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**Problem Set 2**

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Problems1-3arebasedoffSolowmodel,Romermodelandclassdiscussion on institutions. Problems 4 -6 are based off Chapter 7. Problems 7 -9 are based off of chapter8.

Consider the following extension of the Solow model with exogenous produc- tivity growth. The expression for total output and the dynamics of capital per effective worker are given by the following expressions:

*Y *= *K** ^{α}*(

∆*k *= *sy **− *(*δ *+ *g*)*k*

where *g *is the growth rate of *A*, *y *is output per effective worker, and *δ *is the depreciation rate of capital.

- Usingtheinformationgivenabove,findthefundamentalSolowequation. Find an expression for steady state capital per effectiveworker.
- What happens to steady state capital if the growth rate of productivity rises?
- Suppose that this economy consists of two types of households: laborers and capitalists. Capitalists own all the capital stock
*K*and are paid arental rate equal to the marginal product of capital. Find an expression for their share of nationalincome. - Assume that laborers save none of their income. If capitalists save 30% of their income, the parameter
*α*= 0*.*3, and the parameter*δ*= 0*.*1, what is the aggregate saving rate*s*? Will income inequality between capitalists and laborers worsen overtime?

Which of the following statements about the role of institutions in economic growth is TRUE and which of the following statements is FALSE? Explain.

- Higher expropriation risk due to low-quality governance and poor insti- tutions might account for low levels of human and public capital in poor nations
- The quality of institutions in countries colonized by Europeans is corre- lated with whether climate/disease allowed European settlers to live in thoseareas
- Low-quality institutions make it difficult to protect property rights and enforcecontracts

Suppose the economy is on a balanced growth path in the Romer model, and then, in the year 2030, research productivity rises permanently to *z*¯^{j}*> z*¯.

- Solveforthenewgrowthrateofknowledgeand
*y*._{t} - Make a graph of
*y*over time (on a ratio scale)._{t} - Why might the parameter
*z*¯ increase in aneconomy?

In this problem, you are asked to use the labor supply – labor demand frame- work developed in class. Illustrate the effect of various shocks using a diagram of labor supply and labordemand.

- Anunusuallywarmsummerincreasesworkers’preferenceforleisuretime. What effect will this shock have on employment andwages?
- A natural disaster damages part of a nation’s public infrastructure. What effect will this shock have on employment andwages?

- Congresspassesalawfundingnationalpre-kindergarteneducationbyrais- ing taxes on investment What effect will this shock have on em- ployment andwages?

Suppose labor income starts at $50,000 and then grows at a constant rate of 2 per cent per year after that. Let *w** _{t}*be labor income in year

*w** _{t}*=

where *w*_{0}= 50*, *000 and *g *= 0*.*02.

- If the interest rate is
*R*, what is the formula for the present discounted value(PDVfromnowon)today(inyear0)oflaborincomeinaparticular future year*t*? - Now add up these terms from
*t*= 0 to*t*= 45 to get a formula for the PDV of labor income. Your answer should look something like that in equation (7.12) of thetextbook. - Write your answer to part (b) so that it takes the form of the geometric series

*PDV *= *w*_{0}(1 + *a *+ *a*^{2}+ *a*^{3}+ *… *+ *a*^{45})*.*

What is the value of *a *that you find?

- Apply the geometric series formula to compute the PDV for the case of
*R*= 0*.*04,*R*= 0*.*03, and*R*= 0*.*What happens when*R*= 0*.*02 and why?

Suppose that college education raises a person’s wage by $30,000 per year, from

$40,000 to $70,000. Assume that the interest rate is 3 per cent and there is no growth in wages. Suppose you are a high school senior and deciding whether or not to go to college. Find the PDV of earnings in the following cases. Also, assume that the work time is still 45 years, adding up to a 49-year non-college workcareer.

- What is the PDV of your labor income if you do not go to college and start workingimmediately?
- Asanalternative,youcouldpay$20,000peryearincollegetuition,attend collegefor4years,andthenearn$70,000afteryou Whatisthe PDV of your net earnings (adjusting for tuition) under thisplan?
- Discuss the economic value of collegeeducation.
- What if you pursue the plan described in (b), but you also expect to be unemployed for 2 years after finishing college (knock on wood). During these years assume that you do not have access to any unemployment insurance. What is the PDV of your net earnings under thisplan?

Label the following statements true or false and justify your answer.

- Supposethatthemoneysupplyisgrowingat10%.Ifthevelocityofmoney is falling at 10%, then inflation iszero.
- Suppose that inflation equals the growth rate of the money Then seigniorage revenues are growing overtime.

Consider a fast-growing emerging market economy where output is growing is at 10% per year. The central bank would like to choose a growth rate of the money supply to keep inflation at 0%.

- Assumethatdemandformoneyisconstantandinelastic(doesnotdepend on nominal interest rates). What should be the growth rate of the money supply to keep inflation at0%?
- Due to the introduction of debit and credit cards, it turns out that the velocity of money is not constant. If more consumers are using these payment technologies, do you expect the velocity of money to be increasing or decreasing? Should the growth rate of the money supply be faster or slower relative to your answer ina)?

- Consider the following expression for the growth rate of the velocity of The growth rate of velocity now depends on the nominal interest rate.Doyouexpectthecoefficient?tobepositiveornegative?Why?

∆*V*

*. *= 0*.*04 + *λ*∆*i*

*V*

* *

- Suppose that the real interest rate remains constant. Use the expression inc)toderiveanexpressionforinflationintermsofmoneysupplygrowth, output growth, and expected inflation. If expected inflation is constant, whatisthegrowthrateofthemoneysupplythatkeepsinflationatzero?

- Anumberofcommentatorsareworriedthatthiscountryis“overheating” and that inflation may start rising in the future. Should the central bank raise or lower the growth rate of the money supplytoday? Why?

** Problem9:**Supposevelocityisconstant,thegrowthrateofrealGDPis3per cent per year, and the growth rate of money is 5 per cent per year. Calculate the long-run rate of inflation in the followingcases:

- Whatistherateofinflationinthisbaselinecase?
- Back to the baseline case, suppose real GDP growth rises to 5 percent peryear.
- Backtothebaselinecase,assusmethatvelocityofmoneyrisesat1percent per year. What happens to inflation in this case? Why might velocity changein thisfashion?

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