Question

The following is a list of housing costs in five different countries along with their CPI.  

1. What is the real cost of year 1 housing using year 2 as the base year for the above 5 countries? (5 points)
2. For which country is the real cost of housing declining?  (2 points)

2. The market for gravel has been estimated to have these supply and demand relationships:

            Supply  Qs= -1000+100P

            Demand  Qd= 100,000 – 100P

where P represents price per unit in dollars, and Q represents sales per week in tons.  

1. Determine the equilibrium price and sales.  (2 points)
2. What is the price elasticity of demand at the equilibrium. Is this elastic, unit elastic, or inelastic? (5 points)
3. Determine the amount of shortage or surplus that would develop at P = $40/ton. (3 points)

3. The market for iPhones has been estimated to have the following supply and demand relationships:

            Supply:           P = 200 + 0.01Q

            Demand:        P = 500 – 0.01Q

where P represents the price and Q represents sales per week.

1. Determine the equilibrium price and quantity. (2 points)
2. Suppose all consumers experienced a rise in salary. As a result, consumers are now willing to pay $50 more for iPhones, so the new demand equation is P = 550 – 0.01Q. What is the new equilibrium price and quantity as a result of this rise in salary? (2 points)
3. As a result of this rise in salary, what is the price elasticity of demand at the equilibrium? Is it the same as before the change? Why or why not. (2 points)

3. Illustrate using demand and supply curves to answer the following questions:

1. If the demand curve is more elastic, how does this affect the amount of tax revenue a government can collect in a market? (2 points)
2. If the demand curve is more inelastic, does this result in bigger or smaller shortages under a price ceiling below the equilibrium price. (2 points)

Answer 1

Question 2:
a. At equilibrium, Qs = Qd
So, -1000+100P =  100,000 – 100P
So, 100P + 100P = 100,000 + 1000
So, 200P = 101,000
So, P = 101,000/200 = 505
Equilibrium price = $505/ton

And, Q =  -1000+100P =  -1000+100(505) = -1000 + 50,500 = 49,500
Equilibrium quantity = 49,500

b. Price elasticity of demand = (dQD/dP)*(P/Q)
dQD/dP = -100
So, Price elasticity of demand = (-100)*(505/49,500) = -1.02
It is elastic as absolute value of elasticity of demand is 1.02 >1.

c. P= $40
Qs= -1000+100P = -1000+100(40) = -1000+4000 = 3000
Qd= 100,000 – 100P =100,000 – 100P = 100,000 - 100(40) = 100,000 - 4000 = 96,000
So, Qd > Qs. Thus, there is a shortage = Qd-Qs = 96,000 - 3,000 = 93,000 tons

Note: For previous question, data is not given to find CPI and post one question at a time.