Pricing Strategy for a Monopolist
Session 1 exercises
Dr. Johannes Fichtinger
1 Pricing strategy for a monopolist
A company produces a single product. The price of this product depends only on the quantity produced. If only one item is offered to the market, the company can charge a price of £1000. For each additional item offered to the market, the company has to lower the price by £10 in order to be able to sell it.
(a) Define all relevant variables of the problem, a possible objective and the constraints of the problem. (b) Write down a formal model suitable for this problem.
2 Pizza at Cranfield
A small supermarket store at Cranfield University sells food, academic supplies, toiletries, magazines, packaged food items, and canned soft drinks, beer and fruit drinks. The manager of the store has noticed that several pizza delivery services near campus make frequent deliveries. The manager is therefore considering selling pizza at the store. He could buy premade frozen pizzas and heat them in an oven. The cost of the oven and freezer would be £27,000. The frozen pizzas cost £3.75 each to buy from a distributor and to prepare (including labour and a box). To be competitive with the local pizza services, the manager believes he should sell the pizza for £8.95 per piece.
(a) Define all relevant variables of the problem, a possible objective and the constraints of the problem. (b) Write down a formal model suitable for this problem.
(c) Determine how many pizzas would have to be sold to reach break even (i. e. to earn at least the cost of all investments).
3 Andy Mendoza’s handcraft dolls (BWT, ch1, ex7+ex16+ex17)
Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering massproducing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be £25,000, whereas labour, material, packaging, and shipping will be about £10 per doll.
(a) If the dolls are sold for £30 each, what sales volume is necessary for Andy to
Dr. Johannes Fichtinger
1 Pricing strategy for a monopolist
A company produces a single product. The price of this product depends only on the quantity produced. If only one item is offered to the market, the company can charge a price of £1000. For each additional item offered to the market, the company has to lower the price by £10 in order to be able to sell it.
(a) Define all relevant variables of the problem, a possible objective and the constraints of the problem. (b) Write down a formal model suitable for this problem.
2 Pizza at Cranfield
A small supermarket store at Cranfield University sells food, academic supplies, toiletries, magazines, packaged food items, and canned soft drinks, beer and fruit drinks. The manager of the store has noticed that several pizza delivery services near campus make frequent deliveries. The manager is therefore considering selling pizza at the store. He could buy premade frozen pizzas and heat them in an oven. The cost of the oven and freezer would be £27,000. The frozen pizzas cost £3.75 each to buy from a distributor and to prepare (including labour and a box). To be competitive with the local pizza services, the manager believes he should sell the pizza for £8.95 per piece.
(a) Define all relevant variables of the problem, a possible objective and the constraints of the problem. (b) Write down a formal model suitable for this problem.
(c) Determine how many pizzas would have to be sold to reach break even (i. e. to earn at least the cost of all investments).
3 Andy Mendoza’s handcraft dolls (BWT, ch1, ex7+ex16+ex17)
Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering massproducing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be £25,000, whereas labour, material, packaging, and shipping will be about £10 per doll.
(a) If the dolls are sold for £30 each, what sales volume is necessary for Andy to