Question

1. There are only three consumers in the doughnuts market. They have different demands for doughnuts.

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

Cooper’s demand is given by Q2=160-4P when P≤40, Q2=0 when P>40.

Carlene’s demand is given by Q3=150-5P when P≤30, Q3=0 when P>30.

1. (10 pts) Derive the market demand curve for doughnuts algebraically.

2. (6 pts) Graph the market demand curve for doughnuts. Pay special attention to any kinks in the market demand.

Answer 1

Market demand is given by

Q=Q1+Q2+Q3

In case of , demand will be equal to

Q=Q1+Q2+Q3

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

Q=410-11P

In case

Q3=0

So,

Q=Q1+Q2+Q3

Q=(100-2P)+(160-4P)+0

Q=260-6P

In case

Q2=0 and Q3=0

So,

Q=Q1+Q2+Q3

Q=(100-2P)+0+0

Q=100-2P

and for P>50

Q1=0, Q2=0 and Q3=0. So,

Q=0+0+0=0

Market demand is summarized as

Q=410-11P for

Q=260-6P for

Q=100-2P for

Q=0 for P>50

b)

Following demand curve can be drawn based upon the above information. Kinks are shown ast P=30 and P=40