In: Economics
Short Answer (50 points) 1. In Smalltown, USA, Big Corporation serves as a monopoly in the electricity market. The demand for electricity is given by ? = 1020 − 2?!. Marginal revenue is given as ??=1020−4?!. ? is measured in thousands of households. Providing electricity to an additional household costs Big Co. $20. In addition, Big Co. uses outdated technology that produces harmful emissions to the local atmosphere. As a result, scientists have concluded that providing each household with electricity results in an external cost of $100, in the form of chronic health problems. a. Draw and label the following on the graph: ??,???,???,???,???.
b. Calculate the equilibrium price and quantity without any government interventions. Label this quantity on the graph as ?!and ?!, respectively.
c. Calculate and label the consumer surplus, producer surplus and external cost at QM. d. (2 points) Is ?! efficient? Why or why not?
e. Calculate the efficient quantity. Label this quantity on the graph as ?!. If the government would like to make sure that no more than the efficient quantity is produced, should they enact a policy to make the firm “internalize the
a. The graph can be seen in the picture below. Here, the MPC=MC (and hence the supply curve) is a straight line as is the MSC=MPC+MEC, because they are not dependent on the quantity sold as given in the question.
b. The equilibrium price and quantity can be calculated as follows -
We equate MR with MC
1020 - 4Q = 20
4Q = 1020 - 20
4Q = 1000
Q = 1000/4
Q1 = 250
P1 = 20
c. The Consumer Surplus can be seen from the shaded region in the diagram below -
To get the value of this region, we need the value of Q2, which is the socially efficient quantity ad obtained in part e below as 225. To get the point where the demand curve intersects with the y-axis, we substitute the value '0' in place of Q in the equation of demand given in the question and subtract the value of P1 from it. We get the point as (1020 - 2*0) = 1020 - 20 = 1000
Hence, the value of CS is = 1/2 * 225 * 1000 = 112500
There is no porducer surplus in this case because the supply curve is perfectly elastic.
d. Q = 250 is not efficient because at this stage the marginal external cost is greater. It may be efficient for the firm, but t has externality effects and is not efficient for the environment and for the society on the whole.
e. The efficient quantity Q2 can be calculated by equating the MSB with the MSC.
Here, MSB is the MR that the firm earns. The MSC is the MC + MEC
MSC = 20+100
Efficient quantity -
MR = MSC
1020 - 4Q = 120
4Q = 1020 - 120
4Q = 900
Q = 900/4
Q2 = 225
Yes, the government should make a policy to internalise this externlity. The way to do this is to tax the output of the firm, so that they can be disincentivised to produce more than the efficient quantity