Answer to Question #250726 in Economics of Enterprise for gokul

Question

1. Assume the following market demand curve: Q = 13 – 0.5P. Assume marginal cost is constant at $2.

Also assume there is a dominant firm with 6 identical competitive fringe suppliers. .

The following information will be useful for this problem:

           Residual Demand = Market Demand – Fringe Supply

           Total Fringe Supply: 3 + 0.5P

a. Calculate the equilibrium price and quantity for the dominant firm and the average fringe firm.

b. Calculate the value consumer surplus (based on total output--the dominant firm + fringe).

c. Calculate the deadweight loss (based on total output--the dominant firm + fringe).

d. Calculate the profit for the dominant firm.

e. Illustrate the Demand, market price, market quantity, consumer surplus and deadweight loss(based on total output--the dominant firm + fringe) .

Answer 1

a.Q=S

13 – 0.5P=3 + 0.5P

-P=-10

P=10

$Q=13 – 0.5P=13-0.5\times10=13-5=8$

$S=3 + 0.5P=3+0.5\times10=3+5=8$

P=10 q=8

the perfectly competitive equilibrium price occurs at a price of $10, and this is also where the demand curve for the dominant firm begins.

Let's determine the price at which the offer of the competitive boundary will be equal to 0. To do this, we need to take the function of the offer of the competitive boundary and find out at what price the quantity will be equal to 0.

q=0

0=3 + 0.5P

P=-1.5

q=13-0.5P=13+0.75=13.75

This gives us two points for the dominant firm's demand curve (0,10) and (-1.5;13.75).   

Using the rise/run equation to find the slope we get a slope of -1.5/3.75. 

MR = MC

MC=2

MC = MR => 2= 10 - (1.5/3.75) Q

2=10-0.4Q

20=100-4Q

5=20-Q

Q=15

optimal quantity of output for this firm is 15

P = 10 - (1.5/3.75)15 =10-6=4

So the price charged by the dominant firm in this example will be 4

b.

Pmax=10

Pmarket=4

q=8

$value consumer surplus =0.5\times8(10-4)=24$

c.

$deadweight loss=0.5\times(P1-Po)(Q0-Q1)=0.5\times(4-10)(8--15)=-21$

d.

Profit=MR-MC=15\times4-2=60-2=58

d.