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Can someone explain how the slope on a PPF shows opportunity cost?

Economics - Financial Markets
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|dw:1347597380071:dw| if the slope is, say, \[\frac{ -7bread }{ 6 milk }\], how is that an opportunity cost? and what is it an opportunity cost of?
|dw:1347674814325:dw|The slope of the line of y = mx + b determines the opportunity cost or trade off. In other words, slope (as denoted by m) is called opportunity cost by economists in this simple case. For now, let x = milk and y = bread. If we were to start at the top left on the y axis, then y = 10 and x = 0 (I've chosen an arbitrary number). Let's also assume the slope (opportunity cost) m = 2. This means that for every unit of y that we give up, we gain 2 units of good x. This is an opportunity cost of 1:2 because we are giving up 2 bread loaves to gain 1 milk carton. To get 2 milk cartons we need to give up 4 bread loaves. The opportunity cost involved here is the fact that we have to "forfeit" our current holding of bread in order to gain a non zero amount of milk. Think of it as two countries - our country has to trade some bread for some milk and in essence our people will have 8 bread loaves left and have 1 milk carton. We lost 2 bread loaves to gain 1 milk carton. If we assume that both a bread and a milk carton have the same value (or utility in economic speak) to our citizens, then we have essentially lost. However, if each unit of bread still has a value of 1, but now instead each milk has a value of 3, then after we have traded, our net or total value (utility) of the 8 bread loaves and 1 milk cartons will be 11 "utility". Remember, that before trading we had only 10 bread loaves and 0 milk cartons for a combined utility of 10.

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