Question

1. In a monopolistic competitive market for blood pressure monitor, suppose the market demand function for the monitor is P=160 – 3Q, where P is the price for monitor, Q and the quantity of monitor demanded. Marginal cost of producing it is MC: P = 20 + Q, where P is the price of the monitor and Q is the quantity of the monitor sold.

1. Use the Twice as Steep Rule, form the marginal revenue function.
2. What are the price and quantity of monitors in this monopolistic competitive market?
3. Compute the consumer surplus and producer surplus.
4. Assume this market has one dominant firms represent a large percentage of the market share. The industrial demand function remains the same as P=160 – 3Q, where P is the price for monitor, Q and the quantity of monitor demanded. The rest firms are a number of small fringe competitive firms and their supply function is P = 40 + 2Q, where P is the marginal cost of producing the monitor by fringe firms, and Q is the quantity of monitor supplied by fringe firms. Form the demand function for the dominant firm. Use the twice as steep rule, form the marginal revenue function from the demand function for the dominant firm.
5. Use the same condition in Question D above. Assume the dominant firm has a constant marginal cost of $10 a unit. What is the quantity of monitor sold in units by the dominant firm? What is the market price for the monitor?

Use the same condition in Question D above. What is the quantity of monitors demanded for the whole market? What is the quantity of monitor sold in units by the fringe competitive firms?

Answer 1

a) P=160-3Q

Using twice steep rule, Slope=3*2 =6

Hence, MR= 160-6Q

b) For equilibrium,

MR=MC

or, 160-6Q=20+Q

or, 7Q=140

or, Q=20

and P=160-3*20 =$100

c)For the demand curve P=160-3Q

When Q=0, P=160, i.e, Y axis intercept is 160

Then Consumer surplus = 1/2*(160-100)*20 = $600

For the supply curve, P=20+Q, when Q=0, P=20, that means yaxis intercept of the supply curve is 20.

Producer surplus = 1/2*(100-20)*20=$800

d) Market demand is P=160-3Q

and Market supply is MC=P=40+2Q

Now, using steep rule, slope of MR curve is 3*2 = 6

The, MR function is MR=160-6Q

For equilibrium, MR=MC

or, 160-6Q=40+2Q

or, 8Q=120

or, Q=15

and P=160-3*15=$115