这个作业是完成工人的生产率、公司收整体经济的影响等相关问题

EC317 – URBAN ECONOMICS

ASSIGNMENT 1

1.(14分)下表总结了东部和西部两个地区的面包和衬衫生产工人的生产率:

东西
面包衬衫面包衬衫
每小时产量6 5 3 1

(3分)在东方和西方生产面包和衬衫的相应机会成本是多少?西方有哪些相对优势?
(3分)假定运输成本为零,汇率为1衬衫3条面包。如果东方的一个家庭花一个小时从事衬衫生产并交换所有面包生产的衬衫,那么这个家庭会更好吗?简要说明您的答案。
(2分)假设b)中执行交易所需的时间为一小时。贸易仍然有益吗?
(6分)鉴于上述情况,城市会发展吗?还有哪些其他条件或假设是必要的?简要说明您的答案。

2.(10分)考虑劳动力共享模型。个体工人不愿冒险,其效用函数由下式给出:

U(M)=5√M

M是他们从工作中获得的收入。工人可以选择在偏远地区或集群中为公司工作。如果个人在偏远地区的公司工作,他们的收入为81英镑。最初假设集群中的转换成本为零,而工人在偏远地区失业的概率为50%。

(2分)假设隔离站点的交换成本最初为£32。集群中的公司将提供什么收入来吸引孤立地点的员工(即,确定职位等同于确定工作)?
(2分)如果转换成本降低到£17,您在a)中的答案将如何变化?
(2分)(a)如果您在偏远地区失业的可能性增加到60%,您的答案将如何变化?
(4分)现在假设工人是爱冒险的,而不是规避风险的,因此他们的效用函数由
U(M)=〖(M-s)〗^ 2

s是转换成本。对于隔离站点,收入为81英镑,转换成本为32英镑。集群中的交换成本为零。风险偏好的这种变化如何影响大城市在劳动力集中方面的优势?

3.(8分)一个行业受集聚经济(和经济不经济)的影响。对于一家独立公司,每家公司的利润为100英镑,在有6家公司的集群中,每家公司的利润最高可增加到160英镑。利润曲线是线性的,正斜率部分的斜率为+£12,负斜率部分的斜率为-£10。
(2个标记)说明此利润曲线。
(6分)集群中企业的均衡数量是多少,每家企业将获得多少利润?这会大于有效的公司数量吗?解释为什么。

4. (16 marks) A consumer chooses how much housing (q, measured in square feet) and how much of a composite good (c) to consume to maximise their utility. Their monthly income is £2,000 and they face a commuting cost of t=£20 per mile per month. The price of the composite good is normalised to 1 and the price of housing is p=£0.50 per square foot.

(3 marks) In a diagram, with the quantity of housing (measured in square feet) on the horizontal axis and the quantity of the composite good on the vertical axis, illustrate this consumer’s budget constraint and their utility-maximising choice, assuming that they choose to live 10 miles away from the central business district (CBD) and their utility-maximising quantity of housing is 1,500 square feet.
(3 marks) Suppose the household chooses to move closer to the CBD, so they buy a dwelling that is 5 miles from the CBD. Assuming the price of housing doesn’t change, illustrate and explain the consumer’s new budget constraint and possible utility-maximising choice (assuming all the standard assumptions about consumer preferences hold).
(4 marks) Is the outcome you illustrated in b) an equilibrium? Why or why not? If not, explain how the price of housing would need to adjust to ensure equilibrium is achieved and how this would affect the consumer’s budget constraint.
(6 marks) Suppose the commuting cost increases to t=30 per mile. How will this affect the consumer’s utility-maximising choice in a)? What would this imply for the price of housing for a given distance from the CBD?

5. (12 marks) Using the urban model, illustrate and explain how a reduction in population and a reduction in commuting costs will affect city size and structure. (Note: your answer should explain the combined effect of these two changes)

6. (40 marks) The Covid pandemic has led to an increase in the number of people working from home. If these working patterns continue once things have returned to normal, what impact do you think this will have on the size and structure of cities? Will it lead to the death of the city? Use the economic theory covered in the module to justify your answer. (Word limit: 800 words)