Question

Aman’s income is Rs 3000 per month. She spends all of it on tickets to concerts and films. Concert tickets cost Rs 150 per ticket and film tickets are available at Rs 100 per ticket. The marginal rate of substitution for concerts with films = F/C, F-number of film tickets, C- number of concert tickets. How many film and concert tickets should she purchase?

Answer 1

Given:

Aman's Income = Rs. 3000

Cost of one Concert Ticket = Rs. 150

Cost of one film ticket = Rs. 100

Marginal rate of substitution for concerts with films = F/C

To Find:

Number of film and concert tickets she purchased.

Solution:

• Let the number of film and concert tickets be x and y
• It is said that Aman used all his income on the tickets.
• The total cost on film tickets = 100x
• The total cost on concert tickets = 150y

100x + 150y = 3000 (equation 1)

Marginal rate of substitution for concerts with films= F/C = x/y

• where, F-number of film tickets, C- number of concert tickets

• Solving equation 1 :

100x = 3000 - 150y

x = 3000 - 150y/100

x = 30 - 1.5y ( dividing by 100)

• Putting the above solution to marginal rate of substitution

F/C = x/y

substituting the value of x

F/C = 30 - 1.5y/y

• Putting F/C = 1 ( keeping marginal rate of substitution as 1)

1 = 30 - 1.5y/y

y = 30 - 1.5y ( cross multiplication)

y + 1.5y = 30

2.5 y = 30

y = 30/ 2.5

y = 12

Thus, she should purchase 12 film and concert tickets.