The U.S. cigarette industry has negotiated with Congress and government agencies to settle liability claims against it. Under the proposed settlement, cigarette companies will make fixed annual payments to the government based on their historic market shares. Supposed a manufacturer estimates its marginal costs at $1.00per pack, its own price elasticity at -2, and sets its price at $2.00. The company’s settlement obligations are expected to raise its average total cost per pack by about $.60. What effect will this have on its optimal price?
To determine the effect of the settlement obligations on the company's optimal price, we need to consider the change in costs and the price elasticity of demand.
First, let's calculate the new average total cost (ATC) per pack after the settlement obligations are imposed. The company estimates its marginal cost (MC) at $1.00 per pack and the settlement obligations are expected to raise the ATC by about $0.60. Therefore, the new ATC would be:
New ATC = Old ATC + Increase in cost
New ATC = $1.00 + $0.60
New ATC = $1.60 per pack
Now, let's consider the price elasticity of demand (-2). Price elasticity measures the responsiveness of demand to changes in price. A price elasticity of -2 means that for every 1% increase in price, there will be a 2% decrease in demand (and vice versa).
To find the optimal price, we need to find the price at which the marginal revenue (MR) equals the marginal cost (MC). Since we know the marginal cost is $1.00 per pack, we need to calculate the marginal revenue.
Marginal revenue can be calculated as the price (P) multiplied by (1+ (1/ absolute value of price elasticity)):
MR = P * (1 + (1 / |E|))
MR = $2.00 * (1 + (1 / |-2|))
MR = $2.00 * (1 + 0.5)
MR = $2.00 * 1.5
MR = $3.00 per pack
To find the optimal price, we set MR equal to MC:
MR = MC
$3.00 = $1.00 + (Increase in cost per pack)
Now, let's solve for the increase in cost per pack:
Increase in cost per pack = $3.00 - $1.00
Increase in cost per pack = $2.00
However, we know that the settlement obligations are expected to raise the average total cost per pack by $0.60. So the actual increase in cost per pack due to the settlement obligations would be $0.60.
Increase in cost per pack (due to settlement obligations) = $0.60
Now, let's find the new optimal price after considering the increase in cost due to settlement obligations:
New optimal price = New MC + (Increase in cost per pack due to settlement obligations)
New optimal price = $1.00 + $0.60
New optimal price = $1.60 per pack
Therefore, the effect of the settlement obligations on the company's optimal price would be a decrease from $2.00 to $1.60 per pack.