be where p=MC, ie $p = \frac{\mathrm{d} c}{\mathrm{d} y}$ or
p= 0.125wy?
or
p=0.375wy
or
9 = = 0375"
or
JF0375173 1/2
, which is the required supply function.

For p=8, we have
31/2 y = 0.3751/21/2
or
y=- 4.6188 1/2
pints. For $w per stone, the supply of stone would be the same
y=- 4.6188 1/2
.

(d) The supply of Jack is
JF0375173 1/2
. With 19 relatives, a total of 20 people to supply, the aggregate supply would be
Y = 20
or
Y = 20 * 0.3751/21/2
or
20p 1/2 Y = 3751/21/2
, which is the required aggregate supply function.