Question

Please show all your work step by step

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(u) = 2.03. Stones cost Jack Sw 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?

Answer 1

(a)

When y = f(x) = 2x^1/3,

x^1/3 = y

Cubing,

x = y³

(b)

Total cost (TC) = w.x

TC = w.y³

(c)

Supply function is the marginal cost (MC) function.

MC = dTC/dy = 3w.y²

p = 3w.y² [supply function]

When w = 8, supply function: p = 24.y²

(d)

Since there are 19 people, aggregate supply (Y) = 19y

y = Y/19

p = 3w.(Y/19)2

p = (3/361).(w.Y²)

Y² = (3w) / (361.p)

Y = [(3w) / (361.p)]^1/2 [aggregate supply]