question archive Q18) 3) (450 points; 25 minutes) In the competitive market for medical scanning devices, there are 400 teaching hospitals in the US who would buy at most one device Market demand in units is given by: Qd=1250 - (1/4)P up to the constraint that at most 400 units will be sold (i
Q18) 3) (450 points; 25 minutes) In the competitive market for medical scanning devices, there are 400 teaching hospitals in the US who would buy at most one device Market demand in units is given by: Qd=1250 - (1/4)P up to the constraint that at most 400 units will be sold (i
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Q18) 3) (450 points; 25 minutes) In the competitive market for medical scanning devices, there are 400 teaching hospitals in the US who would buy at most one device
Market demand in units is given by: Qd=1250 - (1/4)P up to the constraint that at most 400 units will be sold (i.e. Qd < 400). Market supply is given by: Qs= -3000 + P.
(a) What is the equilibrium price and quantity of devices sold?
(b) The government seeks to restrain healthcare spending by taxing teaching hospitals $1000 per machine bought. What is the equilibrium quantity of devices sold, and what price do firms receive? Is there any deadweight loss, and, if so, how much?
(c) If, instead of imposing a tax, the government provided a subsidy, would there be any deadweight loss? (No calculation is necessary to answer this question.)
4. (450 points; 25 minutes) In a small country, Gelbium, yearly demand for mail delivery is Q=110,000- 10,000 p. where p is expressed in Gelbium Marks (GM) and Q is expressed as the number of pieces of mail. The marginal cost of delivering a piece of mail is constant and equals 1 Gelbium Mark. There is no fixed cost.
(a) Suppose the government runs the mail service. If the government wants to maximize the social surplus, how much should it charge for mail delivery?
(b) Suppose the government privatizes mail delivery. It sells the monopoly right to deliver mail to a commercial firm. The firm is free to set its price. How much will the firm charge for delivering a piece of mail? What is the maximum (yearly) amount the government can charge for the monopoly rights? What is the effect of this privatization on total welfare?
(c) Assume that the government, after having sold the monopoly rights, gives a subsidy of 2 Gelbium Marks per piece of mail that the firm delivers. What will be the impact of this subsidy on consumer surplus and on firm profits (relative to unsubsidized monopoly)? What will be the welfare effect?
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Q18. Problem #3. The demand can be at most 400. Afterwards, demand is perfectly inelastic (e.g. if you lower the price, the same amount will be demanded: 400). Re-arranging the supply and demand functions: P = 5000 - 4 Qd; P = 3000 + Qs
3a) Equilibrium Price and Quantity are determined by setting Qs = Qd and then checking to make sure that Qd < 400: -3000 + P = 1250 - (1/4) P Ù P = $3400 From the demand curve: Q = 1250 - (1/4)P = 1250 - (1/4)*(3400) = 400 Q = 400 scanners, P = $3400 per scanner 3b) Now there is a tax. Quantity will not increase with a tax, so consider the elastic portion of the demand curve.
Let Ps = price received by seller, Pb = price paid by the buyer, and the tax is Pb - Ps = $1000. Qs = Qd Î -3000 + Ps = 1250 - (1/4) Pb 4 Ù -3000 + Ps = 1250 - (1/4) (Ps + 1000) Ù (5/4)Ps = 4000 Ù Ps = $3200 Q = -3000 + Ps = -3000 + 3200 = 200. 200 scanners are sold, and the price that firms receive is $3200 per scanner. [Note that the price buyers pay is Pb = Ps +1000 = $4200] To calculate deadweight loss of a tax, calculate the area of the DWL triangle, or calculate the change in total surplus. Area of DWL triangle: ½ * (4200 - 3200) * (400-200) = $100,000
3c) Now there is a subsidy in the amount of $1000 per machine. Quantity will not decrease with a subsidy, so consider the perfectly inelastic portion of the demand curve
With a perfectly inelastic demand, the quantity demanded and sold does not change with the subsidy, so there is no distortion and no deadweight loss. The entire subsidy is passed on to the consumers. $400,000 is simply transferred from taxpayers to teaching hospitals.
