1.1 Cost curves Porygon Inc. produces distilled water. Its total cost for producing 3/ gallons of distilled water is y 3/2 314 Cm 1 000 000 + E _ 10, 000 + 1,000, 000 What is Porygon's average total cost, average xed cost, average variable cost, and marginal cost? 1.2 Isoprot curves In this problem you will prove that wherever the marginal cost function intersects an isoprot curve, it is at the minimum price attained by that isoprot curve. (We assume here that the marginal cost function is strictly increasing.) An isoprot curve is dened as the set of quantity- price pairs (q, p) that yield the same prot k 104601) =k where each different number k identies a different isoprot curve. a) b) C) d) First, taking k as given, solve the isoprot equation for p as a function of q. Call this function 1Pk(q)- Next, take the derivative of IPk(q) function with respect to q. de_(q) The rst order condition for minimizing IPk(q) sets dq =0. Rearrange this rst order condition to isolate digq) on the left hand side. If you have done everything right so far, the right hand side of the equation above should equal IPk(q). This means that at the quantity that satises the rst order condition for minimizing IPk(q), marginal cost at that quantity is equal to IPk(q). To complete the proof, we need to check the second order condition. To be at a local minimum of IPk(q ), the second derivative '12qu needs to be positive. Compute #12311, and show that it 13 positive when $qu = 0. There are (at least) two special isoprot curves. What are the more common names for the isoprot curves at k = 0 and at k = F