Problem 1

Denver and Salt Lake City have the following demand for restaurant waiters:

= 120 5

= 62.5 2

The supply in both cities is the same, and it is given by: = 20 + 3.

1. Given this, are both markets in location equilibrium? Explain your answer extensively [Hint: recall supply and demand from microeconomic theory] (10 points).
2. If the supply of workers shifts to = 40 + 3, which city would have a higher impact on wages? Why? Interpret your answer using all the knowledge acquired in our lectures and microeconomic theory (20 points).
3. There was an influx of skilled workers in Salt Lake City which increased restaurants' demand so much that demand for waiters shifted to = 100 2, what would happen in the market for waiters in these two cities assuming that the supply remains as = 20 + 3? Explore all possible channels of this external shock in this market. I am looking for good explanations here (10 points).

Problem 2

Suppose there are two regions that can produce two goods: computers; inputs.

Output per Hour	Region A		Region B
Computer	Inputs	Computer	Inputs
20	5	20	40

1. Discuss the conditions under which a trading city will or will not develop. Suppose an innovation in transportation decreases transaction time (costs). How much of a decrease in transaction time must result in order for a trading city to develop? Explain it carefully and extensively (20 points).
2. Explain potentially how agglomeration economics could it into this. You may want to define agglomeration economics first then explain your answer. (10 points)

Problem 3

As an individual, you can choose between your housing consumption and the consumption of other goods by the following function.

(, ) = ^{3/4 1/4}

where h is your housing consumption and x is the consumption of all other goods. You also know that your daily transportation cost depends on how distant you are from the city center, which is given by the following formula:

() = 2

Where 2 is your daily transportation cost per mile and you decide to live 10 miles from the city center. Considering that your daily rate is 220 dollars and the price of housing is twice the price of other goods (consider the price of other goods as a numeraire), please answer the questions below.

1. What would be your optimal consumption of housing and other goods? Interpret your answer in all possible ways (8 points).
2. Imagine that you decide to live 20 miles away from your office in the city center, show how your consumption will change (7 points).
3. Now, consider that you remain living 10 miles away from the city center, but your daily cost per mile of transportation increased by 25%, interpret the optimal decision by exploring all channels (7 points).
4. If your sibling has a different utility function described below

(, ) = ^{2/5 3/5}

How would your sibling choose and react differently from you in letters a, b and c? And interpret all outcomes by exploring the full spectrum of these decisions (yours and your sibling - 8 points).