I first looked at your first question, and then I look at your answers. There seems to be a dis-connect. Your answers dont seem to match the questions. Here are my answers
b) The cost of producing y is equal to the number of number of stones needed times w. x= (y/2)^3. So C(y) = w*(y/2)^3
c) The supply function is equal to the marginal cost function. So MC(y) = 3*w*(y/2)^2
d) I need to think a bit about converting the MC curve into a supply function as y=f(w)
I don't agree with your answers because none of those are one of the options to the correct answers:
y^3/8, y/2, 2y^(1/3), 2y, y^2/4, 8y, 4y^2
wy^3/8, wy^2/4, wy/2, 4wy^2, 2wy^(1/3), 8wy, 2wy
(8p/3w)^(1/2), (3pw/8)^2, 3pw^2/8, (8w/3p)^(1/2), pw^2/8, 8p/w, 8p/3w
(p/3)^(1/2), p/3, p^2, 3p, 9p^2, (3/p)^(1/2), p
160pw, 160p/w, 60pw^2/8, 5pw^2/2, 20(8p/3w)^(1/2), 160p/3w, 20(8w/3p)^(1/2)
Ok, I see where you are going. I saw your answer y^3/8 and went huh?? What you really needed to answer was (y^3)/8. I attribute the problem to it being difficult to express mathematical terms here on the Jiskha site. I said y=f(x)=2x^(1/3). However my re-arranging terms, and getting the x all by itself, x=(y^3)/8. So, you are correct.
b) you are correct, (except for re-writing your answer as (w)(y^3)/8. Which, by the way, is equal to my answer.
c) You are correct. setting MC=p, then rearranging terms gets y=((p*8)/(3*w))^(1/2)
d) you are correct.
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