You live in a town with 300 adults and 200 children, and you...

You live in a town with 300 adults and 200 children, and you are thinking about putting on a play to entertain your neighbors and make some money. A play has a fixed cost of \$2,000, but selling an extra ticket has zero marginal cost. Here are the demand schedules for your two types of customer: a. To maximize profit, what price would you charge for an adult ticket? For a child's ticket? How much profit do you make? b. The city council passes a law prohibiting you from charging different prices to different customers. What price do you set for a ticket now? How much profit do you make? c. Who is worse off because of the law prohibiting price discrimination? Who is better off? (If you can, quantify the changes in welfare.) d. If the fixed cost of the play were \$2,500 rather than \$2,000, how would your answers to parts (a), (b), and (c) change?

You live in a town with 300 adults and 200 children, and you are thinking about putting on a play to
entertain your neighbors and make some money. A play has a fixed cost of \$2,000, but selling an extra ticket has zero marginal cost. Here are the demand schedules for your two types of customer:
a. To maximize profit, what price would you charge for an adult ticket? For a child's ticket? How much profit do you make?
b. The city council passes a law prohibiting you from charging different prices to different customers.
What price do you set for a ticket now? How much profit do you make?
c. Who is worse off because of the law prohibiting price discrimination? Who is better off? (If you
can, quantify the changes in welfare.)
d. If the fixed cost of the play were \$2,500 rather than \$2,000, how would your answers to parts (a), (b), and (c) change?

Key Concepts

Welfare Analysis

Welfare analysis examines the impact of pricing strategies on the well?being of different market participants, including both consumers and the producer. It involves evaluating changes in consumer surplus and producer surplus when transitioning from discriminatory pricing to uniform pricing, highlighting who benefits and who loses as a result of such policy changes.

Profit Maximization

Profit maximization is the process of determining the price and output level that yields the highest possible profit, calculated as total revenue minus total costs. In scenarios where marginal costs are zero and there are fixed costs, the focus lies on maximizing ticket sales revenue while covering fixed costs, thereby ensuring sustainable profitability.

Fixed Cost Sensitivity

Fixed cost sensitivity relates to how changes in fixed costs affect the overall profitability and pricing decisions of a business. When fixed costs change, the break-even point and optimal pricing strategies may shift, influencing both the scale of operations and the net profit outcome, and necessitating a revised analysis of pricing strategies under different cost structures.

Uniform Pricing

Uniform pricing involves setting a single price for all consumers regardless of differences in demand or willingness to pay. This approach may be mandated by law or employed for simplicity, but it often leads to inefficiencies by not fully extracting consumer surplus from each segment, potentially resulting in lower overall profits compared to price discrimination.

Price Discrimination

Price discrimination refers to the practice of charging different prices to different groups of consumers based on their willingness to pay or other segmentation criteria. This strategy allows a seller to capture more consumer surplus by setting prices that are tailored to different market segments, rather than having a single uniform price for everyone.

Demand Analysis

Demand analysis is the study of how the quantity demanded by consumers varies with different price levels. Understanding the separate demand schedules for different consumer groups is crucial for determining how prices can be optimized to maximize revenue and profit, especially in situations where each group has a different valuation of the product.

Transcript

00:01 Okay, guys, this is chapter 15, question six.

00:05 In this question, we're given this table, that's the price and quantity demand is scheduled for a play that we want to put on to make a little bit of extra money in a town with 300 adults and 200 children.

00:19 And so in the first part of the question, we're asked, if we want to maximize profits and we can charge different prices to adults and children, how much would we charge for an adult ticket and how much would we charge? for a child's ticket and then how much profit would we make so remember that if we're going to maximize profit we want to maximize profits we're going to set our cost set our price that the marginal cost equals the marginal revenue and in this case the marginal cost equals zero and so this table is going to be pretty big here so bear with me, but we're going to have adults and we're going to have kids.

01:09 We have price, quantity, revenue, and marginal revenue for adults.

01:15 We have price, quantity, revenue, and marginal revenue for kids.

01:20 And then we have total revenue and then the total marginal revenue.

01:26 So for a price of 10, we see that no children and no adults go.

01:31 So i'm not even going to write that down.

01:32 But for a price of nine, we have 100 adults for a total revenue for adults of 900, a marginal revenue for adults of 900.

01:41 And then for a price of nine, we have no kids, no revenue, no marginal revenue for the children.

01:46 So the total revenue is 900 and the total marginal revenue is 900.

01:53 For a price of eight, we see that there are 200 adults.

02:01 That's going to be revenue for adults for 600 or 60.

02:04 1 ,300, a marginal revenue of 700, and there's still no children that are going to go for a price of 8.

02:11 So we have our total revenue is 1 ,600, and our marginal revenue is 700.

02:17 And then 7, we see 300 people will go.

02:21 That's 2 ,100 in revenue, 500 for marginal revenue.

02:28 And 7, we still have no children that go.

02:31 So we have 2 ,100 ,500.

02:38 So then we're going to do six, five, and the last one we're going to do is four, because that's the only one that's relevant for the question.

02:44 But you should continue when you do this by yourself to fill out the remainder of the table.

02:50 There are only 300 people in town.

02:52 So decreasing the price from 7 to 6, there's still only going to be 300 adults, which means now there's only 1 ,800 in revenue, and so we are minus 300 in marginal revenue.

03:03 And at a price of six, there's still no children.

03:07 So we have 1800 and we have minus 300.

03:11 So we can see that now the price for adults has crossed below the marginal cost.

03:16 And so the optimal ticket price for adults is going to be 700.

03:22 You can probably guess since i ended up four that the four is going to be the relevant price for kids.

03:32 So i'm going to skip five just for remedy's sake and say now there's still only 300 adults.

03:39 So the price of four, 300 are going to show up.

03:43 We're going to have 1 ,200.

03:44 It's still going to be a minus 300 marginal revenue.

03:46 You'll see that when you fill in number five yourselves.

03:50 For a price of four, we're going to have 100 kids.

03:56 Sorry, for a price of four, we're going to have 200 kids...