Profit, Cost, and Revenue. October 28, 2013
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1 October 28, 2013
2 Maximizing profit A fundamental issue for a producer is how to maximizing profit.
3 Maximizing profit A fundamental issue for a producer is how to maximizing profit. π(q) = R(q) C(q)
4 Maximizing profit A fundamental issue for a producer is how to maximizing profit. π(q) = R(q) C(q) MC = C : Marginal cost; MR = R : Marginal revenue
5 Estimating maximum profit if the revenue and cost are given by the curves R and C, respectively, in the figure. $ (thousands) C 150 R q (quantity)
6 Profit =Revenue Cost $ (thousands) C 150 R q (quantity)
7 Profit =Revenue Cost Profit is represented by the the vertical distance from curve C to curve R, marked by vertical arrow. $ (thousands) C 150 R q (quantity)
8 Profit =Revenue Cost Profit is represented by the the vertical distance from curve C to curve R, marked by vertical arrow. Arrow is going down = No profit $ (thousands) C 150 R q (quantity)
9 Profit =Revenue Cost Profit is represented by the the vertical distance from curve C to curve R, marked by vertical arrow. Arrow is going down = No profit Arrow is going up = Making profit $ (thousands) C 150 R q (quantity)
10 Profit =Revenue Cost Profit is represented by the the vertical distance from curve C to curve R, marked by vertical arrow. Arrow is going down = No profit Arrow is going up = Making profit Profit is maximized if the arrow is going up and has the largest distance. $ (thousands) C 150 R q (quantity)
11 We now analyze the marginal costs and marginal revenues near the optimal point. MC<MR MC>MR R C MC=MR
12 We now analyze the marginal costs and marginal revenues near the optimal point. Global maxima and minima occur at critical points or at the endpoints of the interval MC<MR MC>MR R C MC=MR
13 We now analyze the marginal costs and marginal revenues near the optimal point. Global maxima and minima occur at critical points or at the endpoints of the interval π (q) = R (q) C (q) = 0 MC<MR MC>MR R C MC=MR
14 We now analyze the marginal costs and marginal revenues near the optimal point. Global maxima and minima occur at critical points or at the endpoints of the interval π (q) = R (q) C (q) = 0 MR = R = C = MC. MC<MR MC>MR R C MC=MR
15 Conclusion The maximum or minimum profit can occur where marginal profit=0. That is where marginal revenue=marginal cost.
16 The (total) revenue and (total) cost curves for a product are given in the Figure. (a) Sketch (roughly) the marginal cost and revenue. (b) Graph the profit function π(q).
17
18 Find the quantity which maximizes the profit if the total revenue and total cost (in dollars) are given by R(q) = 5q 0.003q 2 C(q) = q where q is quantity and 0 q 1000 units. What production level gives the maximize profit?
19 Maximize Revenue At a price of $80 for a half-day trip, a white-water rafting company attracts 300 customers. Every $5 decrease in price attracts an additional 30 customers. Find the demand equation.
20 Maximize Revenue At a price of $80 for a half-day trip, a white-water rafting company attracts 300 customers. Every $5 decrease in price attracts an additional 30 customers. Find the demand equation. Express revenue as a function of price
21 Maximize Revenue At a price of $80 for a half-day trip, a white-water rafting company attracts 300 customers. Every $5 decrease in price attracts an additional 30 customers. Find the demand equation. Express revenue as a function of price What price should the company charge per trip to maximize revenue?
22 Maximize Revenue At a price of $80 for a half-day trip, a white-water rafting company attracts 300 customers. Every $5 decrease in price attracts an additional 30 customers.
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