# Consumer Purchasing Behavior using Applied Statistics Assignment Solution

Suppose a consumer is willing to pay 12€ for the first unit of a good X, 11€ for the second unit, 10€ for the third unit, etc, 1€ for the twelfth unit and 0€ for the thirteenth unit. The price of one unit of the good is 5.25€.

a) i) How many units of the good X will the consumer buy? (N.B. no decimals are allowed in this answer).

ii) How much money will he/she spend?

iii) What is the maximum amount of money that the consumer would be willing to spend in order to buy that quantity?

b) Next year the price of the goods will be reduced to 1.75€.

i) How many units will the consumer buy?

ii) How much will the consumer surplus change?

c) Why is the consumer surplus used for the measurement of social welfare?

Solution:

 Qty Amount willing to pay 1 12 2 11 3 10 4 9 5 8 6 7 7 6 8 5 9 4 10 3 11 2 12 1 13 0

a

i) The customer will buy up to the unit that what he is willing to pay is greater than or equal to the market price. Since the market price is €5.25, he will be willing to buy up to the quantity at which what he is willing to pay more equals €5.25. From the table, he will buy 7 units

ii) The customer will spend €5.25×7=€36.75

iii) He is willing to spend €12 on the first, €11 on the second … €6 on the seventh. The maximum amount he is willing to pay is 12+11+⋯+6=€63

b

i) When the price reduces to €1.75, he will buy up to the quantity at which what he is willing to pay equals €1.75 from the table that is the 11th unit. The consumer will buy 11 units.

ii) The price he will pay is€5.25×11=€57.75. The price he will be willing to pay is€12+11+⋯+2=€77.

The consumer surplus next year is €77-€57.75=€19.25

The consumer surplus this year is €63-€36.75=€26.25

The consumer surplus will change by €19.25-€26.25=€7

The consumer surplus will reduce by €7

C

Consumer surplus is used as a measure of consumer welfare because it is the difference between maximum willingness to pay and what consumers actually pay. So for a single price change, it can be used to approximate changes in welfare as we can determine whether the consumer is better off or worse off.