1. What price do you charge the public?

The price elasticity of demand (PED) is defined as the percentage change in quantity demanded resulting from a 1% change in price. The formula for maximizing revenue (and usually profits in cases of constant marginal costs) when demand is elastic is:

$P = \frac{MC}{1 + \frac{1}{PED}}$

Where:

• $P$ = price you should charge
• $MC$ = marginal cost per pill = $1
• $PED$ = price elasticity of demand = -1.1

Substituting into the formula:

$P = \frac{1}{1 + \frac{1}{-1.1}} = \frac{1}{1 - 0.909} = \frac{1}{0.091} \approx 11$

Thus, the optimal price for the public is approximately $11 per pill.

2. What would happen to profits if you charged twice as much?

If you were to charge twice the optimal price ($22 per pill), the demand would fall significantly because the price elasticity is relatively elastic (-1.1). Given that the price elasticity of demand is greater than -1 in absolute terms, the percentage drop in demand would be higher than the percentage increase in price, leading to a reduction in total revenue and profits.

Thus, charging $22 would decrease overall profit, as the decrease in quantity sold would outweigh the increase in price.

3. What role does the $100 million in development costs play in your pricing decision?

The $100 million development cost is a sunk cost, meaning it has already been incurred and cannot be recovered regardless of future pricing decisions. From an economic perspective, sunk costs should not directly affect pricing decisions. The focus should be on marginal cost (which is $1 per pill) and the elasticity of demand in order to maximize profit.

However, practically speaking, the firm may set a long-term pricing strategy to recover these development costs over time. Yet, they should not allow this to cloud optimal pricing decisions based on current market conditions.

4. The Medicaid agency has made a take-it-or-leave-it offer of $2 per pill. Do you accept? Why or why not?

Since the marginal cost of producing each pill is $1, selling the pill for $2 would still yield a profit margin of $1 per pill. However, this offer is significantly below the $11 optimal price for maximizing profit in the general public market.

You would need to consider factors like:

• Quantity: If Medicaid purchases a large volume, the lower price may be justified by the higher sales volume.
• Public relations: Accepting Medicaid's offer might improve the company’s public image and provide goodwill.
• Market Segmentation: You could sell to Medicaid at a lower price while maintaining a higher price for the general public, provided that there's no market overlap or possibility of arbitrage (reselling the pills).

In conclusion, you may want to accept the Medicaid offer if the volume is large enough to offset the lower price, but you would need to weigh this against potential impacts on public pricing and overall profitability.

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Do you want to delve deeper into any of these explanations or require further clarifications?

Here are 5 related questions that extend this discussion:

1. How would changing the price elasticity of demand affect the optimal pricing strategy?
2. What pricing strategies could be used to address different market segments, such as Medicaid and the general public?
3. How might fixed costs, such as the $100 million development cost, be recovered over time?
4. What could be the long-term impact on profits if market elasticity changes over time?
5. How could government regulations on drug pricing affect this pricing decision?

Tip: When determining prices, focus on marginal costs and demand elasticity, rather than fixed costs, for optimal pricing strategies.