Question

13. There are two types of consumers buying VR (Virtual Reality) systems. The demand from the first type is given by q(p) = 10 − p, while the demand for the second type is given by q(p) = 20 − p. With the current technology, there is a constant marginal cost C of producing these systems. If total welfare is 50, which statement is incorrect about the competitive equilibrium?

(a) There are 10 VR sets produced and consumed.

(b) Only the second type of consumer buys these systems.

(c) Producer surplus is equal to 0.

(d) The competitive equilibrium price is 5.

14. (Continued from above question) Assume the technology improves and the marginal cost goes down to 8. What is total welfare in the competitive equilibrium?

(a) 74

(b) 72

(c) 4

(d) 2

Answer 1

13).

Consider the given problem here there are two types of consumers. Now, the demand curve for each types are given by.

=> P1 = 10 - q1 and “P2 = 20 - q2”. Now, if “MC=5”, => then both types of consumers will be able to purchase the good, = > at the competitive equilibrium “P1=P2=MC”. So, by “P1=MC=5”, we get.

=> P1=10-q1=5, => q1=5 and “P2=20-q2=5”, => “q2=15”. So, the total surplus is given by.

=> W = CS1+CS2 = 0.5*(10-5)*5 + 0.5*(20-5)*15 = 12.5 + 112.5 = 125, => W = 125. So, here the total welfare is given by “125” not “50”, => “d” is incorrect.

14).

Now, the “MC” decrease to “8” from “5”, => the “q1” and “q2” are given by.

=> q1=10-8=2 and “q2=20-8=12”. So, the total welfare is given by.

=> W = CS1 + CS2 = 0.5*(10-8)*2 + 0.5*(20-12)*12 = 2 + 72 = 74, => W = 74. So, here the correct answer is “a”.