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hitation is the time the leader, the older (and thus easier to copy) are the technologies that the follower ology was invented-thus the farther the follower lags behind the ratio of technology in Country 1 to technology in Country 2, where the func- To formulate this assumption mathematically, we say that , is a function of wants to imitate. tion that describes the relationship is denoted as c(): Hc = c (A). We make three assumptions about this "cost of copying" function. First, we as sume that it is downward sloping-that the cost of copying falls as the technol ogy gap between the two countries increases (i.e., as the ratio of Countru GURE 8.3 Steady State in the Two-Country Model Growth rate of technology, A TAIL Pi A₂ -A₁

hitation is the time the leader, the older (and thus easier to copy) are the technologies that the follower ology was invented-thus the farther the follower lags behind the ratio of technology in Country 1 to technology in Country 2, where the func- To formulate this assumption mathematically, we say that , is a function of wants to imitate. tion that describes the relationship is denoted as c(): Hc = c (A). We make three assumptions about this "cost of copying" function. First, we as sume that it is downward sloping-that the cost of copying falls as the technol ogy gap between the two countries increases (i.e., as the ratio of Countru GURE 8.3 Steady State in the Two-Country Model Growth rate of technology, A TAIL Pi A₂ -A₁

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please note: for part i. of the question - the cost of copying is changing for the FOLLOWER COUNTRY (Country 2).
since a new technology was invented-thus the farther the follower lags behind copy. Alternatively, we could say that what affects the cost of imitation is the time the leader, the older (and thus easier to copy) are the technologies that the follower To formulate this assumption mathematically, we say that , is a function of the ratio of technology in Country 1 to technology in Country 2, where the func- wants to imitate. tion that describes the relationship is denoted as c(): Mc = We make three assumptions about this "cost of copying" function. First, we as- sume that it is downward sloping-that the cost of copying falls as the technol- ogy gap between the two countries increases (i.e., as the ratio of technology in Country 1 to technology in Country 2 increases). Second, we assume that as the ratio of A₁/A₂ goes to infinity, the cost of copying falls to 0. In other words, if the gap in technology were infinitely large, then imitation would be costless. Finally, we assume that as the ratio of A₁/A₂ approaches 1, the cost of copying approaches the cost of invention. This means that if the follower country is very near the technology leader, it gets little benefit from copying technology rather than in venting its own. (The cost-of-copying function is not defined if A₁/A₂ is less than 1 because in this case, there would be nothing for Country 2 to copy.) Figure 8.2 shows what the cost-of-copying function might look like. FIGURE 8.2 Cost of Copying for the Follower Country Cost of copying, c 14₁ c(A₁/A₂) A₁/A₂ 8.3 Modeling the Relationship between Technology Creation and Growth FIGURE 8.3 Steady State in the Two-Country Model Growth rate of technology, A TAIL Pi YAZL (A₁/A₂)ss Â₁ YA,2 ·L₂. He A₁/A₂ Given a value of μc, the rate of technology growth in Country 2 is given by an equation in the same form as the growth rate of technology in Country 1: Â₂ = We are now in a position to look at the steady state of the model. The key insight is that, in the steady state, the two countries will grow at the same rate. Figure 8.3 shows why this is the case: It graphs the growth rate of A in each coun- try as a function of A₁/A2, the ratio of technology in the leader country to technol- ogy in the follower country. If this ratio were 1-that is, if Country 2 had the same level of technology as Country 1-then we would know that technology would be growing more quickly in Country 1 than in Country 2. The reason is that, in this case, the two countries would have the same cost of creating new technologies, whereas Country 1 has a higher value of YA than does Country 2. By contrast, if this ratio were infinite, then the cost of acquiring new technologies in Country 2 would be 0, and Country 2 would be experiencing faster technological growth than Country 1. Thus, at some ratio of A₁/A₂ between 1 and infinity, the two countries will have the same growth rates of A, and the ratio of the levels of technology in the two countries will remain constant. This will be the steady state. Note also that this steady state is stable: If the ratio A₁/A₂ starts off above the steady state, then A₂ will grow faster than A₁, and the ratio will fall. If the ratio starts off below the steady state, the opposite will occur.
Transcribed Image Text:since a new technology was invented-thus the farther the follower lags behind copy. Alternatively, we could say that what affects the cost of imitation is the time the leader, the older (and thus easier to copy) are the technologies that the follower To formulate this assumption mathematically, we say that , is a function of the ratio of technology in Country 1 to technology in Country 2, where the func- wants to imitate. tion that describes the relationship is denoted as c(): Mc = We make three assumptions about this "cost of copying" function. First, we as- sume that it is downward sloping-that the cost of copying falls as the technol- ogy gap between the two countries increases (i.e., as the ratio of technology in Country 1 to technology in Country 2 increases). Second, we assume that as the ratio of A₁/A₂ goes to infinity, the cost of copying falls to 0. In other words, if the gap in technology were infinitely large, then imitation would be costless. Finally, we assume that as the ratio of A₁/A₂ approaches 1, the cost of copying approaches the cost of invention. This means that if the follower country is very near the technology leader, it gets little benefit from copying technology rather than in venting its own. (The cost-of-copying function is not defined if A₁/A₂ is less than 1 because in this case, there would be nothing for Country 2 to copy.) Figure 8.2 shows what the cost-of-copying function might look like. FIGURE 8.2 Cost of Copying for the Follower Country Cost of copying, c 14₁ c(A₁/A₂) A₁/A₂ 8.3 Modeling the Relationship between Technology Creation and Growth FIGURE 8.3 Steady State in the Two-Country Model Growth rate of technology, A TAIL Pi YAZL (A₁/A₂)ss Â₁ YA,2 ·L₂. He A₁/A₂ Given a value of μc, the rate of technology growth in Country 2 is given by an equation in the same form as the growth rate of technology in Country 1: Â₂ = We are now in a position to look at the steady state of the model. The key insight is that, in the steady state, the two countries will grow at the same rate. Figure 8.3 shows why this is the case: It graphs the growth rate of A in each coun- try as a function of A₁/A2, the ratio of technology in the leader country to technol- ogy in the follower country. If this ratio were 1-that is, if Country 2 had the same level of technology as Country 1-then we would know that technology would be growing more quickly in Country 1 than in Country 2. The reason is that, in this case, the two countries would have the same cost of creating new technologies, whereas Country 1 has a higher value of YA than does Country 2. By contrast, if this ratio were infinite, then the cost of acquiring new technologies in Country 2 would be 0, and Country 2 would be experiencing faster technological growth than Country 1. Thus, at some ratio of A₁/A₂ between 1 and infinity, the two countries will have the same growth rates of A, and the ratio of the levels of technology in the two countries will remain constant. This will be the steady state. Note also that this steady state is stable: If the ratio A₁/A₂ starts off above the steady state, then A₂ will grow faster than A₁, and the ratio will fall. If the ratio starts off below the steady state, the opposite will occur.
Consider figure 8.2 and 8.3 on pages 218 and 219 from the textbook. . Consider each of the following scenarios separately. 11. I Suppose in the leader country (Country 1) there is a rise in cost of copying at every level of technology gap (A1/A2), possibly caused by factors influencing the cost of copying other than technology gap (possibly education). Show how these graphs will be affected as a result of this new change. On your well labeled graphs you must clearly indicate the shift of the relevant curve (s) and the direction of the shift. Explain your answer in 2-3 sentences. Suppose pandemic reduces population growth decreasing the number of workers available to both the countries by same amount. Show how these graphs will be affected as a result of this new change. On your well labeled graphs you must clearly indicate the shift of the relevant curve (s) and the direction of the shift. Explain your answer in 2-3 sentences.
Transcribed Image Text:Consider figure 8.2 and 8.3 on pages 218 and 219 from the textbook. . Consider each of the following scenarios separately. 11. I Suppose in the leader country (Country 1) there is a rise in cost of copying at every level of technology gap (A1/A2), possibly caused by factors influencing the cost of copying other than technology gap (possibly education). Show how these graphs will be affected as a result of this new change. On your well labeled graphs you must clearly indicate the shift of the relevant curve (s) and the direction of the shift. Explain your answer in 2-3 sentences. Suppose pandemic reduces population growth decreasing the number of workers available to both the countries by same amount. Show how these graphs will be affected as a result of this new change. On your well labeled graphs you must clearly indicate the shift of the relevant curve (s) and the direction of the shift. Explain your answer in 2-3 sentences.
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