1.   (Gini Coefficient) We use the Gini coefficient to measure across countries, across cities, and       within cities. In class, we saw what is called the “Lorenz curve.” The relative area between the     curve and the 45 degree line, as well as between the curve and the x-axis, corresponds to the Gini coefficient. For the following questions, explain in your own words what the following                 observations would mean about inequality in city Alpha and what this would imply about the       city’s Gini coefficient (i.e. is it high, low or somewhere in between. Try to guess-timate a value if it helps.):

a.   The Lorenz curve is a straight line with a consistent 45 degree angle from the 1st to the 100th percentile of the population.

i.      Answer: The Gini coefficient is equal to 0 and this means that the proportion of income/wealth shared among all members of the population is exactly equal.

b.   The Lorenz curve is flat from the 1st to the 98th percentile of the population, then shoots up at the 99th percentile to the 45 degree line.

i.      Answer: The Gini coefficient is nearly equal to 1 and all wealth is held by 1% of the population, so the wealth distribution in the city is incredibly unequal.

2.   (Within- and Across-City Inequality and Segregation) Consider two cities: Green and Blue.   Green is a small city whose economy only started to grow at a fast pace in the last 10 years. Blue is a large city that has been growing steadily for the last 60 years, and also recently started to       expand rapidly economically. This expansion happened at around the same time as Green.

a.   Assume that the expansions are due to growth in industries that employ primarily racial  minorities (especially Black and Latinx workers) who tend to be low income. Which city most likely has more segregation and on what dimensions? Explain your reasoning.

i.      Answer: Larger cities (in this case, Blue) tend to have more segregation, not just in terms of income (workers from both ends of the wealth and income

distribution are attracted to working there), but also in terms of education (similar reasoning) and race (again, similar reasoning). These three characteristics             coincide such that higher income/education and non-Black and Latinx                  individuals will cluster in some parts of the city and lower income/education and Black and Latinx individuals will cluster in others due to the affordability of        housing.

b.   Now suppose that the expansion in Blue is happening because of an influx of tech       companies establishing headquarters there, while the expansion in Green is due to       expansion in manufacturing. What do you think will happen to inequality within these cities? Across these cities?

i.      Answer: In Blue, inequality due especially to gaps in educational attainment and race will increase, as tech firms hire primarily highly educated White and Asian

workers. Manufacturing firms hire a range of workers, from those with low          education to those with high education, and across race, depending on the type of position, so there may not be as much inequality due to education level in Green. The equilibrium wage in Blue will likely be higher than the equilibrium wage in  Green as a result of the tech expansion, increasing across city inequality.

3.   (Labor Elasticity of Supply) From 2011 to 2012, the cost of living in city Gamma increased from 60 to 140 dollars per person. The workforce in this time period increased from 30 to 50 workers.

a.   What is the workforce elasticity of cost of living? Explain what this measure means in your own words.

i.      Answer:

1.   e(cost of living, workforce) = % change in cost of living / % change in workforce

2.   = (((140-60)/60)*100)/(((50-30)/30)*100)

3.   = (80/60)/(20/30)

4.   = 2

5.   A 1% increase in the workforce is associated with an increase in the cost of living by 2%

b.   What does this mean for cost of living-adjusted wages?

i.      Answer: To increase the labor supply by 1%, wages need to increase by 2%

c.   What is the (cost of living-adjusted) wage elasticity of workforce supply?

i.      Answer:

1.   e(workforce, wage) = 1/e(cost of living, workforce) = 1/e(wage, workforce) = 1/2

2.   A 1% increase in wages is associated with a 0.5% increase in the labor force

d.   What does this imply about the slope of the labor supply curve?

i.      Answer: The labor supply curve is inelastic, i.e. an increase in wages yields a less than proportional increase in the labor force.

1.   (Labor Supply and Demand) As we saw in class, the labor supply equation is given as   =    +   , while labor demand is   =    +   .

a.   Let   =  0,   =  200,   =  2 and  =  −2. What is the total quantity of labor in equilibrium? Show your work.

i.      Answer:

1.     +    =   +    , let ∗  =  =

2.     +   ∗  =   +  ∗

3.   2∗  = 200 − 2∗

4.   4∗  = 200

5.   ∗  = 50

b.   What is the wage in equilibrium? Show your work.

i.      Answer: Plug in the total quantity of labor in equilibrium into either the labor

supply or demand equation

1.    =   +   ∗

2.    = 0 +  2 ⋅ 50

3.    = 100

4.   OR

5.    =   +  ∗

6.    = 200 − 2 ⋅ 100

7.    = 100

c.   Now suppose amenities in the city where the firms are located have declined, and firms are now willing to pay an extra $40 for workers (even if they there are no workers          available), i.e.   = 40. What is the total quantity of labor and the wage in equilibrium?

i.      Answer:

1.   Total quantity of labor

a.     +   ∗  =   +  ∗

b.   40 +  2∗  = 200 − 2∗

c.   4∗  = 160

d.   ∗  = 40

2.   Wage in equlibrium

a.    =   +   ∗

b.    = 40 +  2 ⋅ 40

c.    = 120

d.   OR

e.    = 200 − 2 ⋅ 40

f.     = 120

2.   (Labor Supply and Demand Curve Shifts) Consider a city where there is suddenly a vast    improvement in public transit (e.g. expanding train lines to more parts of the city with better   quality service). What happens to equilibrium wages and quantity of labor? Why do you think these changes happened? Assume no change in the labor demand curve and no tax increase.

a.   Answer: The labor supply curve will shift to the right because this is an improvement in   amenities in the city, which would also increase the equilibrium quantity of labor because more people will move to the city. This will also decrease wages because there are now   more people competing for the same jobs, so firms can hire more cheaply.

3.   (Urban Labor Markets) Explain in your own words why high-skilled service jobs (e.g. financial services, consulting) were not generally considered exportable by economists, and why that has    changed.

a.   Answer: Services more generally were all considered local/non-tradeable jobs because they could only service local customers. Improvements in communications technology allowed high-skilled service workers to provide services in real time to non-local         customers. This notion of non-exportable services was also partially influenced by the idea that tradability was synonymous with manufacturing, and so was more goods-      oriented.

4.   (Urban Labor Markets) What is one service that is not yet tradeable, but you would like to       become tradeable, and why? How do you think the provision of this newly tradeable service will affect within-city inequality? Across-city inequality? (Don’t say it won’t affect inequality at all  unless you can provide very good rationale.)

a.   Answer: A tradeable service is one where the firm or worker providing the service can be fully remote (i.e. their client is not in the same location as themselves).