A monopolist faces a demand curve P = 70 - 1Q, with marginal revenue MR = 70 - 2Q, and MC = 20. Price is expressed in dollars.?

a)How to graph the three functions on one diagram. b) How to compute the profit-maximizing output and price combination on the graph. c) How to compute the efficient level of output (where MC = demand) on the graph d) How to compute the deadweight loss associated with producing the profit-maximizing output rather than the efficient output ?

Dec 5, 2016

Profit maximising quantity and price combination.
Price =$.45 Quantity $= 25 u n i t s$DWL =$312.5

Explanation:

Given -

$p = 70 - Q$------ -----------[Demand function]
$M R = 70 - 2 Q$---------------[Marginal Revenue function]
$M C = 20$--------------------[Marginal Cost function]

Profit Maximising Price and Output combination

Condition for maximum profit

$M R = M C$

$70 - 2 Q = 20$
$- 2 Q = 20 - 70 = - 50$
$Q = \frac{- 50}{- 2} = 25$
Profit maximising quantity $= 25$ units

Substitute $Q = 25$ in demand function to find the price

$p = 70 - Q$
$p = 70 - 25 = 45$

Profit maximising price =$45 Condition for Efficient level of output $D = M C$$70 - Q = 20$$- Q = 20 - 70 = 50$$Q = 50$Efficient level of output $= 50$units Dead Weight Loss is the green colour area. DWL $= \frac{25 \times 25}{2} = 312.5$----- [Area of the green shaded area - height of the triangle is 25 and base of the triangle is 25] DWL =$312.5