Question

Ally's demand function for ice cream cones is q=5-p, and Ben demand function is q=6-2p. Assume Ally and Ben are the only consumers in the market.

a) what is the aggregate demand of both ally and ben

b)suppose the market is perfectly competitive and the supply function is q=.5p-1. what is the equilibrium price and quantity?

c) suppose it is a monopoly market instead and the marginal cost of the monopolist is 2q+2. what is the optimal price the monopolist charges to maximize its profit?

Answer 1

Ally demand function is q = 5-p

Ben demand function is q = 6 - 2p

1Aggregatte demand is the addition of ally's demand and ben's demand

we have Q = 5-p + 6- 2p = 11 - 3p.

2. If Market is Perfectly competitive

and Supplly function is Q = 5p -1

The Equilibirium quantity is equating demand and supply curve which is

5p-1 = 11 - 3p

8p = 12

p = 12/8 = 3/2 = 1.5

The quantity is Q = 5p -1 = 5(3/2) - 1

= 15/2 -1 = 7.5 -1 = 6.5

The price is 1.5 and the quantity sold is 6.5

C) if it is a monopoly and we have MC = 2Q +2

For monopolist MR = MC

MR ( Marginal Revenue)

To find Marginal revenue , we first find TR (Total Revenue ) = PQ

We know Demand Curve is Q = 11-3P

we get P = (11-Q)/3

The TR is PQ

= ((11-Q)/3) * Q

= 11Q/3 - Q^2/3

We get MR by differentiating TR by Q

dTR/dQ = 11/3 - 2Q/3

Equating MR = MC we get

11/3 -2Q/3 = 2Q +2

11/3 -2 = 2Q +2Q/3

5/3 = 8Q/3

5 = 8Q

Q = 5/8

For Price

we substitute Q in the demand equation

P = (11-Q)/3

= 83/24

= 3.45

The Price is 3,45v and the quantity sold is 5/8.