Chapter 7, Problem 10P

a)

To determine

Person A’s yearly profit.

Explanation of Solution

Profit can be calculated using the following equation:

$\text{Profit}=\text{Total revenue}-\text{Total cost }\mathrm{......}\text{ (1)}$

Person A will maximize at $\text{MC}=\text{MR}$.

$\begin{array}{c}\text{MR}=200-0.2\text{Q}\\ \text{MC}=150\\ 150=200-0.2\text{Q}\\ \text{Q}=\frac{50}{0.2}\\ =250\end{array}$

$\text{Q}=2000-10\text{P}\mathrm{......}\text{ (2)}$

Rewrite Equation (2) as $\text{P}=\frac{2000-\text{Q}}{10}$        (3).

Substitute the value of Q in Equation 3.

$\begin{array}{c}\text{P}=\frac{2000-250}{10}\\ \text{P}=175\end{array}$

$\begin{array}{c}\text{TR}=\text{P}\times \text{Q}\\ =175\times 250\\ =43,750\\ \text{TC}=150\times 250\\ =37,500\end{array}$

Substitute the values of TR and TC in Equation (1).

$\begin{array}{c}\text{Profit}=43,750-37,500\\ =6,250\end{array}$

The calculated value shows that Person A’s yearly profit is $6,250.

b)

To determine

Person A’s new profit.

Explanation of Solution

$\begin{array}{c}\text{New demand is, Q}=2,500-5\text{P}\mathrm{......}\text{ (4)}\\ \text{New marginal revenue is, MR}=500-0.4\text{Q}\\ \text{MC}=150\\ \text{MR}=\text{MC}\\ 500-0.4\text{Q}=150\\ 500-150=0.4\text{Q}\\ \text{Q}=\frac{350}{0.4}\\ =875\end{array}$

Rewrite Equation (4) as $\text{P}=\frac{2,500-\text{Q}}{5}\mathrm{......}\text{ (5)}$.

Substitute the value of Q in Equation 5.

$\begin{array}{c}\text{P}=\frac{2,500-875}{5}\\ =325\\ \text{TR}=325\times 875\\ =2,84,375\\ \text{TC}=875\times 150\\ =1,31,250\end{array}$

Substitute the vales of TR and TC in Equation (1).

$\begin{array}{c}\text{Profit}=2,84,375-1,31,250\\ =1,53,125\end{array}$

The calculated value shows that Person A’s new profit is $1,53,125.

c)

To determine

The effect of technological advancement on Person A’s profit.

Explanation of Solution

$\begin{array}{c}\text{MC}=120\\ \text{FC}=1,000\\ \text{Q}=2,500-5\text{P}\mathrm{......}\text{ (6)}\\ \text{MR}=500-0.4\text{Q}\\ \text{MR}=\text{MC}\\ 500-0.4\text{Q}=20\\ 500-20=\text{0}\text{.4Q}\\ \text{Q}=\frac{500-20}{0.4}\\ =1,200\end{array}$

Rewrite Equation (6) as $\text{P}=\frac{2,500-\text{Q}}{5}\mathrm{......}(7)$.

Substitute the value of Q in Equation (7).

$\begin{array}{c}\text{P}=\frac{2,500-1,200}{5}\\ =260\\ \text{TR}=260\times 1,200\\ =3,12,000\\ \text{TC}=\text{FC}+\left(\text{MC}\times \text{Q}\right)\\ =1,000+20\times 1,200\\ =25,000\end{array}$

Substitute the values of TR and TC in Equation (1).

$\begin{array}{c}\text{Profit}=3,12,000-25,000\\ =2,87,000\end{array}$

The calculated value shows that Person A’s new profit is $2,87,000.

d)

To determine

Summarise the lessons from the problem.

Explanation of Solution

The calculations of parts (a), (b), and (c) show that the superstar phenomenon definitely helps to increase profits.