Question

Problem 5 Read the following text excerpt: "Improvements during the past decade in the safety and effectiveness of liver, heart, and kidney transplants induced a rapid growth in the demand for organs, which now far exceeds supply. It is essential to find ways to raise the supply of organs and ease the suffering and long wait that many sick persons now endure. That delay can cost lives: Almost 70 persons die each month while waiting for livers to become available. When demand exceeds supply for ordinary goods, the price is raised to suppliers in order to induce them to increase the quantities provided. Using similar incentives would induce more people to allow their organs to be used for transplants after they die." (New York Times, Jan 20th 1997) To illustrate the text excerpt, let us consider the supply and demand for kidneys. First the supply curve. Even at a price of zero, donors supply about 8000 kidneys per year in the US. But many other people who need kidney transplants cannot obtain them because of a lack of donors. It has been estimated that 4000 more kidneys would be supplied if the price were $20,000 (note: here we assume that this price is also received by the donors who were willing to give their kidney for free). This implies the following linear supply curve: Supply: Qs = 8000+ 0.2P It is expected that at a price of $20,000 the number of kidneys demanded would be 12,000 per year. Like supply, demand is relatively price inelastic; a reasonable estimate for the elasticity of demand at the $20,000 price is 0.33. This implies the following linear demand curve: Demand: QD = 16,000 -0.2P These supply and demand curves are plotted in the diagram below, which shows the market- clearing price and quantity of $20,000 and 12.000, respectively. Because the sale of kidneys is prohibited, supply is limited to 8000 (the number of kidneys that people donate). This constrained supply is shown as the vertical line S'. (a) What is the gain in consumer surplus from the prohibition of the sale of kidneys? (b) What is the loss in producer surplus from the prohibition of the sale of kidneys? (c) What is the deadweight loss of the prohibition of the sale of kidneys?

Answer 1

supily is os = 8000 +0-2P demand: = 16,000—0-2P market clearing Price & oty is given by ! Qs "8000 +0:28 = 16800 eze 0.4p> 8000 Pa 20,000) de 8000 +0.2(20000) in 19=19000 But supply is limited at 8=8000 '( new diffey) s' = 8000 Curier 80000 A is (new supply) - Supply 40,000 20, COO - - © 80001 2000 16000 74 under demand corre a Consumer abone surplus = area fruce line Producer suples pluce line 2 abone area rindu supply corne

Consuma surplus efore the prohibition = ara of A ABC = x_183,000-20000) 7 (12000) 2 36 000 900D مسلم) الطلبيه لماهير مياطنط ميل = ava o В СБО = area of BKD 8 area of DKDC = 20,00 * 8000 + LX (1000-3000) (20,000). = 160,000,000_740.000.000 = 200,000,000 Consumes suspeus after the prohibition. - area of AFDO - area of D AMP + area of MEDO x 180.000 ~40,000) (2008) + (40,000 X 8000) 320,000,000 = 160,000,000 + = 480,000,000 Producer surplus after - area o - (surce the prohibelun =o Price =0 at 9 = 8000)

la Grain i CS:_120,000,000 [480,000,000 - 360.000.000 Olldass in PS : 200,000,000 - 0 -3200,000,000 (c) Dead weight loss = area of AF DC < 140.000) (1 2000-8000) 2 - =80,000,000 Method 2 (a) Gain in cs: area of BRDO - area of DKFC = 8000 x 20,000 X (12000–200 }(40,000-20,000) = 160,000,000 - 40,000,000 = 120,000,000 (6) Loss in Ps : area of B CDO Centere Producer surplus - 200,000,000 [doot - atps before probibition (c) Dead weight loss Gain in CS t Loss in PS 0 = 120,000,000 - 200,000,000 = -80,000,000. (sunce its a loss

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