Assignment: Intermediate Microeconomic Theory SOLVING PROPLEMS
Problem Set 1-
Please make sure that your problem set is legible and stapled. Please write your name and section number on your problem set. On your graphs, please label axes, curves, intercepts, and all points relevant to the question. Explain your work thoroughly in order to receive full credit. Possible points are given in parentheses.
1. Consider the market for apartments in Tempe.
There is only one local apartment owner, Lord Land, who supplies apartments on a monthly ba- sis. The number of apartments supplied depends on the monthly rental price for apartments (R).
Tenants rent apartments by the month. The number of apartments demanded in a given month depends on the monthly rental price of apartments (R) and on the number of tenants looking for apartments (T).
The equations describing the supply and demand relationships are as follows:
Qs =5R+300 Qd = 3T - 15R
(a) What is the demand for apartments when there are 3, 100 tenants looking for apartments that month? Note: your answer should be a function of R.
(b) What is the equilibrium rent when T=3,100? What is the equilibrium quantity of apartments when T=3,100? Show these solutions graphically.
(c) Tempe is concerned about the welfare of its citizens. To help tenants, the city passes a rent-control policy that requires landlords to charge no more than $400 per month. How many apartments are rented when T=3,100? Show this solution graphically.
(d) Tempe is now concerned about the welfare of Lord Land. To help him out, they pass a minimum-rent policy that requires tenants to pay at least $620 per month. How many apartments are rented when T=3,100? Would this policy be successful? Describe in two sentences or less.
(e) What is the effect of the policy described in (d) when there are 6, 200 tenants? Describe in two sentences or less.
2. Consider the labor market for food truck workers at an upcoming 3-day (72 hour) music festival at Tempe Beach Park. Assume that all workers and all food trucks are identical.
Workers supply labor by the hour. The number of labor hours supplied on the day of the festival depends on the price of labor (P), also known as the hourly wage, and the number of available workers to work (W).
The food trucks buy (i.e., hire) labor by the hour. The number of labor hours demanded on the day of the fair depends on the price of labor (P) and on the number of expected festival attendees (F).
The equations describing the supply and demand relationships are as follows:
Qs = 15P + 10W Qd = 1 F - 5P
(a) What is the supply of labor hours when there are 15 workers available to work? What is the demand for labor hours when there are 900 expected festival attendees? Note: your answers should be functions of P.
(b) What is the equilibrium price of labor hours when W=15 and F=900? What is the corresponding equilibrium quantity of labor hours? How many hours does each worker supply? Show the first two solutions graphically.
(c) Consider that case where some of the workers become ill and there are now only 11 available workers. What are the new equilibrium price and quantity of labor hours when F=900?
(d) What is the effect (on equilibrium wage and employment) of an increase in expected festival attendees from 900 to 1, 500 when there are 15 available workers to work? Show the comparative statics on a graph.
(e) Consider a similar situation to (d) where there is an increase in expected festival atten- dees. In this case, consider that F increases to 4, 700. How many hours would each of the fifteen workers supply? Does this make sense? Explain in two sentences or less.