Consider a monocentric city in which the cost of commuting is $10 per mile per month. A household located eight miles from the city center occupies a dwelling with 1,200 square feet at a monthly rent of $600. Nonland cost per dwelling is $200, and there are four houses per acre.
a. What is the price (per square foot) of housing at u = $8? What is the bid rent at u = $8?
b. Assume that the demand for housing is perfectly inelastic. What is the price of housing at u = 5?
c. Assume that housing firms do not engage in factor substitution. What is the bid rent at u = 5?
d. How do the answers to (b) and (c) change if the demand for housing is price-elastic and firms engage in factor substitution? Would the prices of housing and land be larger or smaller?
Take a shot, what do you think. (what do you mean by u=$8 ??)
commting
a. To find the price per square foot of housing at u = $8, we need to calculate the land rent and divide it by the square footage of the dwelling.
First, let's calculate the land rent:
Land rent = Cost of commuting per mile * Distance from the city center
Land rent = $10/mile/month * 8 miles = $80/month
Next, let's calculate the total rent:
Total rent = Land rent + Nonland cost per dwelling
Total rent = $80/month + $200/month = $280/month
Finally, let's calculate the price per square foot:
Price per square foot = Total rent / Square footage of the dwelling
Price per square foot = $280/month / 1,200 square feet = $0.2333 per square foot
The bid rent at u = $8 is $80/month.
b. If the demand for housing is perfectly inelastic, the price of housing at u = 5 will be the same as at u = $8. Therefore, the price of housing at u = 5 is also $0.2333 per square foot.
c. If housing firms do not engage in factor substitution, the bid rent at u = 5 will be the same as at u = $8. Therefore, the bid rent at u = 5 is also $80/month.
d. If the demand for housing is price-elastic and firms engage in factor substitution, the prices of housing and land will be larger. With price-elastic demand, as the price of housing decreases, the quantity demanded increases. Housing firms, in order to meet the increased demand, will need to obtain more land for construction. This will drive up the price of land, and consequently, the price of housing. Therefore, both the prices of housing and land would be larger in this scenario.
a. To find the price (per square foot) of housing at u = $8, we need to calculate the cost per square foot of the dwelling.
First, we need to calculate the land rent per acre. Since there are four houses per acre, we divide the monthly rent per acre by four:
Land rent per acre = ($600 + ($200 nonland cost per dwelling))/4
= ($800)/4
= $200
Next, we need to calculate the land rent per square foot. Since there are 43,560 square feet in an acre, we divide the land rent per acre by 43,560:
Land rent per square foot = $200/43560
= $0.0046 per square foot
Finally, we add the cost of commuting to get the total housing cost per square foot:
Price (per square foot) = Land rent per square foot + Cost of commuting per square foot
= $0.0046 + ($10/mile/month * 8 miles) / (1,200 square feet)
= $0.0046 + $0.0067
= $0.0113 per square foot
The price (per square foot) of housing at u = $8 is $0.0113, and the bid rent at u = $8 is also $0.0113.
b. If the demand for housing is perfectly inelastic, the price of housing at u = 5 would simply be the same as the price (per square foot) calculated above, which is $0.0113.
c. If housing firms do not engage in factor substitution, the bid rent at u = 5 would remain the same as the bid rent at u = 8. Therefore, the bid rent at u = 5 would also be $0.0113.
d. If the demand for housing is price-elastic and firms engage in factor substitution, the prices of housing and land would change.
With price-elastic demand, a decrease in the commuting cost would result in an increase in the bid rent. This means that as u decreases from $8 to $5, the bid rent would be higher at u = 5 compared to u = 8.
Additionally, if firms engage in factor substitution, they would be able to adjust their production inputs (such as land and labor) to optimize their costs. This means that they may find ways to produce housing more efficiently, leading to lower costs and potentially lower housing prices.
In summary, if the demand for housing is price-elastic and firms engage in factor substitution, the prices of housing and land would likely be smaller at u = 5 compared to u = 8.