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3. Swedish Automobiles Are the Best (SAAB) sells two types of vehicles: a truck and a car. The monthly inverse demand or price equation for trucks is estimated as P_{t} = 65 - 0.05Q_{t} (where Q_{t} is the number of trucks sold and P_{t} is the price per truck in thousands). For cars, it is: P_{c} = 55 - 0.1Q_{c}. It costs SAAB $27 (thousand) to produce each additional truck and $21 (thousand) to produce each additional car, so MC_{t} = 27 and MC_{c} = 21. Assume no fixed cost, so TC = MC*Q. State the total profit equation AND marginal profit for trucks: 2 points

          3. Swedish Automobiles Are the Best (SAAB) sells two types of vehicles: a truck and a car. The monthly inverse demand or price equation for trucks is estimated as P_{t} = 65 - 0.05Q_{t} (where Q_{t} is the number of trucks sold and P_{t} is the price per truck in thousands). For cars, it is: P_{c} = 55 - 0.1Q_{c}. It costs SAAB $27 (thousand) to produce each additional truck and $21 (thousand) to produce each additional car, so MC_{t} = 27 and MC_{c} = 21. Assume no fixed cost, so TC = MC*Q. State the total profit equation AND marginal profit for trucks: 2 points
        
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Principles of Economics
Principles of Economics
Gregory Mankiw 8th Edition
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3. Swedish Automobiles Are the Best (SAAB) sells two types of vehicles: a truck and a car. The monthly inverse demand or price equation for trucks is estimated as P_{t} = 65 - 0.05Q_{t} (where Q_{t} is the number of trucks sold and P_{t} is the price per truck in thousands). For cars, it is: P_{c} = 55 - 0.1Q_{c}. It costs SAAB $27 (thousand) to produce each additional truck and $21 (thousand) to produce each additional car, so MC_{t} = 27 and MC_{c} = 21. Assume no fixed cost, so TC = MC*Q. State the total profit equation AND marginal profit for trucks: 2 points
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Transcript

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00:01 All right.
00:01 So for a, we want to find a profit.
00:05 So the profit function, p of x, y, is going to be our revenue.
00:12 So it'll be their revenue from america plus a revenue from europe minus the cost.
00:17 So the revenue from america is 13 minus, i'm sorry, is 13.
00:26 So it's going to be x times 13 minus 0 .2x.
00:34 And then plus the revenue from europe, which is going to be y times 17 minus 0 .1y minus our cost function, which is 19 plus 5 times x plus y.
00:57 So we simplify this to be 13x minus 0 .2x squared.
01:08 Plus 17y minus 0 .1 y squared minus 19 plus 5x plus 5y so for b we want to find how many cards should be sold in the market to maximize profit so we need to find the derivative of x y so we're going to find the derivative of x y so we're going to find the derivative respect to x and then find a derivative of respect to x and then find a derivative of so derivative of respect to x we have this would be 13 minus 0 .4 x and then this would be plus 17 minus 0 .2y minus 19 or actually that goes away and then plus 5 and plus 5 or actually to the back.
02:25 We need to find the partial derivatives.
02:33 So we need to find px.
02:35 So partial derivative of respect to x, so that's 13 minus 0 .4x plus 5.
02:47 Do we ever set that equal to 0? and then find a partial respect to y...
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