For step 4, how do you determine the consumer surplus from the information given in the exercise?

Managerial Economics and Business Strategy 9th edition

Chapter 11, End of Chapter, Problems and Applications,Exercise 15

Page369

Here is the step-by-step explanation, verified by an educator:

Step1of4

The optimal quantity to be sold is determined by equating price to marginal cost.

The marginal cost is derived by partially differentiating the total cost function with respect to Q.

\text{MC = }\frac{\partial\text{TC}}{\partial\text{Q}}

MC=Q

TC

\begin{aligned}\text{}&= \frac{\partial\text{(0}\text{.5Q)}}{\partial\text{Q}} \\\text{}&= 0\text{.5}\end{aligned}

=Q

(0.5Q)

=0.5

Step2of4

Equate the inverse demand function with the marginal cost and solve for Q to determine the optimal quantity to be put in the packed.

\begin{aligned}8-1.5Q&=0.5\text{\,} \\8-0.5&=1.5Q \\Q&=\frac{7.5}{1.5} \\&=5\text{\,units }\end{aligned}

81.5Q

80.5

Q

=0.5

=1.5Q

=1.5

7.5

=5units

Step3of4

The per-unit price is determined by substituting the value of Q in the inverse demand function.

\begin{aligned}&=8-\left( 1.5\times 5 ight) \\&=8-7.5 \\&=0.5 \\ \end{aligned}

=8(1.55)

=87.5

=0.5

Step4of4

The optimal price to be charged for the package is the total value of the package for the consumer. The total value of the package to the consumer is the sum of consumer surplus and the total amount paid for the package. The consumer surplus is the area of the triangle below the demand curve and the price line.

Totalvalue=Consumersurplus+(perunitpricenumberofunitsinpacket)

=[1/25($8$0.50)]+($0.505)

=[1/25$7.5]+$2.5

=$18.75+$2.5

=$21.25

Final answer

5 units

$21.25