Adam owns a cabbage farm and he makes his two sons, Brian and Charlie, work in t

Question

Adam owns a cabbage farm and he makes his two sons, Brian and Charlie, work in the farm without wages. Assume that his two sons do not have alternative employment and the only input that Adam pays for is fertilizer. If he uses x units of fertilizer, which costs $1 per unit, he will produce 10squareroot x cabbage. What is the total units of the fertilizer needed to produce y cabbages? What is the total cost of the amount of fertilizer needed to produce y cabbage? If the only way that Adam can vary his output is by varying the amount of fertilizer applied to his farm, compute his marginal cost as a function of y. If the price of cabbages is $2 each, how many cabbages will Adam produce? How many units of fertilizer will he buy? How much is his profit by doing so? Suppose that the price of fertilizer and the price of cabbage remain as before, but Adam learns that his two sons can find summer jobs now. They would together earn $300 for the summer, which Adam could pocket, but they will not be able to work in the farm. Without their labor, he will not be able to produce anything. Should he continue to grow cabbages or should he let his sons get the summer jobs?

Explanation / Answer

1) To produce y cabbage Adam needs x fertilizer so y = 10sqrt(x) so x = y2/100 as price of x is 1 per unit so TC = y2/100

2) MC = dTC/dy = 2y/100 = y/50

3) as price of each additional cabbage is 2 so MR=2

for profit maximization MC=MR

y/50=2 so y=100

Revenue = 2*100 = 200

x = y2/100 = 100

TC = 100*1 = 100

Profit = 200-100 = 100

d) Now TC = 300 + y2/100

for breakeven

300 + y2/100 = 2y

y2-200y+30000=0

the roots of this equation is not real so it better to let his sons do summer job.

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