The price elasticity of demand for senior citizens purchasing coffee from McDonald's is −5,while non-senior citizens have a price elasticity of demand equal to −1.25.If it costs McDonald's $0.02 to produce a coffee,the optimal price for a cup of coffee for non-senior citizens and the resultant marginal cost under third-degree price discrimination are:
A) $0.004 and $0.02.
B) $0.02 and $0.80.
C) $0.10 and $0.02.
D) $10 and $0.20.

Question

Quizplus · Accepted Answer

For non-senior citizens, the price elasticity of demand is -1.25. Using the formula for price elasticity of demand, we have:

-1.25 = (% change in quantity demanded) / (% change in price)

We can rearrange this to solve for the percentage change in quantity demanded:

% change in quantity demanded = -1.25 x % change in price

If we increase the price by x%, the quantity demanded will decrease by 1.25x%.

Under third-degree price discrimination, McDonald's can charge different prices to different groups based on their price elasticity of demand. The optimal prices will be such that the marginal revenue for each group is equal to the marginal cost. Since the marginal cost of producing a coffee is $0.02, we need to find the prices that will result in a marginal revenue of $0.02 for each group.

For senior citizens, the price elasticity of demand is -5. Using the same formula as above, we can calculate that if we increase the price by x%, the quantity demanded will decrease by 5x%. So the marginal revenue for senior citizens is:

MR = (P x (1 - 5x%)) - $0.02

For non-senior citizens, we know that the optimal price will result in a marginal revenue of $0.02, so we can set up the equation:

(P x (1 - 1.25x%)) - $0.02 = $0.02

Solving for P, we get:

P = $0.10

So the optimal price for non-senior citizens is $0.10. The marginal cost is still $0.02.

Note that we didn't actually need to use the price elasticity of demand for senior citizens in this case. We only needed it for the other group to set up the equation.

The Price Elasticity of Demand for Senior Citizens Purchasing Coffee