Question

Assume that the demand for sugar is given by the function ? = 17 − 3?; [or ???? = 17 − 3?]

and the supply of sugar is given by the function: ? = 2 + 2?. [or ??? = 2 + 2?]

For simplicity here, we are assuming that MWTP and MPC are linear.

a. What is the free market equilibrium price and quantity of sugar? Show your work.

b. Suppose that the production of sugar leads to downstream water quality issues such that downstream users are experiencing Marginal External Costs (MEC) of $5 per quantity. Thus, for any quantity, an MEC of $5 would have to be added onto the MPC to get Marginal Social Cost (MSC). Given this external cost, what would the MSC function be?

c. Given the MEC identified in part (c) and the resulting MSC, what is the socially efficient quantity of sugar production? What about the socially efficient price? How does this new quantity and its associated price compare to the market outcome without intervention?

Answer 1

a. Under free market equilibrium, demand = supply. So,
17 − 3? = 2 + 2?
So, 2Q + 3Q = 17 - 2
So, 5Q = 15
So, Q = 15/5 = 3

And, P = 2 + 2? = 2 + 2(3) = 2 + 6 = 8

The free market equilibrium price and quantity of sugar is 3 units and 8 respectively.

b. MSC = MPC + MEC = 2 + 2? + 5 = 7 + 2Q
So, MSC = 7 + 2Q

c. Social efficient quantity is such that MWTP = MSC
So, 17 - 3Q = 7 + 2Q
So, 2Q + 3Q = 17 - 7
So, 5Q = 10
So, Q = 10/5 = 2
the socially efficient quantity of sugar production is 2 units.

And, P = 7 + 2? = 7 + 2(3) = 7 + 6 = 13
The socially efficient price is 13.

The new quantity is smaller and its associated price is larger compared to the market outcome without intervention.