Problem $3.$ In a local wholesales market for wheat in Yorkton Saskatchewan, there are

$1,000$ farmers

looking to sell their wheat crop. Each farmer recognizes that his individual production

choices do not affect the market price, thus this market is considered to be perfectly

competitive. The farmers have a cost function given by $c[Yi]=32+10Yi+2Y^{2}i,,$

$2,$dots,$1,000.$

$($a$)$ Identify the fixed and variable costs of a single farmer. What are the average

fixed, average variable, and average total costs? What is the marginal cost?

Present the marginal cost and all the averages costs in a graph.

$($b$)$ What is the supply function of an individual farmer in this industry? What is

the industry's supply function?

$($c$)$ The demand for wheat in this market is given by $D[p]=9,500-50p.$ What is

the market price? How much each farmer will sell? What is the profit an

individual farmer is making?

$($d$)$ Now assuming the firms' long run cost function is $Y^{3}i-8Y^{2}i+42Yi$ and the

demand given in part $($c$)$ also represents the long$-$run demand, find the number of

farmers who will be in this

market in the long$-$run.