Answer to Question #169545 in Microeconomics for Harry Shergill

Question

A perfect competitive industry faces a demand curve represented by Q = 10,000 – 10P. Also suppose that an individual firm belonging to that industry faces a marginal cost function given by MC (Q) = 4Q + 100 Here Q represents quantity of output produced and P is the price. What would be the equilibrium market price? How much does each firm produce in equilibrium? and also find how many firms would be there in the industry in the long run?

Answer 1

The individual firm's optimal output level occurs when MC=MR. Let's first find the inverse demand function:

$$P=1000-0.1Q.$$

By the definition of total revenue, we have:

$$TR=PQ=(1000-0.1Q)Q=1000Q-0.1Q^2.$$

Then, we can find marginal revenue:

$$MR=\dfrac{dTR}{dQ}=1000-0.2Q.$$

Finally, we can find $Q$:

$$4Q+100=1000-0.2Q,$$ $$4.2Q=900,$$ $$q=214.$$

Then, we can find the equilibrium price by substituting Q into the MC:

$$P=4\cdot214+100=\$956.$$

Let's calculate the market quantity by substituting P into the demand function:

$$Q=10000-10\cdot\$956=440.$$

We can calculate the number of firms as follows:

$$nq=Q,$$ $$n=\dfrac{Q}{q}=\dfrac{440}{214}\approx 2\ firms.$$