Price Discrimination Assignment A movie theatre has a cost function which entail

Question

Price Discrimination Assignment A movie theatre has a cost function which entails the rent of the commercial building of $50 per day (fixed cost) and a marginal cost of $5 per viewer. There are eight potential viewers (four of them are students and four of them are not) with buyer values given in the table below Students $19 $13 $11 $3 Others $22 $18 $16 $10 a) Assume that the movie theater cannot price discriminate and has to decide on the price it charges all viewers. Create a table in which you represent the price, the corresponding quantity demanded, the total revenue, the marginal revenue, the marginal cost, and the profit of the movie theater. b) Determine the optimal price of a movie ticket and the profit of the movie theater in the short run if the seller does not price discriminate. What is the optimal decision of the movie theater in the short run and in the long run about staying or exiting the business? Explain how you reached your conclusion. c) Assume now that the movie theatre can give price discounts to students. Explain the concept of price discrimination and the type of price discrimination in the context of the current example. Is this direct or indirect price discrimination? Explain the market conditions which allow sellers to price discriminate (discuss in detail at least three conditions). d) Determine the optimal ticket prices for students and for others. Determine the revenue of the movie theatre. Determine the optimal decision of the movie theatre in the short and in the long run. Explain your approach.

Explanation / Answer

In this problem, A movie theater business has been discussed. It has to incur $50 per day as rent. It is fixed cost of the day. Variable cost is $5 per viewer. There are 8 viewers (4 students and 4 others), Each of them has willigness to pay. Firm cannot charge different price to different customers. Charging different price is known as price discrimination. Considering different possible prices following table are formed.

Quantity

demand

Total

Revenue

Marginal

Revenue

Marginal

Cost

Total

cost

Total

Profit

In this table, Price are changed in such a manner that one viwer can be added. Total revenue is the product of price charged and quantity of views. Marginal cost is always $5 per viewer. With it add fixed cost rent of $50 to get total cost. Excess of total revenue over total cost is profit.

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Answer (b): Optimal price is the price which maximizes profit. Here firm is not making economic profit by charging same price to all customers. However minimum loss is $6. So optimal price is $16. In short run although there is no economic profit, firm can recover variable costs. so in short run, it will continue business with the expectation of making at least normal profit in the long run. Otherwise, it will not continue.

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Answer (c): Now movie theater has decided to allow price discount to students. Thus different price will be charged to different customers. In this example, a price will be set in general. It will be fixed in such a manner that all viewers other than student can view it. Then try to ascertain how much price a student is willing to pay. On the basis of this willingness, discount will be allowed. Suppose price of movie has been fixed as $16. Then ascertain a student who is ready to pay $13. Allow $3 discount so that he can watch the movie. This strategy of discrimination is known as indirect discrimination.

Amswer d: Optimal price of movie to other viewers will be $16. It is the price that 4th other customers is ready to pay. Others are willing to pay more than this amount. So all 4 other viewers will watch movie. TR from them will be $16x4=$64.

For students price fixed will be $10. At this price three students will watch. Thus total revenue from student will be $30. Note that 4th student will not watch the movie as the willigness to pay is only $3 for him. At this price, marginal cost is not recovered. So fixation of $3 price for student is not possible.

Thus total revenue is $64+$30=$94. Total cost is $50+$5x7=$85. So optimal profit is $94-$85=$9. This is the optimal situation in both short and long run.

Price

Quantity

demand

Total

Revenue

Marginal

Revenue

Marginal

Cost

Total

cost

Total

Profit

(P) (Q) TR=PQ MR MC=5 50+TVC TR-TC $22 1 $22 $22 5 $55 -$33 $19 2 $38 $16 5 $60 -$22 $18 3 $54 $16 5 $65 -$11 $16 4 $64 $10 5 $70 -$6 $13 5 $65 $1 5 $75 -$10 $11 6 $66 $1 5 $80 -$14 $10 7 $70 $4 5 $85 -$15 $3 8 $24 -$46 5 -$49

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