Tackle all of them, the question is okay

I. Suppose a region's workforce of 14 million is initially split equally between two cities, X and Y. The urban utility curve peaks at 4 million workers, and beyond that point the slope is $3 per million workers. The initial equilibrium utility level is $60. Suppose city X experiences technological innovation that shifts its utility curve upward by $12. (a) Draw a pair of utility curves, one for X and one for Y, and label the positions immediately after the innovation (before any migration). You do not need to draw the utility curve to the left of 4 million population. (b) How do workers in each city Iespond to the innovation? What is the direction of migration flows. (c) What are the new equilibrium employment levels in city X and city Y, respectively? (d) What are the new equilibrium utility levels in city X and city Y, respectively? (e) Draw the new equilibrium in the graph. 2. Answer the following questions about diversified V.S. specialized cities (a) What kind of agglomerations are mostly provided by diversified Cities? By specialized cities? (b) Urban Economists Duranton and Puga present evidence that in France over 7 out of 10 firms relocate from diversified to specialized cities. What makes firms start their lifecycle in diversified cities and relocate to specialized cities? (c) Auto industry emerged in Detroit which was a diversified city at the beginning of the 20th century. But major firms like Ford and General Motors did not leave Detroit. Is this consistent with your answers to a previous question? Why yes Or no?

Assume the same demand and cost structures as in problem 4, but now firm 1 enters the market first and firm 2 follows, as in the Stackelberg model from lecture (both firms are guar- anteed to enter; the only choice is quantities produced).

Question 6 We will modify the game from above. Firm 2 now has the possibility of suing Firm 1 for violating lunar regolith preservation laws, after observing the first firm's choices. The lawsuit is costly for both parties, because it requires hiring a bunch of experts and stopping operations for a while. The lawsuit does not affect quantities or prices in the market. We'll model lawsuit costs as both firms having to pay an extra cost equal to one if there is a lawsuit. That will provide firm 2 with a means to "punish" firm 1 for overproducing. The game has three stages. In the first, firm 1 enters and chooses the quantity q1. In stage 2, firm 2 observes firm 1's choices as decides whether to start the lawsuit or not. At the last stage, firm 2 chooses its quantity produced q2 and "the market" determines the price given the quantities produced by both firms. In order to derive the subgame perfect Nash Equilibrium of this game, we proceed using backward induction. What should we look for when solving the second-to-last step (stage 2) using backward induction? (a) q2 as a function of q1 and of whether the lawsuit is in place. (b) Whether to create the lawsuit or not as a function of q1 and q2. (c) q1 as a function of q2 and whether the lawsuit is in place. (d) Whether to create the lawsuit or not as as a function of q1.

(e) q2 as a function of q1 only.

Derive the excess demand function z(p) for the economy, for example:

Let us take a simple two-person economy and solve for a Walrasian equilibrium. Let consumers 1 and 2 have identical CES utility functions,

ui(x1, x2) = x1+ x2 , i = 1, 2, where 0 < < 1. Let there be 1 unit of each good and suppose each consumer owns all of one good, so initial endowments are e1 = (1, 0) and e2 = (0, 1). Because the aggregate endowment of each good is strictly positive and the CES form of utility is strongly increasing and strictly quasiconcave on Rn+ when 0 < < 1

In addition, find all the Pareto ecient allocations of the economy. Which of them are in the core of the economy?

1. a labour force can be broken down as follows:

- potential labour force participants: 40 million

- employed: 28 million

- not working, but actively seeking work: 1.5 million

-full-time students: 3 million

- retired: 4.9 million

- not working, discouraged because of lack of jobs: 600,000

-not working, household workers: 2 million

a) using the numbers above, calculate this economy's labour force participation rate

b) using these numbers above, calculate this economy's unemployment rate.

2. Consider two individuals, Carole and Mo, who each have a job opportunity that pays a wage of $20 per hour and allows them to choose the number of hours per week they'd like to work. Carole has stronger preferences for leisure than Mo. Ultimately, both Carole and Mo choose to work more than zero hours per week.

Draw (and upload) one graph that includes:

Carole and Mo's income-leisure constraint Carole's utility-maximizing indifference curve (UC) and choice of leisure hours (LC) Mo's utility-maximizing indifference curve (UM) and choice of leisure hours (LM) [Note: There are multiple, though similar, ways to draw this graph. Focus on ensuring that the constraint, indifference curves and hours worked align with the information provided above.]

3. Consider an individual who lives in an economy without a welfare program. They initially work T-L0 hours per week, where (T-L0)>0. They earn an hourly wage (W) and no non-labour income.

a) Draw a graph that reflects this individual's income-leisure constraint, utility-maximizing indifference curve (U0), choice of leisure hours (L0) and income (Y0).

b) Now, assume that a welfare program has been implemented in this economy. The welfare benefit is smaller than the individual's initial income level (Y0) and there is a 50% clawback on any labour income earned. The individual now maximizes their utility by working and collecting a partial welfare benefit.

On the same graph as part a, draw this individual's new income-leisure constraint, utility-maximizing indifference curve (U1), choice of leisure hours (L1) and income (Y1).

4. Consider an individual who initially works T-L0 hours per week, where (T-L0)>0. They earn an hourly wage (W) and no non-labour income.

a) Draw a graph that reflects this individual's income-leisure constraint, utility-maximizing indifference curve (U0) and choice of leisure hours (L0).

b) The government then implements a wage subsidy program in which worker wages are increased by 10%. This wage subsidy program has no limits, so there is no phase-in/out. This wage subsidy produces both an income effect and a substitution effect on the worker's choice of leisure hours. Assume that the substitution effect is stronger than the income effect.

On the same graph as part a, draw this individual's new income-leisure constraint, utility-maximizing indifference curve (US) and choice of leisure hours (LS).

[Note: When incorporating the 10% wage subsidy into the graph in part b, I am not expecting perfect precision. Just try your best to draw the new income-leisure constraint as though a 10% wage subsidy has been added.]

5. Consider an individual who was employed prior to having a child. Now, they face daycare costs (M) if they choose to go back to work. Assume that they earn an hourly wage (W) and their non-labour income (YN) is greater than their daycare costs (YN > M). Despite the daycare costs, this individual chooses to work T-L0 hours per week.

Draw a graph that reflects this individual's income-leisure constraint (both with and without daycare costs), utility-maximizing indifference curve (U0) and choice of leisure hours (L0).

6. Consider an individual who had been planning to retire in five years. Unfortunately, they've just been laid off and the highest-paying job they've been able to find pays a lower hourly wage than did their previous job.

a) Using the concepts of the income and/or substitution effect, describe why we might expect this individual to retire earlier than they originally planned.

b) Using the concepts of the income and/or substitution effect, describe why we might expect this individual to retire later than they originally planned.