Question

Suppose the market for allergy medicine is perfectly competitive, despite the presence of only 4 firms producing and selling allergy medicine. The demand for allergy medicine is Q_d = 100 - p, where Q_d is the total number of allergy medicine bottles demanded in the market, measured in thousands per year, and p is the price of a bottle of allergy medicine, measured in dollars per bottle. Each firm has a total cost function of $LaTeX: C\left(q\right)=\frac{q^2}{2}+50$ , where q is the firm's production in thousands of bottles and cost is measured in dollars. Given this, each firm's marginal cost is MC = q.

What is the equilibrium price of an allergy medicine bottle in this perfectly competitive market? How many bottles does each firm produce? What is the total equilibrium output?

Answer 1

Following information is given to us

• Q(D)=100-p(demand for allergy medicine)
• Total cost=q^2/2+50
• Marginal cost=q
• p=Price;q=Quantity
• We know Firm will produce at point where marginal revenue is equal to marginal cost owing to profit maximization condition which will give us equilibrium price and quantity
• Marginal revenue is derivative of total revenue with respect to quantity
• Total revenue=Price * Quantity
• From very first equation we get p=100-q,so total revenue=p*q=(100-q)*q=100q-q^2
• Marginal revenue=d(TR)/d(q)=d(100q-q^2)/d(q)=100-2q

a.) Equating MR=MC we get;100-2q=q;q=33.33 or 100/3

b.) Putting q 's value in very first equation we get 100/3=100-p which gives us p=$200/3 or $66.67

c.) Equilibrium output will be price * quantity=200/3*100/3=$20000/9 or $2222.222,since their are four firms total output will be 4*2222.22=$8888.88

Answer is complete.Thank you!