Question

6. There are only three consumers in the doughnuts market. They have difference demands for doughnuts.

   Andre’ demand is given by ?1 = 9 − ? ?h?? ? ≤ 9, ?1 = 0 ?h?? ? > 9. Cooper’s demand is given by ?3 = 15 − 3? ?h?? ? ≤ 5, ?3 = 0 ?h?? ? > 5. Carlene’s demand is given by ?2 = 6 − 2? ?h?? ? ≤ 3, ?2 = 0 ?h?? ? > 3.

   a) (10 pts) Derive the market demand curve for doughnuts algebraically. b) (6 pts) Graph the market demand curve for doughnuts. Pay special attention to any kinks in the market demand.

Answer 1

Solution:

Given,

Andre's demand curve for doughnuts:

Q1 = 9 - P

where P ≤ 9. When P > 9, Q1 = 0.

Carlene’s demand curve:

Q2 = 6 − 2P

where P ≤ 3. Wh?? P > 3,  Q2 = 0.

Cooper’s demand function:

Q3 = 15 − 3P

?here P≤ 5. Wh?? P> 5, Q3 = 0 .

a) The market demand curve is the horizontal summation of all the individual demand curves in a given market. It plots the quantity demanded of the good by all individuals at varying price points.

Here, let Q be the market demand curve for doughnuts and it will also be a function of price (P) which is written as f(P).

In order to derive the market demand curve algebraically, the demand curves of all the three consumers of the doughnut market are added together,

Therefore, Q = f(P) = Q1 + Q2+ Q3

=> Q = ( 9 - P) + (15 − 3P) + ( 6 − 2P)

=> Q = 9 +15+6 -P -3P -2P

=> Q = 30 - 6P, is the market demand curve/function for doughnuts when P 3.

Now imposing the various price contraints,

When P > 9, Q1 = 0, then Q = 0 as neither of the three consumers will demand doughnuts at this price.

When P > 3,  Q2 = 0, then Q = 24 - 4P as only Andre and Cooper will demand doughnuts at this price.

When P > 5, Q1 = 0, then Q = 9 - P as only Andre will demand doughnuts at this price because it is less than his willingness to pay.

b) The following photograph presents the market demand schedule and market demand curve for doughnuts (done on excel).

It is observed that he market demand curve is kinked at (4,5). A kinked demand curve is obtained when the demand curve is not a straight line but has a different elasticity for higher and lower prices. This may be attributed to the fact that the market is comprised of many consumers, here 3, and each of them behave differently to price cuts and price increases and also have different willingness to pay for the product in question. For instance, here Carlene will not demand doughnuts if the price rises above 3 units while Andre is willing to pay upto 9 units. Hence, a kink in the market demand curve is observed.