Question

1. A firm producing plastic bags is polluting the air of the neighborhood. In the following table the marginal private costs (MPC) of the firm for different quantities of plastic bags are reported together with the inverse demand for plastics bags.

   2.4	Quantity	2.4	MPC (£)	2.4	Selling price (£)
   2.4	1	2.4	11	2.4	28
   2.4	2	2.4	12	2.4	26
   2.4	3	2.4	13	2.4	24
   2.4	4	2.4	14	2.4	22
   2.4	5	2.4	15	2.4	20
   2.4	6	2.4	16	2.4	18
   2.4	7	2.4	17	2.4	16
   2.4	8	2.4	18	2.4	14
   2.4	9	2.4	19	2.4	12

2. Polluting the air creates an externality. We know that the value of the externality is £20 for each quantity level. On a graph with Q on the horizontal axis, plot the MPC, the marginal social costs and the demand. Show the equilibrium in the market. Why is the equilibrium inefficient?

Answer 1

Solution:

Marginal social cost = marginal private cost + value of externality

Since the value of externality is $20 for each quantity level, marginal social cost = marginal private cost + 20

Then, using the given table and above equation, we can plot the points of required curves as follows:

In the above graph, we show the marginal private cost curve by orange line, marginal social cost by red line and demand curve by blue line.

Since, the firm do not take in the social cost it imposes on economy (by way of polluting), it will operate at point where the price equates it's marginal private cost. This is the point which indicates equilibrium in the economy (marked by point E in graph above). However, optimal outcome requires the social cost of externality to be considered, hence the point showing the efficient and optimal outcome is where price equals the marginal social cost (marked by point O in graph above).

Clearly, the equilibrium is inefficient as it creates the dead weight loss (the shaded area in graph above: triangle PEO). Notice that beyond quantity of 0 plastic bags, the social cost is much higher than the extra price the firm receives for each unit. This higher cost further results in loss beyond optimal level, eating up the surplus and thus, rendering the equilibrium level of quantity (which lies beyond the optimal point) as inefficient.