Question

Rochester Irrigation, Inc., operates in the highly competitive center pivot irrigation market. Prices for its RII-X pivot control switches are stable at $50 each. This means that P = MR = $50 in this market. Engineering estimates indicate that relevant total and cost function for the RII-X model are: TC=$78,000+18Q+0.002Q^2

The level of output to maximize profits is

Profits at this level of output is

Average Cost at this level of output is

Answer 1

Profit = Total revenue - Total cost = P*Q - TC = 50Q - (78,000+18Q+0.002Q^2) = 32Q - 78000 - 0.002Q^2

So, 0.004Q = 32
So, Q = 32/0.004 = 8,000

So, profit is maximized at Q = 8,000

The level of output to maximize profits is 8,000.

Profits = 32Q - 78000 - 0.002Q^2 = 32(8,000) - 78,000 - 0.002(8000^2) = 256,000 - 78,000 - 128,000 = 50,000
Profits at this level of output is $50,000

Average cost = TC/Q = (78,000/Q) + (18Q/Q) + (0.002Q^2/Q) = (78000/8000) + 18 + 0.002(8,000) = 9.75 + 18 + 16 = $43.75
So, average Cost at this level of output is $43.75