Probem A: The data in the first two columns of the table belows shows a research$-$based production function of how much potatoes are produced using different levels of irrigation water. You are a potato grower trying to determine how much water to use. Complete the table and answer the questions that follow. Assume potatoes sell for $$8\mathrm{.}00$ per cwt and water may cost either $$16\mathrm{.}00$ or $$32\mathrm{.}00$ per unit.

Water Units Potatoes $($cwt$)$ Total Physical Product Average Physical Product Marginal Physical Product Marginal Value Product Marginal Input Cost $($$$16/$unit$)$ Marginal Input Cost $($$$32/$unit$)$ Marginal Revenue Marginal Cost $($$$16/$unit$)$ Marginal Cost $($$$32/$unit$)$

$01600$

$11933333\mathrm{.}033$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$22084824\mathrm{.}015$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$32195919\mathrm{.}711$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$42296917\mathrm{.}310$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$52367615\mathrm{.}27$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$62408013\mathrm{.}34$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$72428211\mathrm{.}72$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$82438310\mathrm{.}41$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$9240808\mathrm{.}9-3$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

$10239797\mathrm{.}9-1$ $$8\mathrm{.}00$ $$8\mathrm{.}00$

Question $1.$ Complete the shaded area of the table by calculating TPP$,$ APP, MPP$,$ MVP$,$ MIC, MR$,$ and MC$.$ Note that MIC and MC should be calcualted at two different water prices; $($$$15$ and $$30)$

Question $2.$ Provide the profit maximizing amount of water to be used at each of the following price combinations.

Potato Price Water Price # of Water Units MVP$=$change in TR$/$ change in input

$$8\mathrm{.}00$ $$16\mathrm{.}00$

$$8\mathrm{.}00$ $$32\mathrm{.}00$

$$15\mathrm{.}00$ $$16\mathrm{.}00$

$$5\mathrm{.}00$ $$32\mathrm{.}00$

Question $3.$ Why does the Marginal Value Product decrease as more water is used?

Question $4.$ Where does Stage III begin in this problem? How do you know?

Question $5.$ If all other inputs $($other than water$)$ cost $$1,550\mathrm{.}00$ per acre, what is the per$-$acre profit level when potatoes are $$8\mathrm{.}00/$cwt and water costs $$16/$unit$?($Show your work.$)$