PART 9Exercise 1: Equilibrium and taxes The government is plagued by dire financial straits and thus plans to tax the consumption of pork (the official reason is the pork damages health). It asks micro-expert Mr. I what effects are to be expected of such a tax.Mr. I thus gets to work. First of all, he determines the aggregate demand function and the aggregate supply function:

with and Use the following values for the drawing: a=7, b=2, c=1, d=1. 1. Mr. I calculates the equilibrium in the instance without taxes. What is the equilibrium price and demand? Also produce a drawing.

XD = XS a bP = c + Dp 7 2P = 1 + P P* = 2 X*= 3P (xD) = = = 3.5 0.5xDP ( xS) = = xS 1

P

Consumer surplus

a/b =3.5XS

E

P=2

XD

Producer surplus

X

Q = 3

2. In order to employ a welfare comparison, Mr. I additionally calculate the consumer and producer surplus. How high are these?

CS = =1/4 (7 2*2) = 2.25

PS = = 2 (1 + *2) = 43. Then Mr. I calculates the equilibrium in the instance with taxes. He thus starts working on a quantity tax in the amount of t. He wonders if who pays taxes to the state plays a role. Can you help him? Also produce a drawing here. Assume here that t=1.5.

PD = PS + t=> xD = a b(PS + t)=> xS = c + dPS xD = xS a b(PS + t) = c + dPS PS = = 1=> PD = PS + t = 2.5X* = XD(PX) = XS(PS) = c + dPS = 2=> T = X*t = 3So, Xs(PS) = 1 + PS Ps = XS 1XD(PS) = 7 2(PS + 1.5) = 4 2PS PS = 2 XD

P

3XS

1

XD

X

2

PS = PD tXD (PD) = a - bPDXS(PD) = c + d(PD t)XD(PD) = XS(PD) a bPD = c + d(PD t)=> PD = = 2.5=> PS = 2.5 1.5 = 1X* = XD(PD) = XS(PD) = c + d(PD t) = 2 T = xt = 3 XS(PD) = 1 +(PD 1.5) PD = XS + 0.5 XD(PD) = 7 2PD PD = 3.5 0.5XD

P

XS (PD)

3.5XS

2.5

2

1XD

321X

4. Mr. I wonders if welfare has changed due to the tax increase. Calculate the consumer and producer surplus in the instance with taxes and the welfare loss or profit from taxes, whereby you can assume that tax income is simply paid back to the citizens. Also draw these amounts in your graph. Explain where the welfare loss or gain comes from. Consumer surplusPD = PS + tPS = 1=> PD = 2.5XD(PD) = 7 - 2PDCS( tax) = CS = CS (tax) CS(no tax) = -1.25=> CS decreasedProducer surplusXS(PS) = 1 + PSPS (tax) = Ps)dP = 3/2PS = PS (tax) PS(no tax) = -2.5=> PS fallingAnd T = 3CS(no tax) + PS(no tax) = 2.25 + 4 = 6.25While T + CS(tax) + PS(tax) = 1 + 1.5 + 3 = 5.5DEADWEIGHT LOSSDWL = -w(tax) + w(no tax) = 6.25 5.5 = 0.75

P

Dead weight lossXs

P2

P1XD

Q2Q1X

5. Explain what happens if (a) b=0.XD(PD) = a bPD = aXS(PD) = c + dPS = c + d(PD t)XD(PD) = XS(PD) a = c + d(PD t) PD = = 7.5

We haveXD(PD) = a = 7XS(PD) = c + d(PD t) = PD P = XS(PD) + pXS(PD)

7.5

x

7

(b) d=0.XD(PS) = a b (PS + t)Xs(PS) = c +DpS = cXD(PS) = Xs(PS) c = a b (PS + t)=> PS = = 1.5XD(PS) = 4 - 2 PS PS = 2 1/2XDXs(PS) = 1=> PS = 1.5

XSP

1.5

XD(PS)XD

X1

(c) the demand is completely elastic. XD(PD) = a bPD PD = Assume PD = g = 5Xs(PD) = c + d(PD t) = 4.5PXS

XD

5

4.5X

(d) the supply is completely elastic. XS = c + dPSPS = Assume Ps = h = 1XD(PS) = 2

P

Xsh = 1

XD

X

2

(e) b=d. Also show your results by means of a drawing.

b = d = 1PD = PS + tXD(PS) = XS(PS)PS = 2.25, PD = 3.75X = a bPD = 7 3.75 = 3.25XS = c + PXS = 1 + PS PS = XS 1XD = 5.5 PS PS = 5.5 - XD

P

XD2.253.253.75XS

PART 10Exercise 1: Price discrimination in monopolies

A regional transport service operates as a single supplier a connection with marginal costs of 0, fixed costs of 100, and the price-demand function . Whereby designates the traveller numbers and cost of a journey.

1. Calculate the price that the monopolist will require. What is his profit? P1 = 20 X1 => X1 = 20 P11 = P1X1 C (X1) = P1(20 P1) C(X1) = P1(20 P1) 100 = 20 -2P1 = 0 P1 = 10 X1 = 10 1 = 0

2. A transport service additionally introduces another connection of the same length and identical costs, but with being the price-demand function.Would you advise the transport service to employ price discrimination? P2 = 40 X2 => X2 = 40 P22 = P2(40 P2) 100 = 40 2P2 = 0 P2 = 20 X2 = 20 2 = 300 = 1 + 2 = 300We have: P1 = P2X1 = 20 P1 = 20 P with P 20X2 = 40 P2 = 40 P with P 40 60 2P with P 20 Xtotal = 40 P 20 < P 40 0 constTOTAL = P Xtotal Ctotal(X) = P(60 2P) 200 = 60 4P = 0 P = 15 X = 30 = 250

Exercise 2: Oligopolistic theory

In a market with invest total demand function only two companies A and B operate. Thus p is the price and X the total quantity of the homogeneous commodity demanded in the market. The identical marginal costs for both companies are 0. 1. Determine the reaction function of both companies under the assumption that they use quantities as strategic variables and simultaneously come to a supply decision. Also depict these by means of a graph. Which quantities of commodities are produced by the companies in the end? Explain the conclusion to this solution by means of a graph.

P(XA,B) = 48 XA - XBMax A = (48 XA - XB)XA = 48 2XA XB = 0 XA(XB) = 24 1/2XB XA = 24 (24 1/2 XA) XA = 16XB = 24 1/2 XA = 16P = 16B = B = 256MaxB B = (48 XA - XB)XB = 48 - XA -2XB = 0 XB(XA) = 24 1/2 XA

P

48

24

16

XB(XA)

XA

481624

2. Now assume that the companies use the price as strategic variables and simultaneously come to a new decision. What quantities of commodity are supplied? Explain the conclusion to this solution. According to the theory of Price competition with homogeneous products The Bertrand Model. P = MC = 0=> X = 48 => = 03. The marginal costs of company B rose to 15. How does the solution look like on now?MC B = 15 => PB = 15 XA = 48 15 = 33XB = 0A = 33 * 15 = 495B = 04. Assume that the companies agree to set the total amounts in such a way that the total collective profit is maximized (cartel solution). What total quantity is now produced? = (48 X)X = 48 2X = 0 X = 24 P = 24 = 576A = B = 288We haveP = 24 if MCB = 15 => PA = 15 - A = 33 * 15 = 495B = 0MCA = MCB = 0

Exercise 3: Oligopolistic theory In a city there are two newspapers, 1 and 2. The demand depends on their own price and the price of rivals.The newspapers' demand functions are

(a) for newspaper 1.

(b) for newspaper 2.

whereby and are the prices of the newspapers. The marginal costs of both newspapers are zero.Calculate the market equilibrium in simultaneous price competition. Explain the conclusion to this solution by means of a graph.MaxP11 = P1 (21 2P1 + P2) = 21 4P1 + P2 = 0 P1 (P2) = 21/4 + 1/4P2MaxP22 = P2 (21 2P2 + P1) = 21 4P2 + P1 = 0 P2(P1) = 21/4 + 1/4P1 P1 = 21/4 + (21/4 + 1/4P1) P1 = 7 P2 = 7 X1 = 14 X2 = 14 1 = 2= 98P2

7

21/4

P17

PART 11Exercise 1: External effects

Consider a chemical factory ('company) and the inhabitants of a neighbouring village ('residents'). The company produces with production function , whereby designates the output quantity and the input quantity.

It can sell its product at a price of per unit and must pay the price for a unit input.

The company's production generates waste gases leading to aggregate 'disutility' (i.e. damage) for the residents depending on the input factor used by the company. 1. What input quantity does the company choose if air pollution is not monitored or penalized and negotiations between the company and the residents are not possible?2. Calculate the input quantity the social planner would use.

3. Depict your results from exercise parts 1. and 2. in a suitable graph (assume in your illustration that). Explain why a welfare loss occurs in the situation described in exercise part 1) and calculate this (for variable).4. Discuss how an efficient allocation can be met within the framework of negotiations.

1. Max = PYY PXX = 2(20X X2) - PXXPXX = C(X) = 0 = 40 4X PX = 0 4X = 40 - PX XP = 10 1/4PX with PX 400 const

2. Max = 2(20x x2) - PXX 1/2X2 = 40 4X Px X = 0

MR MCPrivate MCSocial MCTotal X = 8 1/5Px XS = 8 -1/5Px with Px 40 0 const2. DN = 1/2x2 = X = MCSMC

X

MR = 40 4XP

1040X

MCP = Px = 20MCP

X20

MCTOTAL = MCP + MCSMCT

3. Px

Welfare loss5MCPX

A

MCTOTALFE25

D24

C20

410MR

WL1 = ABD BDE = 50 12.5 = 37.5WL2 = ABCF BCF = 48 8 = 40WL = - CDF + CDEF = -2 + 4.5 = 2.5WL = DEF = (4-5)(25-20) = 2.5