Chapter 14, Problem 14.1P

a)

To determine

To find: The calculation of profit maximizing price, quantity, and profit.

Explanation of Solution

$\begin{array}{c}\text{Inverse demand curve, P = 53 – Q}\\ \text{MR = 53 - 2Q }\mathrm{....}\text{ (twice the slope)}\end{array}$

$\begin{array}{c}\text{Now, MR = MC}\\ \text{53 - 2Q = 5}\\ \text{Q = 24}\\ \text{Now, P = 53 - 24 = 29}\\ \text{Thus, Profit = TR - TC}\\ \text{=}\left(29\right)\left(24\right)-\left(5\right)\left(24\right)\\ =\$576\end{array}$

$\text{Consumer surplus = }\frac{1}{2}\left(53-29\right)24=288$

Therefore, Quantity = 24, Price = $29, and Profit = $576

b)

To determine

To find: The output level under perfect competition.

Explanation of Solution

$\begin{array}{c}\text{Equate, P = MC}\\ \text{Q = 53 - P}\\ \text{P = 53 - Q}\\ \text{Now, 53 - Q = 5}\\ \text{Q = 48}\end{array}$

Thus, the output level produced by industry is 48.

c)

To determine

To find: Consumer surplus and the deadweight loss.

Explanation of Solution

$\begin{array}{c}\text{Consumer surplus = }\frac{1}{2}\times \text{area rectangle}\\ \text{=}\frac{1}{2}\times {\left(48\right)}^2\\ =1152\end{array}$

Sum of profit and consumer surplus = 576 + 288 = 864. Thus, Consumer surplus is more than the sum of profit and consumer surplus.

$\begin{array}{c}\text{Deadweight loss = }\frac{1}{2}\left(29-5\right)\left(48-24\right)\\ =288\end{array}$