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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise In this problem, p and C are in dollars and x is the number of units. A monopoly has a total cost function C 1000 + 72x + 12x2 for its product, which has demand function p = 216-3x-2x . Find the consumer's surplus at the point where the monopoly has maximum profit. Step 1 We must first find the point where profit is maximized. Because the demand for x units is p = 216-3x-2xi, the total revenue is the following R(x)-px = (216-3x- (216-3x - 2x2) Step 2 We can now find the profit function. P(x) = R(x)-C(x) = 216x-3x2-2x3-( 1000+ 72x + 12x2. 112r2+72r +10001) 2x3 -152+144x 100023 15a2 144 1000 Step 3 Next, we find where P(x) is maximized. We find a critical point of P, and test that it is a maximum p'(x) 0 = =0 -6(x +8) Since a negative value doesn't make sense for this problem, x- Submit Skip (you cannot.come back) Show transcribed image text
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise In this problem, p and C are in dollars and x is the number of units. A monopoly has a total cost function C 1000 + 72x + 12x2 for its product, which has demand function p = 216-3x-2x . Find the consumer's surplus at the point where the monopoly has maximum profit. Step 1 We must first find the point where profit is maximized. Because the demand for x units is p = 216-3x-2xi, the total revenue is the following R(x)-px = (216-3x- (216-3x - 2x2)
Step 2 We can now find the profit function. P(x) = R(x)-C(x) = 216x-3x2-2x3-( 1000+ 72x + 12x2. 112r2+72r +10001) 2x3 -152+144x 100023 15a2 144 1000 Step 3 Next, we find where P(x) is maximized. We find a critical point of P, and test that it is a maximum p'(x) 0 = =0 -6(x +8) Since a negative value doesn't make sense for this problem, x- Submit Skip (you cannot.come back)
Show transcribed image text Casey DurganLv2
22 Aug 2019