Question

George enjoys drinking coffee everyday. The following utility function describes his preferences for daily coffee consumption: u(x) = min{5x,20}where x is the number of coffee drinks he has that day. Assume each drink costs 2. Which statement is incorrect?

(a) His reservation price for the first drink is 5.

(b) His reservation price for the fifth drink is 5.

(c) His willingness to pay for three drinks is 15.

(d) Consumer surplus is equal to 12

Answer 1

Soln. Utility function, U(x) = min { 5x, 20}, number of coffee consumed that day

Cost of each coffee = 2

Suppose George drinks one coffee, then cost of coffee = 2 and utility function, U(x) = min{5,20} = 5

Suppose George drinks two coffee, then cost of coffee = 4 and utility function, U(x) = min{10,20} = 10

Suppose George drinks three coffee, then cost of coffee = 6 and utility function, U(x) = min{15,20} = 15

Suppose George drinks four coffee, then cost of coffee = 8 and utility function, U(x) = min{20,20} = 20

Suppose George drinks five coffee, then cost of coffee = 10 and utility function, U(x) = min{25,20} = 20

Hence, after five coffees, utility function will always be 20

Option a is not correct as reservation price states the maximum price a buyer can pay for a product and from the question, it cannot be deduced that his reservation price for first coffee is 5.

Option b is also not correct and reason is same as mentioned for option a.

The utility function measures the willingness of buyer to pay for a product to satisfy his requirement. For three coffees, his willingness to pay is 5*3 = 15 and hence option c is correct.

Option d is wrong as consumer surplus is different for different number of coffees and cannot be fixed at 12.