Question

6. Vertical Summation

You own your own retail outlet, and you and your neighbour (the owner of the shop next door) are considering hiring a night-time security guard to watch over the two shops. The market price for security guards is constant at €20 per hour. From the perspective of you and the other shop owner, this is the supply curve for security guards. Your willingness to pay for a security guard can be summarized by the following demand curve (where Q is hours of security and P is in euros):

D1: P11

=

16 – 2Q

Your neighbour's demand for a security guard is:

D2: P22

=

64 – 8Q

The equation for the collective demand curve is   . On the graph below, plot this collective demand curve for a security guard using the blue line (circle symbols). Next, use the orange line (square symbols) to plot a horizontal line at the market price of a security guard. Then place a black point (+ symbol) at the intersection of those two curves to indicate the optimal quantity of night security guard hours.

Collective DemandMarket PriceOptimal Quantity01234567880706050403020100PRICE (Euros per hour)QUANTITY (Hours of security)

Answer 1

We can add the demand curves vertically to get the collective demand curve. We add the price each consumer is willing to pay based on their demand curves. The price level will be same for both the consumer. So, P = P11 + P22

P11 = 16 – 2Q

P22 = 64 – 8Q

Now, P = P11 + P22

or, P = 16 – 2Q + 64 – 8Q

or, P = 80 - 10Q

The equation for the collective demand curve is, P = 80 - 10Q

PC Euros per hour) For Dii Toloo 16 > Collectives demand owwe O For D2 Tool For collective demand; PS 08 720 Market Price 10 8010 o 1 2 3 4 5 6 7 8 - t optimal Chours of security) E is the point of intersection between the collective demand ewere and market price which is constant at $20 Hence, the optimal quantity of night security guard hours is 6.