Question

In: Economics

Consider the following two groups of consumers in the market for movie tickets – Students and...

  1. Consider the following two groups of consumers in the market for movie tickets – Students and Working Adults. Suppose the Marginal Cost of selling to either group is the same and equal to $4. At the monopoly price for each group, demand elasticities are as follows:

|ES|= 3 and |EW|= 2

  1. What is the Lerner Index of Market Power in the student market?
  2. What is the Lerner Index of Market Power in the Working Adult market?
  3. What is the monopoly price charged to Students?
  4. What is the monopoly price charged to Working Adults?
  5. Explain the relationship between the differences in Lerner index of the two groups and the difference in price to the two groups.

Solutions

Expert Solution

Lerner Index is used as tool to measure Market Power of any firm. It gives the markup of a firm over its Marginal Cost. The same can be formulized as:

L = P – MC / P

Or

L = 1 / | E|

L = Lerner Index

P = Firm’s Price

MC = Marginal Cost

| E | = Elasticity of demand

Extremes of Lerner Index:

· Perfect Competition – A perfectly competitive firm quotes that price which is equal to its marginal cost. Thus here; L = 0.

· Monopoly - Since a monopolistic firm faces a downward sloping demand curve, which means it charges a price which is higher than the marginal cost. Thus, L> 0.

So, Lerner Index always lies between the values of 0 and 1. If a firm’s “L” tends more towards 0, it generally behaves like a perfectly competitive firm. If a firm’s “L” tends more towards 1, it has greater market power and operates like a monopoly.

Considering the above theory we can solve the below answers:

Given MC = $ 4

|ES| = 3

|EW| = 2

Let Ps = Price charged to students & Pw = Price charged to Working Adults

Let Ls = Lerner Index of students & Lw = Lerner Index of Working Adults

a) Lerner Index of Market Power in student market

Ls = 1 / |ES| = 1 / 3 = 0.33

b) Lerner index of market power in working adult market

Lw = 1 / |EW| = 1 / 2 = 0.5

c) Monopoly price charged to students

Ls = Ps– MC / Ps

Since Lerner index in student market is 0.33:

0.33 = Ps – 4 / Pw

0.33*Ps = Ps – 4

4 = Ps -0.33Ps

Solving for Ps, we get 4 = 0.67Ps

Thus Ps = 4/0.67 = $ 5.97 which is the monopoly price charged to students.

d) Monopoly price charged to working adults

Lw = Pw – MC / Pw

0.5 = Pw – 4 / Pw

0.5Pw = Pw -4

4 = Pw – 0.5Pw

Solving for Pw, we get 4 = 0.5Pw

Pw = 4/0.5 = $ 8 , which is significantly higher than the marginal cost.

Rahul Sunny answered 2 years ago
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