PS03__Answers_ - EC 340 Spring 2011 Problem Set 3 1. Here...

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Unformatted text preview: EC 340 Spring 2011 Problem Set 3 1. Here is a production possibilities frontier with increasing opportunity cost: 100 90 70 40 10 20 30 40 Suppose that the economy starts by producing 10 units of X. What is the opportunity cost of producing 10 additional units of X? What is the opportunity cost of producing 10 additional units of X if the economy is already producing 20 units of X? If the economy is already producing 30 units of X? First, my apologies for not labeling the axes. I should ALWAYS label the axes, but somehow this slipped through. Assuming (as I intended) that the vertical axis represents the quantity of Y and the horizontal axis represents the quantity of X, we know that when the economy produces 10 units of X it also produces 100 units of Y. Increasing X production from 10 to 20 results in Y production falling from 100 to 90, a loss of 10 units of Y. So the opportunity cost of producing the extra 10 X is 10 units of Y. Similarly, starting at 20 units of X, an extra 10 units (increasing production to 30 units of X) means reducing Y production to 70 units. This is a loss of 20 additional units of Y, so the opportunity cost of those 10 units of X is 20 units of Y. Finally, increasing production of X from 30 to 40 results in a loss of 30 more units of Y, so the opportunity cost of these 10 units of X is 30 units of Y. 2. Given the information in question 1, what can you conclude about the production of X if the price of X in terms of Y is 3? The economy produces where the opportunity cost of producing X equals the price of X in terms of Y. From the geometry of the PPF, it must be the case that the slope of the PPF equals ‐3 somewhere between the point where the quantity of X produced equals 30 and the quantity of X produced equals 40. So the quantity of X produced will be somewhere between 30 and 40. 3. In the example illustrated in question 1, does the opportunity cost of producing Y increase, decrease, or remain the same as more Y is produced? 4. The opportunity cost of Y is increasing as more Y is produced. One easy way to verify this is to rotate the graph so that the Y‐axis becomes the horizontal axis. The picture then looks qualitatively similar to the diagram that is drawn for this problem set, with the slope of the PPF becoming more and more negative as more and more Y is produced. Assume two goods (X and Y). Draw a production possibilities frontier and consumption possibilities for a country that imports good X when trade is permitted. (To keep the diagram uncluttered, do not illustrate autarky). Show where this economy will produce on the PPF and where it might consume on the consumption possibilities frontier. 5. Exports of Y QY SY D Y SX DX QX Imports of X Assume two goods (X and Y). Draw a production possibilities frontier and consumption possibilities for a country that imports good Y when trade is permitted. (To keep the diagram uncluttered, do not illustrate autarky). Show where this economy will produce on the PPF and where it might consume on the consumption possibilities frontier. Imports of Y QY D Y SY DX SX Exports of X QX 6. 7. Suppose that there are 3 goods (X, Y, and Z) and two inputs (Labor and Capital). The amounts of labor and capital used to produce each of the three goods are given in the table below. Rank order the three goods in order of their capital intensity (most capital intensive, next most capital intensive, then least capital intensive). X Y Z Amount of capital per unit 1,000 4 50 Amount of labor per unit 2,000 1 40 Capital per Worker 1/2 4 5/4 The key is to calculate the amount of capital used per worker in the production of each good. In this example, good Y is the most capital intensive since it uses 4 units of capital per worker. Good Z is the next most capital intensive, using 5/4 units of capital per worker, and good X is the least capital intensive, using only ½ unit of capital per worker. What is the difference between the terms “capital abundant” and “capital intensive”? The term “intensive” refers to a comparison of how much capital is used per worker in the production of various goods. The term “abundance” refers to a comparison across countries in their supplies of capital per worker. ...
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