Please answer the question 5-7. Suppose that a farmer\'s cost of growing y units

Question

Please answer the question 5-7.

Suppose that a farmer's cost of growing y units of com is given by c(y) = y^2/20 + y. What is his supply curve of corn as a function of the price of corn? If the price of corn is $5 per unit, how much corn will this farmer grow? The government now introduces a Payment-in-Kind (PIK) program. If the farmer decides to grow y units of corn, he will get 40 - y/2 units from the government stockpiles. Compute the farmer's profit as a function of his output and the market price of corn, taking into account the value of payments-in-kind received. At the market price p, what will be the farmer's profit maximizing output of corn -excluding PIK program? Draw this supply curve in a graph. If the price is $2, how many units of com will he produce? How many units of corn will he get from the government stockpiles, assuming that he chooses to be in the PIK program? Derive the total supply curve of corn - including the corn from the PIK payment -and draw it in the graph. Compare this with the graph you drew in (4). Suppose that there is one other identical farmer in the market. Derive the aggregate market supply counting everything - including the corn from the PIK payment - and draw them in the graph you find in (6).

Explanation / Answer

1) TC = y2/20 + y

MC = dTC/dy = y/10 + 1

Now for finding supply curve MC = price = p

p = y/10 + 1

y = 10p - 10

2) if p = 5 then y = 10*5-10 = 40

3) Profit including PIK = Revenue - total cost + earning from PIK = py - y2 /20 -y + p(40-y)/2

4) Profit maximizes when MC=MR

MC = y/10 + 1

MR = p

p=y/10 + 1

y = 10p-10

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