Question

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

for doughnuts.

Andre'demand is given by Q1-100-2P when P 50, Q1 =0 when P> 50.

Coopers demand is given by Q2 =160-4P when P 40, Q=0 when P> 40.

Carlene's demand is given by Q3 =150-5P when Ps 30, Q =0 when P> 30.

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

a)

It is given that there are three consumers for doughnuts - Andre, Coopers and Carlene

For Price P<=30, all the 3 consumers respond to changing price as per their respective individual demand function.

Thus, for the price P<=30, the market demand is given by the horizontal summation of individual demand function.

Hence, for the price P<=30, the market demand function is given by:

Q= Q1+Q2+Q3

Q=(100-2P) + (160-4P) + (150-5P)

Q=410-11P

For the Price 30 < P <=40, there are two consumers - Coopers and Andre who respond to changing price as per their respective individual demand function. Thus, for the price 30< P<= 40, the market demand is given by the horizontal summation of individual demand function.

Hence, for the price 30 < P <= 40, the market demand function is given by:

Q = Q1 + Q2

Q = (100 - 2P) +( 160-4P)

Q=260 - 6P

For the price 40 < P <= 50, there is only one consumer - Andre, who respond to changing price as per their respective individual demand function. Thus, for the price 40< P<= 50, the market demand is the individual demand function of Andre.

Hence, for 40 < P <= 50, the market demand function is:

Q=100-2P

Hence, the market demand function is given by:

Q = 410-11P, for P<=30

260 - 6P, for 30 < P <= 40

100 - 2P, for 40 < P <= 50

b) On Plotting the given demand function, the result is:

The kink in the market demand curve is observed when P=40 and P=30