Question

How do you find competitive equilibrium when given a certain number of producers and consumers?

For example, there are 1000 consumers each with demand for a good p = 100-q, and 10 producers each with a marginal cost of production = 10.

As well, how do you find the monopoly equilibrium for this example?

Thanks!

Answer 1

Individual demand curve is given by p=100-q

Then, total demand for 1,000 consumers is p = 100-(q/1,000)

Now, total revenue TR = p*q = 100q-(q²/1,000)

Then, marginal revenue MR = dTR/dq = 100-(q/500)

Again, each of the 10 producers have MC = 10

Then, for equilibrium in the monopoly market,

MR=MC

or, 100-(q/500) = 10

or, q/500 = 90

or, q = 500*90

or, q=45,000 units is the equilibrium quantity

and p=100-(q/1,000) = 100-(45,000/1,000) = 100-45 = $55 per unit is the equilibrium price