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UNIVERSITY OF MASSACHUSETTS BOSTON Accounting and Finance MBAAF 601 Managerial Economics

Prof. Konan Homework # 2

Instructions: Answer all questions below. Make sure to show your work whenever appropriate. TOTAL: 100 points 1. Suppose the federal government requires beer drinkers to pay a $1.5 tax on each case of beer purchased. (In fact, both the federal and state governments impose beer taxes of some sort.) a. Draw a supply-and-demand diagram of the market for beer without the tax. Show the price paid by consumers, the price received by producers, and the quantity of beer sold. What is the difference between the price paid by consumers and the price received by producers? b. Now draw a supply-and-demand diagram for the beer market with the tax. Show the price paid by consumers, the price received by producers, and the quantity of beer sold. What is the difference between the price paid by consumers and the price received by producers? Has the quantity of beer sold increased or decreased? Answer: a. The Supply and demand curve of the beer market without tax Price Supply

E P

Demand

Q

Quantity

Without tax, Supply curve and Demand curve intersect at point E, which is the equilibrium of the market. The price paid by customer and the price received by producers are both equal to P. The quantity of beer in the market is Q. 1

The difference between the price paid by customer and producer without tax is 0. b. The new diagram for the beer market after applying $1.5 tax Price

Supply PC t=1.5 P PS D2

D1

QT Q Quantity After imposing $1.5 tax, the price of beer will increase, and reduce quantity. As the result demand curve will shift to the left. A new demand curve (D2) illustrates for that reduction. Customer now have to pay at higher price (PC) but the price received by seller is equal to PS. The new quantity of beer sold after imposing tax is QT. The difference between the price paid by customer and price received by producer is equal to t and t =$1.5. The quantity of beer sold decrease to QT after tax 2. A market is described by the following supply and demand curves: QS = 2P QD = 400 - 3P a. Solve for the equilibrium price and quantity. b. If the government imposes a price ceiling of $70, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus? c. If the government imposes a price floor of $70, does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus? d. Instead of a price control, the government levies a tax on producers of $20. As a result, the new supply curve is: QS = 2(P-20)

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Does a shortage or surplus (or neither) develop? What are the price, quantity supplied, quantity demanded, and size of the shortage or surplus? Answer: a. The equilibrium price and quantity P=80 Qs=Qd ⇔2 P=400−3 P ⟹ 5 P=400 ⟹ Q=160 The equilibrium price is $80 and the equilibrium quantity is 160 units b. Government imposes a price ceiling of $70 Qs at P = 70 is below the equilibrium price, therefore the price ceiling is binding. Market price is $70 Quantity supplied = Qs= 2P = 270 = 140 Quantity demand 400- 3P= 400-370=190 Shortage = Qd-Qs= 190-140=50 units If government impose a price ceiling of $70, it will result a shortage in the market.

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c. Government imposes a price floor of $70 Since a price floor is $70 which is not binding because the equilibrium price is already above the price floor. Therefore, the market price will be $80 Quantity demand = 400 – 3P = 400 – 3  80 = 160 Quantity supply = 2P = 2  80 = 160 The quantity supplied will be 160 and the quantity demand will be 160. Therefore, a price floor of $70 will result no shortage or surplus. d. The government levies a tax on producers of $20. New equilibrium price and quantity Qs = Qd  2(P-20) = 400 – 3P  5P = 440

P=88 {Qd=136

At P = 88, Qd = 136, Qs = 2  (88-20) = 136 So with this tax, the market price is $88, the quantity supplied and the quantity demand will be 136 units. There is neither a shortage nor surplus 3. One of the largest changes in the economy over the past several decades is that technological advances have reduced the cost of making computers. a. Draw a supply-and-demand diagram to show what happened to price, quantity, consumer surplus, and producer surplus in the market for computers. b. Forty years ago, students used typewriters to prepare papers for their classes; today they use computers. Does that make computers and typewriters complements or substitutes? Use a supply-and-demand diagram to show what happened to price, quantity, consumer surplus, and producer surplus in the market for type- writers. Should typewriter producers have been happy or sad about the technological advance in computers? c. Are computers and software complements or substitutes? Draw a supply-anddemand diagram to show what happened to price, quantity, consumer surplus, and

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producer surplus in the market for software. Should software producers have been happy or sad about the technological advance in computers? d. Does this analysis help explain why software producer Bill Gates is one of the world’s richest people? Answer: a. With the advance of technology, the cost of making computer has reduced. Therefore, the supply curve shifts to the right as the diagram below: Price A S1 S2 E1 B C E2 Demand D

F    

Q1 Q2 Quantity The supply increase, therefore, the supply curve shifts to the right from S1 to S2. The equilibrium changes from E1 to E2. The price decline from B to C but the quantity increase (from Q1 to Q2). Consumer surplus initially is ABE1 now increases to ACE2 Producer surplus deceases from DBE1 to FCE2

b. Student have change their preferences from type writer to computers, so computers and typewriters are substitute goods.  In the typewriters market, with the fall in demand, the demand curve shifts to the left. The equilibrium point moves from E1 to E2 with cheaper price and smaller quantity.  Consumer surplus decreases from ABE1 to FCE2  Producer surplus falls from DBE1 to DCE2 The graph below shows how the changing in demand for typewriters

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Price Supply A F E1 B C

E2

D

D2

D1

Q1 Q2

Quantity

Type wr i t e rpr odu c e r ss hou l db es a da b outt het e c h nol o g i c a la d v a nc e me nti nc omp ut e r b e c a us ei tl e a d st ot h ed e ma ndf o rt he i rpr od uc ti sl e s s c . Co mput e ra nds of t wa r ea r ec omp l e me ntg o ods .Wi t ha ni mpr o v e me nti n t e c hno l o gy ,t hed e ma ndf o rc o mput e ra n ds of t wa r eb o t hi nc r e a s ea ndt h e i rc ur v es h i f tt o t her i g h t . Th ed i a gr a mb e l o ws h o wst hes u pp l ya ndde ma ndc ur v ef ors of t wa r ema r k e t Pr i c e A Supp l y

F E2 B

C

E1

D

D2 D1 Q1

Q2

Qu a nt i t y



Wi t ht hei n c r e a s ei nd e ma n d, t hed e ma n dc ur v emo v e sf r om D1t oD2 , a st h er e s u l tt h ep r i c eg oup ( f r o mCt oB)a n dt h eq u a nt i t yi nc r e a s e sf r o m Q1t oQ2 .  I n i t i a l l y ,c on s ume rs u r p l u si sat r i a n g l eFCE1 , no wi ti nc r e a s e st oABE2  Th ep r od uc e rs u r p l usa l s oi n c r e a s e sf r o mt r i a n g l eDCE1t ot r i a n g l eDBE2  Sof t wa r ep r o du c e r ss h ou l db eh a p p yb e c a u s et e c hn ol o g ya d v a n c el e a dt ot h eh i g h e rd e ma n don c o mpu t e ra nda l s os o f t wa r ea st h e ya r ec omp l i me ntg oo ds . d . Do e st h i sa na l y s i sh e l pe xp l a i nwh ys o f t wa r ep r o du c e rBi l lGa t e si so n eo ft hewo r l d’ sr i c he s tpe o pl e ?

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Yes, this diagram illustrates that with the improvement of technology, the demand in software will increase. In real, computer has improved significantly that also lead to a huge profit for companies related to technologies such as the biggest one - Microsoft. As the result, the owners of these companies become the world’s richest people 4. Consi d e rh o whe a l t hi n s ur a n c ea ffe c t st h eq u a nt i t yo fh e a l t h c a r es e r vi c e sp e r f o r me d. Su pp os et ha tt h e t yp i c a lme d i c a lpr o c e d ur eh a sac o s tof$1 20 ,y e tap e r s onwi t hh e a l t hi n s u r a nc ep a y so n l y$ 2 4o u to f p oc k e t . He ri n s ur a nc ec omp a n yp a y st her e ma i n i n g$ 9 6. ( Th ei n s u r a nc ec o mpa n yr e c ou pst he$9 6 t h r ou g hpr e mi u ms ,b u tt h ep r e mi u m ap e r s o np a y sdo e sno td e pe n do nh o wma n yp r o c e d ur e st h a t p e r s onc ho os e st ou n de r t a k e . )

a. Draw the demand curve in the market for medical care. (In your diagram, the horizontal axis should represent the number of medical procedures.) Show the quantity of procedures demanded if each procedure has a price of $120. b. On your diagram, show the quantity of procedures demanded if consumers pay only $24 per procedure. If the cost of each procedure to society is truly $120, and if individuals have health insurance as described above, will the number of procedures performed maximize total surplus? Explain. c. Economists often blame the health insurance system for excessive use of medical care. Given your analysis, why might the use of care be viewed as “excessive”? d. What sort of policies might prevent this excessive use? Answer: a . Show the quantity of procedures demanded if each procedure has a price of $120. Price

$120

Supply

$24 Demand No of medical procedures Q1

Q2

The figure above shows the demand curve in the market for medical care. This figure illustrates that at a procedure costs $120, quantity is Q1. Health insurance is a normal good, so the demand curve has the downward slope. However, as the supplier are ready to pay 96$ for any number of procedures, the supply curve is perfectly elastic – which means the price doesn’t change when the quantity change. 6

b .I ft hec u s t ome rp a yo nl y$ 2 4, t heq u a n t i t yd e ma n dwi l lb eQ2b e c a u s et h ec o s tt os oc i e t yi s$ 1 20 , t he n umb e ro fpr o c e du r e sp e r f o r me di st o ol a r g et oma x i mi z et o t a ls ur p l us . Th eq u a nt i t yt h a tma xi mi z e s t o t a ls ur p l usi sQ1wh i c hi sl e s st ha nQ2 c . Excessive happens when consumers pay less than the initially cost. When consumer

pay less than the real cost, the economy’s total surplus is reduced d . To prevent this, the government can eliminate insurance that consumer have to pay

the marginal cost for medical procedure. Another one is let company decide whether the procedure should be performed. 5. Af t e re c o no mi c sc l a s so n ed a y , y o u rf r i e n ds u g g e s t st h a tt a x i n gf oo dwo ul db eag o odwa yt or a i s e r e v e nuebe c a u s et h ed e ma ndf orf oo di sq ui t ei n e l a s t i c . I nwh a ts e ns ei st a xi n gf oo da“ g oo d”wa yt o r a i s er e v e nu e ?I nwh a ts e ns ei si tn o ta“ g o od”wa yt or a i s er e v e nu e ?

Answer: On the one hand, taxing food is a good way to raise revenue. The food demand is price inelastic. When food price increases (because of tax), people still have to buy it because there is no substitute for food, therefore, the total revenue may increase. On the other hand, food is the essential goods. If the price of food is high, many people cannot have food which may lead to some s o c i a li s s ue s .Wh e nt h eg o v e r nme nt l e v yt a xo na n yi t e m,t he yha v et ot a k eal o o ka tt h eo v e r v i e wofb ot he c on omya nd s o c i e t y .Th e yc a nno tt r a de offb e t we e nt ot a lt a xr e v e nuea n ds oc i e t yp r ob l e ms . 6. Suppose that a market is described by the following supply and demand equations: QS = 2P QD = 400 - 3P a. Solve for the equilibrium price and the equilibrium quantity. b. Suppose that a tax of T is placed on buyers, so the new demand equation is QD = 400 – 3(P+T) Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold? c. Tax revenue is T x Q. Use your answer from part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 400. d. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Recalling that the area of a triangle is 1⁄2xbasexheight, solve for deadweight loss as a function of T. Graph this relationship for T between 0 and 400. (Hint: Looking sideways, the base of the deadweight loss triangle is T, and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.) e. The government now levies a tax of $300 per unit on this good. Is this a good policy? Why or why not? Can you propose a better policy? Answer: 7

a. Solve for the equilibrium price and the equilibrium quantity. P=80 Qs = Qd  2P = 400-3P  5P = 400 → Q=160

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b . Wi t ht a x , n e we q ui l i b r i u mi s

Qs = Qd  2P = 400 – 3(P+T) 5P= 400 - 3T → P =80−0.6 T  Pr i c er e c e i v e db ys e l l e r s :P= 80−0.6 T Since T > 0, ( 80−0.6 T) 0, ( 80+0.4 T ) >80 , so the price paid by customer increase 01 . 2T  Qu a nt i t ys o l d :2 P=2 ( 80−0.6 T ) =16 Since T>0, 160 -1.2T...