Economics Question! Help!! Part 2!?

Question

I was hoping someone could show me a walk-through of this one, thank you!

Mike can get blood from a stone. If he has "x" stones, the number of pints of blood he can extract from them is f(x)=2x^1/3. Stones cost Mike $w each. Mike 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 Mike's supply function when stones cost $8 each? _______ When stone's cost $w each? _______

D. If Mike 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?

Please walk me through this; thanks!!

Answer 1

A:

y=2 (x^(1/3))

x^1/3=y/2

x=(y/2)^3

B:

TC=w*x= w*(y/2)^3 = y^3 * w/8

C:

Supply is MC curve above AVC in short-run and ATC in long-run. You don't have any fixed costs in your case so ATC=AVC and AVC=TC/y = wy²/8 - this means that AVC and ATC always lays below MC so Mike will supply at any positive price. But you should consider demand curve too and market type (monopoly/competition).

MC=(TC)' = 3wy²/8

p=3wy²/8

y=√(8p/3w)

y(w=8)=√(p/3)

D:

19 relatives means that at any price quantity supplied will be (19+1)-times more than original one-producer supply,

y=20√(8p/3w)