They give P,=p2=5 Since prices are higher under monopoly the consumers are going to prefer earlier arrangement 4. A monopoly produces and delivers goods to consumers who are located at varying distances from the factory. It costs m per unit to produce the good and l per mile to transport a unit of the good. Resales are impossible. Calculate the price that a monopoly charges consumers at location t miles if demand is q, =a-bp, where q, and p, are the quantity and price at location t. How does p, change as t increases? Who bears the freight cost? If the monopolist charges different prices to different consumers, is it price discrimination? If yes which degree of price discrimination is this? The price that the monopolist must charge the consumer at location t is given as solution to the profit maximization problem with respect to the consumer at location t Mall, =p, (a-bp)-m(a-bp)-t(a-bp) First order condition for the choice of p, gives a-2bp +mb+t6=0 b、a+(m+1 26 Here in the expression as t i.e. the distance rises the monopolist charges higher price. The monopolist transfers the freight cost to the consumers but not totally. The price rises by only t/2) Since higher prices at more distant places just reflect the cost of serving the consumers based on the definition of price discrimination this is not price discrimination 5. Suppose there are 100 residents (uniformly-spaced) living on a ten-mile long street. Each resident has a willingness to pay for pizza of $30 and would buy I pizza per week. It costs a resident $I to travel one mile. Two pizza shops are considering opening shops along the street (Hint: In the Hotelling model a ten mile long city with 1 /mile transportation cost is equivalent to a l mile long city with $10/mile transportation costs. You can use this equivalence to make theThey give 5 * 2 * 1 pp == Since prices are higher under monopoly the consumers are going to prefer earlier arrangement. 4. A monopoly produces and delivers goods to consumers who are located at varying distances from the factory. It costs m per unit to produce the good and $ 1 per mile to transport a unit of the good. Resales are impossible. Calculate the price that a monopoly charges consumers at location t miles if demand is t −= bpaq t , where qt and pt are the quantity and price at location t. How does pt change as t increases? Who bears the freight cost? If the monopolist charges different prices to different consumers, is it price discrimination? If yes which degree of price discrimination is this? The price that the monopolist must charge the consumer at location t is given as solution to the profit maximization problem with respect to the consumer at location t. )()()(tt t t −−−−=Π − bpatbpambpapMax t First order condition for the choice of pt gives: b btma p tbmbbpa t t 2 )( 2 0 * ++ =⇒ =++− Here in the expression as t i.e. the distance rises the monopolist charges higher price. The monopolist transfers the freight cost to the consumers but not totally. (The price rises by only t/2) Since higher prices at more distant places just reflect the cost of serving the consumers based on the definition of price discrimination this is not price discrimination. 5. Suppose there are 100 residents (uniformly-spaced) living on a ten-mile long street. Each resident has a willingness to pay for pizza of $30 and would buy 1 pizza per week. It costs a resident $1 to travel one mile. Two pizza shops are considering opening shops along the street. (Hint: In the Hotelling model a ten mile long city with $ 1 /mile transportation cost is equivalent to a 1 mile long city with $10/mile transportation costs. You can use this equivalence to make the