- ELI5
- Complete Exam May 2022 - AI2155
- 1. Development of Cities - Advantages, Rank-size rule & Central Place Theory, City-Proper (10 points)
- 2. Urban Growth (10 points)
- 3. Economic Base Analysis and Labour market (10 points)
- 4. Land Rent (15 points)
- 5. Transportation (10 points)
- 6. Housing economics and policies (10 points)
- 7. Cost-Benefit Analysis and Local Government (15 points)
- Complete Exam AI2155 - August 2022
- 1. Development of Cities: (15 points)
- 2. Economic Base Analysis (10 points)
- 3. Land Rent (15 points)
- 4. Transportation (15 points)
- 5. Housing economics and policies (15 points)
- 6. Cost-Benefit Analysis (10 points)
- Exam Prep Abukars Powerpoint
ELI5
Complete Exam May 2022 - AI2155
1. Development of Cities - Advantages, Rank-size rule & Central Place Theory, City-Proper (10 points)
b) Three conditions must be satisfied for a city to develop. Explain how the absence or presence of these conditions can cause the existence of cities. (3p)
c) Explain how the rank-size rule is related to Central Place Theory (3p)
d) Explain how the rank-rule size estimation outcome could be different when city-proper or urban agglomeration data in a same country is used. (2p)
Answer and Solution ✅
Nr | Term to Explain | Explanation |
a) | Absolute Advantage 🏆 | Refers to an advantage that cannot be replicated. Given the time and place it is impossible to produce one more unit. |
a) | Competitive Advantage 💪 | Refers to a firm having the lowest opportunity cost of producing that certain product compared to other products |
b) | Three conditions must be satisfied for a city to develop 🚜 📈 🚊 | 🚜1) Agricultural Surplus → There needs to be a surplus of food
📈2) Scale economies of production = Efficiency of production needs to increase
🚊3) Scale economies of transportation = Efficiency of transport needs to increase |
c) | Rank-size rule relation to Central Place Theory 📊📍 | They describe “models” and theories about the distribution of cities. For example a country based on the city’s size and population or the city size determined by the threshold and range of the goods and services they offer. |
d) | Rank-rule size estimation differs from city-proper or urban agglomeration data in the same country. | City-Proper = Legal Boundry → Excludes surrounding suburbs or neighbouring municipalities.
Urban agglomerations = “Hearbeat Boundry” of a city → Includes surrounding suburbs and satellite towns to account for people who live outside the city, but work in the city. |
2. Urban Growth (10 points)
b) Why the demand curve for urban labor market model is negatively sloped? (3p)
c) Describe the impact on the city’s equilibrium wage and employment of an increase in export production. Depict graphically your answers. (3p)
Answer and Solution ✅
Nr | Term to Explain | Explanation |
a) | The four sources of economic growth | 1. Capital Deepening💰 = Capital per-capita increases
2. Technological Progress 🦾 = Increases Efficiency and/or productivity.
3. Increase in Human Capital 🤹 = More skilled workers
4. Agglomeration Economies = Companies Clustering, knowledge spillover, share inputs and labor-pool |
b) | The negative slope of the demand curve in a urban labor market model. | 1. Substitute Effect: Higher wages → Increased production cost → substitution of manpower machines to reduce cost of production.
2. Output Effect: Higher wages → Higher production costs → Higher Prices → Less demand → Less workers needed
3. Agglomeration Effect: Total employees increase → More demand for housing → Raises housing and living Costs |
A local firm increases export and capital is allocated to increase production, which means: 1. More people are hired to increase production 2. Workers are given a higher wage to increase production (incentive)
Eg. The exports impacts the demand for labor, it increases which leads to higher wages since the supply is fixed in the short term.
3. Economic Base Analysis and Labour market (10 points)
b) Calculate the Economic Base Multiplier using the location quotient method. What does this number indicates. (3p)
c) Calculate the Relative Diversity Index (RDI) for Yourcity. (3p)
Answer and Solution With Steps ✅
Code | Sector | YourCity
(Thousands) | Employment
Rate YourCity (e) | My Land
(Thousands) | Employment
Rate Myland (E) | Location
Quotient (Q) | Basic Employment | Diversity Calculation
Abs(e-E) |
100 | Mining, Agricultural | 5,1 | 0,0039 | 565 | 0,0047 | 0,8298 | N/A | 0,0008 |
200 | Construction | 90,3 | 0,0682 | 5 510 | 0,0456 | 1,4957 | 29,93 | 0,0226 |
300 | Manufacturing | 155,5 | 0,1174 | 18 473 | 0,1528 | 0,7684 | N/A | 0,0354 |
400 | Transport Etc. | 67,0 | 0,0506 | 6 360 | 0,0527 | 0,9602 | N/A | 0,0021 |
510 | Wholesale Trade | 83,8 | 0,0633 | 6 657 | 0,0551 | 1,1489 | 10,86 | 0,0082 |
520 | Retail | 263,2 | 0,1987 | 21 883 | 0,1811 | 1,0972 | 23,32 | 0,0176 |
600 | Finance, Real Estate | 92,8 | 0,0701 | 7 053 | 0,0584 | 1,2004 | 15,49 | 0,0117 |
700 | Services | 397,6 | 0,3002 | 34 883 | 0,2886 | 1,0402 | 15,37 | 0,0116 |
800 | Government | 169,5 | 0,128 | 19 516 | 0,1615 | 0,7926 | N/A | 0,0335 |
👆Tot: 1324,8 | 👆Tot: 120 900 | Sum 👆94,96 | Sum 👆0,1435 | |||||
Multiplier: 13,95 | RDI: 6,97 |
Step 1. Calculate Total Employed People in YourCity and MyLand
Sum YourCity = 1324,8
Sum MyLand = 120 900
Step 2. Calculate the employment share of the sector in the specific region (MyLand and YourCity)
- Specific Region Employment Share = (Employment in the sector in the specific region) / Total employment in the specific region
Step 3. Calculate the location quotient
- Location Quotient = Specific Region Employment Share / Reference Region Employment Share
- Location Quotient = (e YourCity) / (E MyLand)
Step 4. Calculate the Basic Employment & Multiplier
If LQ > 1
→ Basic Employment = ((LQ-1)/LQ))*(Sector Specific Region Employment)
Economic Base Multiplier = (Sum Basic Employment)/(Specific Region Employment)
Multiplier: (1324,8 / 94,96) = 13,95
Lastly ✅ - Step 5. Compute Diversity & RDI
Diversity = Abs(e-E) for each row ⚠️ The Values are postive (>0) ⚠️
RDI = 1/(sum(Diversity))
4. Land Rent (15 points)
b) Calculate the bid rent function for each of the following three sectors of business users of land in a monocentric city. Plot each bid rent function for u = 0, 1, 2, 3, 4, 5. On the vertical axis, have R(u) range from $0 to $10,000 or more if you need. Use the following profit statement to derive the bid rent function for each sector where the p (price), q (quantity), w (wage), and t (transportation cost) values are given below for each sector, and u varies from 0 to 5. (4p) →
Quantity $ (q) | Price $ (p) | Wage $ (w) | Transportation Cost $(t) | |
Manufacturers
| 25 000 | 0,28 | 0,12 | 0,04 |
Stores | 10 000 | 9,00 | 8,20 | 0,40 |
Offices | 500 | 240 | 228 | 4 |
c) Explain the spatial layout of this monocentric city. Describe how the land use pattern in relation to distance from the city center. (4p)
d) If transportation costs in the office sector increase with $.5, will the rent in city center increases or not and if so how much will it increase? (3p)
Answer ✅
a) Effects associated with building height amenities
Travel Time: Both During construction & for tenants using it later. How many days will tenants or workers spend in the elevator through out their stay in the building? It also increases friction to use the amenities, ie. increased opportunity cost.
Complexity of construction: A rooftop pool is no easy feat to construct, maintain or calculate load for.
Negative Externalities: Any tall thing blocks sunlight eg. neighbours are lose daylight. Tall buildings usually means large cranes that can’t be placed within the property. Also effecting the surrounding area. However, the negative effects that lead to deadweight loss could be compensated according to Kaldor-Hicks -Criterion resulting in a more fair “win-win” type of situation.
Positive Effect of tall buildings - Agglomeration occurs since more people are and companies can fit into the same space and use the same utilites. It’s one of the positive aspects of tall buildings.
b) Compute bid rent function and plot the results in graph for a monocentric model (u = 0,1,2,3,4,5 and R(u) = 0,1,2….10000)
u | Stores | Offices | Manufacturers |
0 | 8000 | 6000 | 4000 |
1 | 4000 | 4000 | 3000 |
2 | 0 | 2000 | 2000 |
3 | 0 | 1000 | |
4 | 0 | ||
5 |
c) Explain the spatial layout of this monocentric city and describe how the land use pattern in relation to distance from the city center
d) If transportation costs in the office sector increase with $.5, will the rent in city center increases or not and if so how much will it increase? (3p)
Increased Cost (tqu): 4,5*500 = 2250
At u=0 no effect → u>0 is affected by this increase in cost. ie. rent bids decrease. Impact on rent from offices is 250 dollars less at all other distances.
Quantity $ (q) | Price $ (p) | Wage $ (w) | Transportation Cost $(t) | |
Offices | 500 | 240 | 228 | 4,5 |
5. Transportation (10 points)
The marginal benefit (demand) is $31.2 for a volume of 200 and drops by $4.0 for each additional 200 drivers. Assume 16 cents per minute opportunity costs of travel time and $2.75 monitory cost (one decimal point is enough to get approximate figures in your estimation of private and social trip costs).
a) Illustrate by diagram the private and social cost curves as well as equilibrium, optimal and congestion taxes. (2p)
b) What is the equilibrium and optimal traffic volume? (2p)
c) What is the appropriate congestion tax? (3p)
d) Calculate the net gain from congestion tax (3p)
Answer and Solution ✅
MB | Marginal Benefit | $31,2 |
OPC | Opportunity Cost | $0,16/min |
MonC | Monetary Cost | $2,75 |
- For volume < 400 → Triptime = 12
- Private Trip Cost = MonC + OPC*(f(vol))
- Total increase in trip time = f’(vol)*f(vol)
- External Trip Cost = (Total Increase in trip Time)*OPC
- Social Trip Cost = External Trip Cost + Private Trip Cost → ETC + PTC
- Marginal Benefit Starts at $31,2 → Drops by $4,0 per 200 drivers
- Equilibrium is where private trip cost meets demand (MB)
- Optimal is where social trip cost meets Demand (MB)
- Appropriate congestion tax is the external trip cost at optimal traffic volume
Volume | Trip Time
f(vol) | Private Trip
Cost (PTC) | f’(vol) | Tot increase
Trip Time | External Trip
Cost (ETC) | Social Trip
Cost | MB |
How To calculate | f(vol) | MonC+OPC*f(vol) | 0,001+0,0003(vol-400) | f’(vol)*f(vol) | Tot increase*OPC | ETC + PTC | MB-4*(vol/200) |
A | B | C | D | E | F | G | H |
200 | 12 | 4,7 | 0 | 0 | 0 | 4,7 | 31,2 |
400 | 12 | 4,7 | 0 | 0 | 0 | 4,7 | 27,2 |
600 | 12,8 | 4,8 | 0,007 | 4,2 | 0,672 | 5,5 | 23,2 |
800 | 14,8 | 5,2 | 0,013 | 10,4 | 1,664 | 6,9 | 19,2 |
1000 | 18 | 5,7 | 0,019 | 19 | 3,04 | 8,7 | 15,2 |
1200 | 22,4 | 6,4 | 0,025 | 30 | 4,8 ←Tax | 11,2 ← Optimal | 11,2 ← Optimal |
1400 | 28 | 7,3 ← Equilibria | 0,031 | 43,4 | 6,944 | 14,2 | 7,2 ← Equilibria |
1600 | 34,8 | 8,4 | 0,037 | 59,2 | 9,472 | 17,9 | 3,2 |
Answers ✅ b) c) d)
b) Equilibrium traffic volume = 1400
Optimal Traffic = 1200
c) Appropriate Congestion Tax = 4,8
d) Net Gain is the Shaded area in the graph
Net gain: ((14,2 - 7,2)*200)/2 = $700
6. Housing economics and policies (10 points)
b) Hedonic pricing models are useful in capturing the values associated with housing attributes. However, hedonic pricing models have certain limitations. Discuss at least two such limitations. (2p)
c) Discuss relevant housing economic concept covered in the course that explains when high income households move to higher quality property and lower income households moves to the vacated property. Illustrate your argument with graphs. (5p)
Answer and Solution ✅
Nr | What to Explain | Explanation |
a) | Housing difference from other goods or assets | 1. Heterogenous Asset Class → No identical assets
2. High Cost → One of the few “goods” that are financed by debt
3. Durability → Made to last 100+ Years.
4. Necessity → I don’t need apples, I need some place to exist.
5. Static Supply in short term → Prices Driven by Demand rather than supply. |
b) | Limitation of hedonic pricing models housing attributes | Homogeneity assumption → Willingness to pay for attributes are constant across all individuals and households
Data availability and quality → It assumes there is data available and that it’s of good quality.
|
c) | Concept that explains when high income households move to higher quality property | FILTERING MODEL
When households with the highest purchasing power can afford a higher quality household. The second highest income earners have to settle with the next best alternative. The moving patterns of high income households is said to create filtering effect, were they buy nice newly built housing units and move, the second highest can move into their previous housing unit. |
c) Red-line is how a filtering Model should be drawn.
7. Cost-Benefit Analysis and Local Government (15 points)
b) Discuss the steps of CBA and how it can be used in the provision of public goods such as parks. With respect to the traditional investment analysis, how are the costs and benefits (marginal value) determined? (5p)
c) Median voter, Tiebout model, and Benefit taxation play a big role in explaining the formation of municipalities. Explain how these concepts or mechanism can influence individual households’ decision to reside in specific municipality in relation to the provision of the quantity of local public goods. (6p)
Answer and Solution ✅
a) If costs or benefits associated with the provision of the public goods are not properly identified and priced accordingly, it can result in a supply that is lower than demand of said good. This in turn creates a welfare loss in terms of not maximizing society’s utility by not providing the good in optimal quantity or offered to society at higher price.
b) CBA to use in a provision of a park
- Analyse the opportunity cost of the land needed to build the park
- Identify and value the benefits and externalities it provides to society
Public goods are hard to value because of they lack “pure profit”. This makes it hard to estimate the benefits and compare it to other projects where an investment generates cashflow which can be compared to other cashflow generating projects.
Public goods are also affected by the free-rider problem, meaning that anyone can use and benefit of the public good more than they contribute to the cost of supplying the good.
c) Median Voter, Tiebout Model and Benefit taxation
Median Voter
| Median Voters Create heterogenous municipalities since the median voters desire always wins.
The Median Voter Model is a political theory that suggests that in a two-party system with a single-dimensional policy space, the party or candidate who positions themselves closest to the median voter's preferences is more likely to win elections. Political parties or candidates have an incentive to position themselves close to the median voter's position in order to maximize their chances of winning elections. This system leads to policy that only caters to the median voter, with an obvious negative externality. The outlier individuals demand for public goods is not taken into account. |
Tiebout Model | Refers to individuals “voting with their feet” ie. choosing the municipality that offers the right amount. This in turn creates homogenous municipalities.
It explores the concept of local public goods provision and suggests that individuals can "vote with their feet" by choosing which local jurisdiction to reside in based on their preferences for public goods and the corresponding tax rates. In a system of multiple local jurisdictions, individuals will sort themselves geographically based on their preferences for public goods and taxes |
Benefit Taxation | Refers to a way to determine individuals demand and benefit that they get from a public good. Benefit taxation leads to more diverse and somehow heterogeneous municipalities.
Benefit taxation is a principle of taxation that suggests individuals or households should be taxed based on the benefits they receive from public goods and services provided by the government. However, would lead to higher taxation of the poor who recieve more of the benefits that the government provides. This principle is often contrasted with the ability-to-pay principle, which argues for taxation based on an individual's income or wealth regardless of the specific benefits they receive. |
Complete Exam AI2155 - August 2022
1. Development of Cities: (15 points)
b) Explain the difference between comparative and absolute advantage. (2p)
c) Why do we observe cities of different size? Explain thoroughly. (3p)
d) Explain how the rank-rule size estimation outcome could be different when city-proper or urban agglomeration data in a same country is used.(2p)
e) Consider a firm that uses corn syrup to produce Coca-Cola. The monetary weight of the Coke is $4.00 per case per mile and the monetary weight of the corn sweetener that goes into the case of Coke is $3.00 per mile. The distance between M (the market) and F (the corn Field and where the corn sweetener is made) is 10 miles. Labor and other production costs are the same at all locations so these will not impact the location decision. Because these costs will impact the production decisions, we’ll say they are $0.00 per case to focus on the calculation of the location decision. Compute the procurement, distribution, and total costs. Use a graph to illustrate where the firm will locate. Label your graph properly and clearly.
Answer ✅
Nr | Thing to Explain | Answer ✅ |
a) | comparative advantage without scale of economies in transportation | For a city to develop, 3 conditions need to be satisfied:
1. Agricultural Surplus
2. Scale economies in production
3. Scale economies in transport
Without SET (3) the city is limited to trade with itself, rather than having agents doing a massive exchange. Therefore the city will not develop to trade their products with other regions and no agglomerations are created. |
b) | Comparative Advantage
vs Absolute advantage | Comparative advantage refers to when a firm has the lowest opportunity cost for producing a certain product.
Absolute advantage is when a firm given the time and resources can produce a certain product with the most quantity than others. |
c) | Why do we observe cities of different size? | Economic Factors - Economies of Scale & Agglomeration Effects
Social Factors - Network Effects, Quality of life
Geographic Factors - Natural Resources, Natural Resources
Historical Factors - Policy Decisions, Path Dependency |
d) | Rank-Rule Vs City-Proper
Urban agglomeration data | Rank Rule - The largest city = 2x the second largest city and so on.
City proper is the legal boundary of a city, and historically humans are shit at drawing lines on maps that should represent the geographicly correct area, based on urban or history of the region. (Eg. Africa)
Urban agglomeration = “Heartbeat Boundry” of a city → Includes surrounding suburbs and satellite towns to account for people who live outside the city, but work in the city. |
e) Assumptions - Where should the factory be? At the market or at the field?
- 🥫Monetary Weight Per Coke Case = $4 per mile
- 🌽 Monetary Weight Corn Case = $3 Per Mile
- Distance between Field = 10 Miles
- Labor + Production Cost = Same for both products ie. $0
Calculation
Factory at Field = We have a distribution cost:
Distribution Cost: 4*10 = 40$
Factory at Market = We have a procurement cost:
Procurement Cost: 3*10 = 30$
2. Economic Base Analysis (10 points)
b) Describe pro & cons of two of the methods discussed in the previous question 2a. (2p)
c) Calculate the Economic Base Multiplier and RDI using the location quotient method. What does this number indicate? (5p)
Answer a) & b) ✅
Nr | What to Explain | Answer ✅ |
a) | Discuss three methods by which jobs can be divided into employment in the 'basic' and 'non-basic' | 1. Assumption Method → We assume the industry with large employment within a sector is basic employment
2. Direct Survey Method → Basic Employment is based on interviews with personel in industries to determine if its basic or not
3. Locational Quotient → Based on regional and national employment data in each sector. See formula in calculations below |
b) | Describe pro & cons of two methods discussed above. | 1. Direct Survey - Accurate and deep study of employment with direct contact, however extremely time consuming ie. high cost, and, lastly it’s subjective.
2. LQ Method - Cost Effective, standardised and statistically indexed. However, it heavily relies on good data quality and assumes all attributes within each sector are alike. |
c) | Economic Base Multiplier and RDI - What does the numbers indicate? | The EBM indicates how the specific region grows as a function of additional basic employment. Basically how many jobs within none-basic employment are created by one basic employment. For GBG that number is 16,63 (Exports makes the region grow)
RDI - Measures employment diversity, and a result of 8,4 for GBG indicates that employment in the region is not that well diversified → Carries a bit of risk with it. |
3. Land Rent (15 points)
i) reduction of transportation cost t (1p)
ii) A decrease of average cost of production c (1p)
iii) An increase in output per acre Q (2p)
Calculate the bid rent function for each of the following three sectors of business users of land in a monocentric city. Plot each bid rent function for u = 0, 1, 2, 3, 4, 5. On the vertical axis, have R(u) range from $0 to $12,000 or more if you needed.
b) Use the following profit statement to derive the bid rent function for each sector where the p (price), q (quantity), w (wage), and t (transportation cost) values are given below for each sector, and u varies from 0 to 5.
Profit = pq - wq - tqu - R
Quantity $ (q) | Price $ (p) | Wage $ (w) | Transportation Cost $(t) | |
Manufacturers
| 22 000 | 0,28 | 0,12 | 0,04 |
Stores | 12 000 | 9,00 | 8,20 | 0,40 |
Offices | 800 | 240 | 228 | 4 |
c) Explain the spatial layout of this monocentric city. Describe how the land use pattern in relation to distance from the city centre. (4p)
d) If transportation costs in the office sector decrease with $.5, will the rent in city center decrease or not and if so, how much will it decrease? (3p)
Solution b) & c)
Quantity $ (q) | Price $ (p) | Wage $ (w) | Transportation Cost $(t) | |
Stores | 12 000 | 9,00 | 8,20 | 0,40 |
Offices | 800 | 240 | 228 | 4 |
Manufacturers | 22 000 | 0,28 | 0,12 | 0,04 |
Assume Profit = 0 → R(u) = pq-wq-tqu
Manufacturers
R(u) = 0,28*22 000 - 0,12*22 000 - 0,04*22 000*u → R(u) 3520-880u
R(u) = 3520-880u
Offices
R(u) = 800*240 - 800*228 -4*800u
R(u) = 9600-3200u
Stores
R(u) = 9,00*12000-8,2*12000-0,4*12000u
R(u) = 9600-4800u
u: 0→5 | 0 | 1 | 2 | 3 | 4 |
Stores R(u) | $9600 | $4800 | $0 | $0 | $0 |
Offices R(u) | $9600 | $6400 | $3200 | $0 | $0 |
Manufacturers R(u) | $3520 | $2640 | $1760 | $880 | $0 |
The Zones → | “Zone 0” | Zone 1 CBD | Zone 2 | Zone 3 |
What to expect in the Zone | Mainly Stores
& Some offices | Mainly offices &
Some Stores | Mainly Offices &
Some Manufacturing | Mainly Manufacturing |
Explanation | Stores need flow and Customers, but all real estate can’t be stores | Offices need
easy transport for workers and access to CBD | Manufacturing needs space but m-plants still need offices | Lowest Rent for manufacturing who really needs space. |
d) Office Transport Cost increase affects on CBD Rents
The bids from offices will decrease in areas where u > 0 eg. → In the city center the office rents will not decrease.
4. Transportation (15 points)
b) Suppose that the relationship between traffic volume and travel time is as follows:
The marginal benefit (demand) is $32.1 for a volume of 200 and drops by $3.66 for each additional 200 drivers. Assume 10 cents per minute opportunity costs of travel time and $3 monitory cost (one or two decimal point is enough to get approximate figures in your estimation of private and social trip costs).
c) Illustrate by diagram the private and social cost curves as well as equilibrium, optimal and congestion taxes. (2p)
d) What is the equilibrium and optimal traffic volume? (2p)
e) What is the appropriate congestion tax? (3p)
f) Calculate the net gain from congestion tax (3p)
a) The four ways congestion tax decreases traffic volume
The four ways congestion tax decreases traffic volume | Explanation |
1. Change In Mode of Transportation
🚗 → 🚊 | Cost of traveling with automobile increases more individuals changes their mode of transport to public. |
2. Change in Travel Time 🕰️ | Congestion Tax Peaks at rush-hour, hence individuals will choose other times to travel. Both to save money and/avoid congestion Tax. This decreases the peak traffic volume. |
3. Different Travel Route 📍 | Individuals will choose other routes than the ones with congestion taxes. |
4. Decreased Trip Time 🏎️ | All of the above decreases the volume of cars on the roads, without congestion the gain is a more efficient roadnetwork eg shorter travel time for the cars who utilize the network which in turn leads to less traffic in peak hours. |
Solution with Steps b → d)
Step 1. Table with Coulmns A → H and calculate Trip Time
Column A = Traffic Volume
Column B = Trip Time function
Trip time = 12.0 + 0.001 * (Volume - 400) + 0.000015 * (Volume - 400)^2
- For volume < 400 → Triptime = 12
Step 2. Calculate Private Trip Cost - Column C
Private Trip Cost = MonC + OPC*(f(vol))
- Opportunity Cost = 10 Cents per minute
- Monetary Cost = 3$
Step 3. Calculate f’(vol) - Column D
f’(vol) = 0.001 + 0.00003*(Volume - 400)
Step 4. Compute Tot Increase Trip Time (Column E)
Total Increase Trip Time = (volume)*f’(vol)
Step 5. Compute External Trip Cost
External Trip Cost = (Total Increase in Trip Time)*OPC
- Opportunity Cost = 10 Cents per minute
Step 6. Compute Social Trip Cost
Social Trip Cost = External Trip Cost + Private Trip Cost → ETC + PTC
Step 7. Compute Marginal Benefit
$32.1 for a volume of 200 and drops by $3.66 for each additional 200 drivers
Step 8. Find Equilibrium, Optimal traffic Volume and appropriate Congestion Tax
- Equilibrium is when private trip costs meets demand (MB) (PTC = MB)
- Optimal Traffic Volume → Social Trip costs meets Demand (MB) STC = MB
- Appropriate congestion tax = External trip cost at optimal traffic volume
Volume | Trip Time
f(vol) | Private Trip
Cost (PTC) | f’(vol) | Tot increase
Trip Time | External Trip
Cost (ETC) | Social Trip
Cost (ETC + PTC) | MB - Demand |
A | B | C | D | E | F | G | H |
200 | 12 | 3 | 0 | 0 | 0 | 3 | 31,2 |
400 | 12 | 3 | 0 | 0 | 0 | 3 | 28,44 |
600 | 12,8 | 4,3 | 0,007 | 4,2 | 0,42 | 4,8 | 24,78 |
800 | 14,8 | 4,5 | 0,013 | 10,4 | 1,04 | 5,6 | 21,12 |
1000 | 18 | 4,8 | 0,019 | 19 | 1,9 | 6,7 | 17,46 |
1200 | 22,4 | 5,3 | 0,025 | 30 | 3 | 8,3 | 13,8 |
1400 | 28 | 5,8 | 0,031 | 43,4 | 4,34 ← (3) | 10,2 ← (2) | 10,14 ← (2) |
1600 | 34,8 | 6,5 ← (1) | 0,037 | 59,2 | 5,92 | 12,5 (Net Gain) | 6,48 ← (1) |
1800 | 42,8 | 7,3 | 0,043 | 77,4 | 7,74 | 15,1 | 2,82 |
Answers ✅
Equilibrium Volume = 1600, when PTC = 6,5 and MB = 6,48
Optimal Traffic Volume = 1400, when MB = 10,14 and STC = 10,2
Appropriate Congestion Tax is 4,34
Net Gain Formula = (12,5-6,48)*(1600-1400)/2 = 592
5. Housing economics and policies (15 points)
a) Suppose population growth is strong for two metropolitan areas. The possibility of building a new one is strongly restricted in one of the cities because the city is located on many islands. The other metropolitan area has much more unused land that is currently used for agriculture. Analyze what will happen in these two cities in the short and long term (Hint: urban growth boundary and land market). Use graph to explain your reasoning. (5p)
b) Discuss possible positive and negative aspects when high income households move to higher quality property and lower income households moves to the vacated property. You need to use housing economic models and concepts covered in the course. Illustrate your argument with graphs. (10p)
Q | Explain | Explanation |
a) | Compare How two metropolitan Areas will develop | Based on the different circumstances the cities will grow differently. The four pillars of urban Growth are
1. Increased Human Capital - Skilled and educated humans
2. Capital Deepening - Capital per capita increases
3. Technological Progress - Lowering average production Cost
4. Agglomeration Effect - Scale Economies like urban or localization economies |
a) | City A - The Islands | The main drawback in the islands growth will have to do with manufacturing. It will be hard to locate industrial innovation due to zoning polices. Eg. In the long run its growth is stifled by the need for landmass. However, if it’s a trade hub aggolmeration effects + a influx of increased human capital can boost the citys growth in the short term. |
a) | City B - FarmVille | Farmville has contrary to “The Islands” a lot more potential for faster growth if they have an agricultural surplus and scale economies in both transportation and in production. However, if the city grows fast horizontally rather than vertically, it’s long term growth can be sifled by an urban growth boundry, congestion and developmental tax. |
b) | High income households move to higher quality property | What the question describes is the filtering model. Basically the rich households constantly demand nicer and nicer housing, moving from their previous purchase to the next one. This means that less rich households have to settle for the next best thing or upgrade when the richer households have moved into to their new luxuary housing. And this chain continues for poorer and poorer households.
Positive Aspects: Continuous moving-chain that leaves properties available. Status games, long term investments, secure neighbourhoods.
Negative Aspects: Price Fluctuations, rising prices, constant demand and limited supply. |
6. Cost-Benefit Analysis (10 points)
b) Median voter, Tiebout model, and Benefit taxation play a big role in explaining the formation of municipalities. Explain how these concepts or mechanism can influence individual households’ decision to reside in specific municipality in relation to the provision of the quantity of local public goods. (6p)
Q Nr | Question | Explanation |
a) | Four Conditions when market equilibrium is pareto efficient | 1. PO = Pareto Optimality - A situation where no indvidual can be made better off without making someone else worse off.
2. MRS = Marginal Rate of Substitution Equality - The marginal rate of substitution is equal across all goods.
3. MCE = Marginal Cost Equality - In a Pareto efficient market equilibrium, prices should be equal to the marginal costs of production
4. NEX - No Externalities - In a Pareto efficient market equilibrium, there should be no externalities, meaning that all costs and benefits are internalized within the transactions and prices.
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b) | Median voter | Median Voters Create heterogenous municipalities since the median voters desire allways wins |
b) | Tiebout model | Refers to individuals “voting with their feet” ie. choosing the municipality that offers the right amount. This in turn creates homogenous municipalities. |
b) | Benefit taxation | Refers to a way to determine individuals demand and benefit that they get from a public good. Benefit taxation leads to more diverse and somehow heterogeneous municipalities. |