Question

A wide range of public projects require land. The government of Ontario recently received funds under the federal infrastructure program to build two new soccer stadiums in the greater Toronto area. To build these sport facilities, the government needs to buy land. The market for land in this region is competitive. The initial private sector demand for this land is given by the following function: D0=15750−0.75P Where, D is quantity demanded in acres and P is measured in dollars per acre. The public demand for land driven by federal infrastructure program shifts the demand function for this land to: D1=20,750−0.75P The supply of land is fixed at 800 acres and does not change due to change in the price of land. So, the supply function is: S=800

(i) Determine the price at which the government would purchase land, the quantity of land in acres it will purchase and the total amount of money it will spend to purchase land.
(ii) Determine the cost of this resource from society's point of view. Explain your results.
(iii) Would it be appropriate to use total cost of land to represent the opportunity cost of this resource from society's point of view? Explain.

Answer 1

The government would purchase 5,750 acres of land at a price of $20,000 per acre, spending a total of $115,000,000. The cost of this resource from society's point of view is zero due to lack of alternative use. The total cost of land does not represent the opportunity cost from society's point of view as there is no alternative use for the land.

Step-by-step explanation:

To determine the price at which the government would purchase land, we need to find the equilibrium price where the demand and supply curves intersect. Equating the demand and supply functions, we get:

15750 - 0.75P = 800

Solving for P, we find that the equilibrium price is $20,000 per acre. Substituting this price into the demand function, we can find the quantity of land purchased by the government:

D1 = 20,750 - 0.75(20,000)

D1 = 5,750

Therefore, the government will purchase 5,750 acres of land. The total amount of money spent to purchase the land can be calculated by multiplying the price per acre by the quantity:

Total amount = $20,000/acre * 5,750 acres = $115,000,000

The cost of this resource from society's point of view can be measured by the opportunity cost, which is the value of the next best alternative foregone. In this case, the opportunity cost would be the value of the land for its next best alternative use. Since the land is not being used in any other way, the cost from society's point of view is zero.

The total cost of land does not represent the opportunity cost from society's point of view because the land is not being used for any other purpose, and there is no alternative use for it. Therefore, the opportunity cost is zero.