Suppose a farmer is a price taker (MR = P = 6) in soybeans with cost functions given byTC = .1q2 + 2q + 30MC = .2q + 2The level of profits isQuestion 4Select one:a.30.b.-10.c.20.d.10.
Question
Suppose a farmer is a price taker (MR = P = 6) in soybeans with cost functions given byTC = .1q2 + 2q + 30MC = .2q + 2The level of profits isQuestion 4Select one:a.30.b.-10.c.20.d.10.
Solution
To solve this problem, we first need to find the quantity (q) that maximizes the farmer's profit. This occurs where marginal cost (MC) equals marginal revenue (MR), which is also the price (P) in this case.
Given that MR = P = 6 and MC = .2q + 2, we can set these two equal to each other and solve for q:
.2q + 2 = 6 .2q = 6 - 2 .2q = 4 q = 4 / .2 q = 20
Now that we have the quantity, we can substitute it into the total cost (TC) equation to find the total cost at this quantity:
TC = .1q^2 + 2q + 30 TC = .1(20)^2 + 2(20) + 30 TC = .1(400) + 40 + 30 TC = 40 + 40 + 30 TC = 110
The total revenue (TR) is price times quantity, so TR = Pq = 620 = 120.
Finally, we can find the profit by subtracting total cost from total revenue:
Profit = TR - TC Profit = 120 - 110 Profit = 10
So, the level of profits is 10 (option d).
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