Fall 2001
1. y = - 2/5 x + 26/5
2. y = 2x
3. The underlying idea of this question is to show the parallel shifts. When we talk about an equation of the form y = mx + b, we are expressing the dependent variable y in terms of the independent variable x. All other variables that might have an affect on y are represented by b. Note that the equations given in this question differ only in the y-intercepts. All three lines represented by these equations are parallel since their slopes are the same. The variables other than x that do affect y are different and this causes parallel shifts. Also note that if x changes, then we move along the line rather than shifting it.
4. a. The PPF is a straight line, negatively sloped. Putting eggs (E) on the vertical and coconuts (C) on the horizontal axis, the y-intercept is 50, the x-intercept is 100.
b. E = 50 – ½ C
c. The opportunity cost of 1 egg is 2 coconuts.
d. The opportunity cost of 1 coconut is ½ eggs.
e. The opportunity cost of the variable on the x-axis is the absolute value of the slope, the opportunity cost of the variable on the y-axis is the absolute value of 1/slope.
f. The slope is constant throughout a linear PPF so opportunity cost is constant. When we have a bowed-out PPF, slope is increasing in absolute value, thus the law of increasing opportunity cost holds.
g. The PPF is a straight line, negatively sloped. Putting eggs (E) on the vertical and coconuts (C) on the horizontal axis, the y-intercept is 50, the x-intercept is 140. The equation is: E = 50 – 5/14 C. Technological improvements shift the PPF out. Note that if only the production of one of the goods experience the technological improvement, then the PPF will rotate. In this case egg collection was not affected by the improvement in technology, so y-intercept remains the same.
5. a. The opportunity cost of 1S is 4L in Japan and ¼ L in the US.
b. The opportunity cost of 1L is ¼ S in Japan and 4S in the US.
c. The US has absolute advantage in the production of S and Japan has absolute advantage in the production of L.
d. The US has comparative advantage in the production of S and Japan has comparative advantage in the production of L.
e. S = L. Then using the PPFs with this condition implies each country produces 20S and 20L, so the total production in this 2-country world is 40S and 40L.
f. Suppose we increase the production of S in the US by 4. Then the new production combination in the US is 24S and 19L. Now increase the production of L in Japan by 4. Then the new production combination in Japan is 19S and 24L. Now allow them to trade 1S for 1L so that the US has 23S and 20L and Japan has 20S and 23L. The surplus from specialization: 3S and 3L. Total production in the 2-country world after specialization is: 43S and 43L.