Question

If an analyst imputes marginal willingness to pay (demand) for green food to be equal to: P = 245 - 1.5Q, what is the change in consumer surplus associated with an increase in Q from 60 to 70 units?

Answer 1

P = 245 - 1.5Q

Calculate P when Q is 0 units -

P = 245 - 1.5Q = 245 - (1.5*0) = 245 - 0 = 245

Calculate P when Q is 60 units -

P = 245 - 1.5Q = 245 - (1.5*60) = 245 - 90 = 155

Calculate consumer surplus when Q is 60 units -

CS = 1/2 * [(P when Q is 0 units - P when Q is 60 units)] * 60 units = 1/2 * (245 - 155) * 60 = $2,700

The consumer surplus when Q is 60 units is $2,700.

Calculate P when Q is 70 units -

P = 245 - 1.5Q = 245 - (1.5*70) = 245 - 105 = 140

Calculate consumer surplus when Q is 70 units -

CS = 1/2 * [(P when Q is 0 units - P when Q is 70 units)] * 70 units = 1/2 * (245 - 140) * 70 = $3,675

The consumer surplus when Q is 70 units is $3,675.

Calculate the change in consumer surplus -

Change in consumer surplus = consumer surplus when Q is 70 units - consumer surplus when Q is 60 units

Change in consumer surplus = $3,675 - $2,700 = $975

Thus, the change (increase) in consumer surplus is $975.