[SOLUTIONS] ECON313 - PS3 (Winter 2023)

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1 ECONOMICS 313 – Section 001 ECONOMIC DEVELOPMENT Winter 2023 Practice PROBLEM SET NO. 3 These problems will be taken up in the conferences during the week beginning March 20 th , 2023. While you do not hand in your answers, it is in your best interest to work on these questions before the conferences. PART I – MULTIPLE CHOICE QUESTIONS: Circle only the best answer (only one answer) 1) According to Endogenous Growth Theory, which of the following cannot be said about knowledge: a. It is a rival good b. It is an excludable good c. Property rights can prevent access to knowledge d. Is produced using labour allocated to research e. All the above can be said about knowledge in Endogenous Growth Theory Answer: A 2) Most cross-country GDP/capita differences between developed and developing countries can be explained by differences in: a. Capital output ratio (K/Y) b. Human capital ratio (H/L) c. Total factor productivity d. Geography e. Religion Answer: C 3) According to Douglass North, Institutions are the humanly devised constraints that structure human interaction and are made up of: a. Formal constraints b. Social norms c. Laws and regulations d. Informal constraints e. All the above Answer: E

2 4) Under uncertainty (or imperfect information), which of the following scenarios is not an example of market failure as a result of adverse selection: a. Only low quality cars will sell in the used car market b. All low risk borrowers will exit the market for credit c. Only high risk borrowers will remain in the market for credit d. All low risk borrowers will behave like high risk borrowers if they obtain credit e. All the above are examples of market failures resulting from adverse selection Answer: D 5) Which of the following are problems associated with asymmetric information: a. Market for Lemons b. Prisoners ’ Dilemma c. Tragedy of the Commons d. Nash Equilibria e. None of the above Answer: A Community 2 Payoff s Bridge Dam Community 1 Bridge 2,1 0,0 Dam 0,0 1,2 Table 1 6) Consider the game in Table 1, on which two neighbouring rural communities must decide on which public good to invest in: building a bridge or building a dam. Which of the following is true: a. [Bridge-Dam] and [Dam-Bridge] are the two Nash Equilibria b. [Bridge-Bridge] and [Dam-Dam] are the two Nash Equilibria c. [Bridge-Bridge] is the unique Nash Equilibria d. [Dam-Dam] is the unique Nash Equilibria e. There are no Nash Equilibria in this Game Answer: B 7) Consider again the game in Table 1. Which of the following is true: a. Playing [Bridge] is the dominant strategy for both players b. Playing [Dam] is the dominant strategy for both players c. Playing [Bridge] is the dominant strategy for Community 1 only d. Playing [Dam] is the dominant strategy for Community 2 only e. There are no dominant strategies for either Community in this game Answer: E

3 8) Consider the Neoclassical production function Y=(A,K,L) where Y is output, A is a Technology parameter, K is physical capital stock, and L is labour. The corresponding Growth Accounting Equation is: where is the growth in output, is the growth in physical capital stock and is the population growth rate. Let , , and . Then: a. National income is growing at 1% b. National income is growing at 6% c. Total Factor Productivity is 1% d. Total Factor Productivity is 6% e. None of the above Answer: C 9) In a standard 2 round, 2 person, Trust Game, each player is given an endowment of 10$. In the first round player 1 must decide how much ( x ) to send to player 2. This amount x gets tripled by the experimenter so that player 2 must decide how much (between 0 and 3 x ) to send back to player 1. The subgame perfect equilibrium will have: a. Player 1 sends 10$ and Player 2 returns 15$ b. Player 1 sends 0$ and Player 2 returns 15$ c. Player 1 sends 10$ and player 2 returns 0$ d. Player 1 sends 0$ and player 2 returns 0$ e. None of the above Answer: D Figure 1 10) Consider figure 1. Suppose a family is at budget constraint BC1 and has optimized their choice of other goods and the number of children at equilibrium E1. Now consider that, with economic development, women’s incomes are increasing so that the opportunity cost of having children has gone up. In such a situation, holding all else constant, the new equilibrium would best be described by: a. Equilibrium E2 on budget constraint BC2 and the family will desire more children b. Equilibrium E3 on budget constraint BC3 and the family will desire more children c. Equilibrium E3 on budget constraint BC3 and the family will desire fewer children d. Equilibrium E4 on budget constraint BC4 and the family will desire more children

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4 e. Equilibrium E4 on budget constraint BC4 and the family will desire fewer children Answer: None of the above – it would be on a budget constraint steeper than BC1 but shifted out to the right of BC1. 11) In the process of economic development, stage II of the demographic transition implies: a. That the birth rate remains high while the death rate falls b. That the birth rate falls faster than the death rate c. That the death rate falls faster than the birth rate d. That neither birth nor death rates decline e. That the death rate stays constant while the birth rate falls Answer: A True False or Uncertain: For each question in this section, please state whether the statement is true as written, and explain why. A good answer will define terms carefully and provide caveats to the statements made or provide details for the statements made, when this is appropriate. To receive maximum points, your answer should discuss intelligently the relevant lecture material. (Indicate clearly which question you are answering) 1 The concept of income convergence means that per capita income growth will be larger in rich countries than in poor countries. This relationship holds up in the data in cross country per capita income and income growth. Definitions: Income convergence: a concept that countries converge in income to their steady state. Income and income growth: a measure of living standards or economic development. Growth is the percentage change in this measure. False Explanation: The concept means, in its ‘pure’ or unconditional form, that poor countries have to grow faster than rich countries. The relationship in the data is not supportive of income convergence, and in fact the data might show the incorrect pattern (rich countries growing faster than poor countries). One way to ‘rationalize’ this – to reconcile the data with the theory – is to propose ‘conditional’ convergence: that different countries converge to different steady states. A diagram could be used to illustrate this point.

5 2. Growth accounting has shown us that most income differences between poor countries and rich countries can be explained by differences in total factor productivity Definitions: Growth accounting (textbook definition) : “The decomposition of an economy’s growth rate into various components: that which is explained by the growth rate of the labor force, that which is explained by the growth rate of capital stock or that which is the residual attributed to total factor productivity.” A word definition something like this acceptable, as is an equation form ( gy =a+α g k+(1- α) g l) where the variables are defined. Total Factor Productivity TFP (textbook definition) : “The part of output that labour and capital productivity can not explain. It is usually thought to be the resul t of technological progress” also described as the Solow residual. True Explanation: We can see this in table 4.1 in the textbook. Developed countries tend to have similar productivity levels (using the US as a benchmark) in terms of output per worker, and physical and human capital as well as the unexplained contribution (TFP, or A). However, looking at relatively poorer countries, physical and human capital productivity differences relative to the US are lower compared to the relative differences in output per worker – the relatively small contributions in A help explain this discrepancy. See how the text describes the case of China on pages 102 and 103 in the print version of the text. 3. The tragedy of the commons can be averted if agents could commit to a Nash Equilibrium Definitions: Tragedy of the commons: when individual incentives to over-extract a common pooled resource (e.g. environment, common lands) leads to a depletion of the resource, such that pursuing self-interest goes against the social good. Nash Equilibrium: the situation (equilibrium) in which each agent has chosen their optimal strategy. False Explanation : Over-extraction occurs when both agents, by their self-interest, maximize their yield of the common resource. This situation is typically modelled with a Priso ner’s dilemma where the dominant strategy for all players is to over-extract. In this situation, the Nash Equilibrium has all players over-extracting, thus leading to the Tragedy of the Commons. For illustration, see the game we saw in class:

6 An excellent answer would say: We could avert the tragedy of the commons if players could commit to not over-extract – i.e. to a cooperative equilibrium (cooperate/cooperate). An even more excellent answer would add: for this to happen, we’d have to see different payoffs such that Cooperate is a dominant strategy; OR, play an infinitely repeated game which should yield the socially optimal outcome. 4. In developing countries, the private and social rates of return to education are the same. Definitions: The private rate of return is the net benefit (private benefit – private cost) to the individual Social rate of return is the net benefit (social benefit – social cost) to society. False. Explanation: At least conceptually, the two are distinct. Empirical evidence demonstrates that the private benefits exceed the private costs and this difference is increasing as the level of schooling increases. Meanwhile, the social benefits are increasing at a decreasing rate while the social costs are increasing at an increasing rate (as the level of schooling increases). So the implications in terms of returns (benefits minus costs) will vary depending on different levels of schooling. In particular, the private returns are highest in tertiary and the social returns are highest in primary.

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7 Quantitative Questions Lucy is finishing primary school and she is deciding whether or not to go to secondary school. Lucy, like everyone else in the world, lives only for two periods after primary school. In the first period, she could work at the diamond mine (without secondary school) for a salary of Y p , or instead, Lucy could go to secondary school. If Lucy does go to secondary school in the first period, she’ll have to pay 5,000 CFA in fees (tuition and books) but she also receives 5,000 CFA from workin g in her family’s business part time while enrolled in school. In the second period, had she not gone to secondary school, Lucy would continue to earn Y p . With a secondary school degree in the first period, Lucy would earn Y s in the second period working a s a doctor’s secretary. Assume that the rate of interes t at which Lucy can borrow or lend money is i . a) What are Lucy’s costs (direct and indirect) of going to secondary school? The direct costs: tuition= 5000 CFA Indirect costs: forgone earnings=Yp in each year b) What a re Lucy’s benefits of going to secondary school? Her earnings Ys in year 2 But she also earns 5,000CFA in year 1 while in school c) Working with present value methods, show that Lucy will go to secondary school in the first period if: Ys >(2+i) Yp PVB=5000+Ys/(1+i) PVC=5000+Yp+Yp/(1+i) Lucy goes to secondary school if and only if PVB>PVC: 5000+Ys/(1+i) > 5000+Yp+Yp/(1+i) Simplifying: Ys/(1+i) > Yp+Yp/(1+i) → Ys> Yp(1+i)+Yp → Ys> Yp(2+i) → QED d) Recall that the internal rate of return to education is the interest rate i=r that makes the prevent value benefits equal to the present value costs. Calculate r expressed as a function of Ys and Yp. What must be true about Ys and Yp if r is to be positive? Using calculations in c): Ys=Yp(2+r) => (Ys/Yr)-2=r r is positive if and only if Ys is more than 2 times greater than Yp

8 e) Returning to your answer in c), explain what would happen to Lucy’s decision if the rate of interest increased? If the interest rate i were to increase, the difference between Lucy’ s PVB and PVC would fall, and eventually may reverse it. So with an i high enough, Lucy will not find it beneficial to go to secondary school and will instead go work in the diamond mine. Question 3 – Corruption Suppose that 2 agents meet to conduct some transaction: a trader and a public official. Each agent has two strategies they can choose from: they can be honest, or they can be corrupt. If both the trader and the public official are honest, the trader receives a payoff of 6 and the public official a payoff of 2. If they are both corrupt, the trader receives a payoff of 2 and the public official a payoff of 6. Meanwhile, if one agent is corrupt and the other honest, then the honest one receives a payoff of 0 and the corrupt one a payoff of -4 (negative because of the chance the honest agent reports the corrupt agent to the authorities). This example is a modification of a game in Wydick’s book Games in Economic Development (2008) a) Depict this game in matrix form with the trader as player A and the public official as player B. Player B (public official) Honest Corrupt Player A (trader) Honest 6 , 2 0 , -4 Corrupt -4 , 0 2 , 6 b) Is any strategy dominant, and why or why not? There are no dominant strategies – A is always better off doing what B does and B is always better off doing what A does. c) How many Nash equilibria are there and why? Show your work There are 2 Nash Equilibria: (Honest/Honest) and (Corrupt/Corrupt), for the reasoning in b) d) How would you change the payoffs to ensure that honest/honest is the only equilibrium? What policy might you recommend for this to happen? One way to do this is to change the payoffs to make the honest strategy a dominant strategy for both players. The way to do this easily is to increase the payoff for players who chose the honest strategy when facing a corrupt opponent. In this case, you would want a payoff x 1 >2 and x 2 >6

9 Player B (public official) Honest Corrupt Player A (trader) Honest 6 , 2 x 1 , -4 Corrupt -4 , x 2 2 , 6 A policy maker could introduce a reward for reporting a corrupt official. Notice that the reward must be greater for the official because he is giving up a higher payoff by being honest. e) Now if you were the public official, how would you change the payoffs to ensure that dishonest/dishonest is the only equilibrium? One way to do this is to change the payoffs to make the corrupt strategy a dominant strategy for both players. This would happen, for instance if there was an increase in the payoff for players who chose the corrupt strategy when facing a corrupt opponent. In this case, you would want a payoff y 1 >2 and y 2 >6 Player B (public official) Honest Corrupt Player A (trader) Honest 6 , 2 0 , y 1 Corrupt y 2 , 0 2 , 6 If there were no way for authorities to penalize a corrupt individual, and the payoffs received by a corrupt agent is greater than the payoff of being honest, then you would get such a situation.. Why would the payoffs to a trader to be corrupt ever be higher when facing an honest official?. It could be that offering a bribe will reduce the waiting time for completing the transaction. Question 4 – Market for lemons Following the example we saw in class (and on page 179-180 in the hard copy of the Roland text), suppose good quality cars are valued on the market at $12,000 but cost the seller $10,000 while low quality cars (the lemons) are valued on the market at $5,000 but cost the seller $4,000. Assume, as in the textbook example, that the probability that a car is of good quality is 50%. a) If the good car is sold at market value, what is the profit per car? $12,000-$10,000=$2,000 per good car b) If the bad car is sold at market value, what is the profit per car? $5,000-$4,000=$1,000 per bad car c) If buyers had perfect information about the quality of car, would any purchase the low quality car? Yes, as long as there is a demand for both good cars and bad cars. (Note the example in class saw bad car vendors incur a loss if there was perfect information which would

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10 restrict supply under perfect information) d) If buyers could not tell whether a car is of good quality or bad quality, what would be the maximum a risk neutral buyer be willing to spend on a used car? Would any high quality cars be sold? Why or why not? EV(used car) = 0.5 x $12,000 + 0.5 x $5,000 = $6,000 + $2,500 = $8,500 Since (risk neutral) buyers can’t tell, they won’t pay more than the expected value of the car, in this case $8,500. This means that the most they would pay for a good quality car is $8,500, which would bring a loss of $1,500 to good car vendors. Good car vendors will not sell at this price, so they will leave the market, and only bad cars will remain. e) Now answer d) if there were only 10% of bad quality cars in the market. EV(used car) = 0.9 x $12,000 + 0.1 x $5,000 = $10,800 + $500 = $11,300 In this case, both good quality and low quality cars will be sold in the market.. The good quality car vendor would expect a profit of $1,300 per car, and the low quality car vendor would get a profit of $7,300 per car. f) Suppose you were a policy maker, what policies would you recommend to solve the asymmetric information problems highlighted in this problem? As long as enforcement were possible and credible, governments could impose disclosure rules, or insist that all cars be sold with a warranty or return policy.

[SOLUTIONS] ECON313 - PS3 (Winter 2023)

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