Question

(a)

Estimates of the marginal cost of a drug are $100 for a 100 pill bottle. If the manufacturer charged $75,000 per bottle, what is the elasticity of demand that they believe they faced?

(b)

The marginal cost is $100 / bottle. Suppose another company comes in to the market to compete with the manufacturer, what is the profit maximizing market price of the drug?

Answer 1

a) Revenue (R) = P*Q

Marginal revenue (MR) = dR/dQ= P +Q*dP/dQ = P*[1+(Q/P)*(dP/dQ)]

= P*(1+1/e_d) … [where, e_d = elasticity of demand]

Now at equilibrium, MR = MC

=> P*(1+1/e_d) = MC

=> 75000*(1+1/e_d) = 100… [Putting the values for price and marginal cost of a 100 pill bottle]

Or, (1+1/e_d) = 1/750

Or, 1/e_d = (-)749/750

Or, e_d = (-)750/749 = (-)1.0013 = (-)1 (approximately)

So, the elasticity of demand is (-)1 (approximately)

b) When another company comes to the market to compete with the manufacturer, depending on the nature of market, the price quantity decision will be made.

As there is a large scope of profit making, the newly entered company will engage in price cut. It will reduce the price by a little margin, which will enable them to grab the whole market. As a response, the manufacturer will set price to a lower level again to capture the full demand. In the same way, the price will be lowered to a level at which both the firm will charge the same price that is nothing but the marginal cost price earning zero profit.

If the market is perfectly competitive, price level would move towards a zero-profit point where P = MC. So, the price will be set at $100 per bottle.