question archive answer them Consider an oligopolistic market with N firms competing à la Cournot
answer them Consider an oligopolistic market with N firms competing à la Cournot
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answer them
Consider an oligopolistic market with N firms competing à la Cournot.. Firm i's cost function is given by
C (q ) cq (i 1,...N)
i i = i =
. Show that the ratio between industry profits and revenue is given by
H / ?
, where H measures
the Herfindahl index of concentration. How would this result change if you considered a conjectural variation model of
oligopoly, assuming, for simplicity, symmetric firms?
it is okay please.
4. Suppose a doctor's visit actually costs $90. In other words, the marginal cost of seeing the doctor is constant at $90. Bob has demand for doctor's visits given by the following equation where ???????? is the quantity demanded and P is the price of a doctor's visit: ???????? = 100−.5????
e. Suppose Bob's insurance plan calls for a $50 co-pay. How many times will Bob go to the doctor? What is the dollar value of the moral hazard with the co-pay? Illustrate with a diagram and calculate.
f. Compare and contrast your analysis in part e. to the situation where the insurance company requires a 20% coinsurance rate instead of a co-pay.
g. Is it possible that the co-pay or coinsurance cold actually reduce social wellbeing? Explain.
Explain what it means to say that a change is an economic improvement - i.e. leads to increased efficiency.
2. Give an example of a situation where applying the Pigouvian solution to an externality problem makes the outcome less efficient than doing nothing. Your example must be a numerical example where taxing is the inefficient or not the least-cost avoider solution.
3. Explain in your own words, Coase's critique of Pigou. [Note: Coase has two criticisms of Pigou's approach to negative externalities such as pollution].
4. What is the Pigouvian solution to negative externalities? How would Pigou deal with positive externalities? What are the difficulties in implementing the Pigouvian solution to externalities in general?
5. An airport has only one airline flying out of it; the land under the flight path belongs to ten landowners. The airline can either do nothing to reduce noise from planes landing and taking off, or spend a million dollars a year to completely eliminate the noise; for simplicity we assume that those are its only alternatives. The landowners can use the land either for housing or as a farmland. Each landowner's property is worth $200,000/year as a farmland; $400,000/year as a housing without airplane noise; $320,000/year as a housing with airplane noise. Suppose the transaction costs are very high, giving the same outcomes as (i) the airline is not liable for noise: (il) the airline is liable for noise, how large is the inefficiency from each rule, relative to the efficient outcome? (i) How large is the inefficiency relative to the efficient outcome when the airline is not liable for noise? (ill) How large is the inefficiency relative to the efficient outcome when the airline is liable for noise? (for this question, you need to elaborate and explain what could be the exception and to what extent this exception will the inefficiency vary)
1. Use the following algebraic model of an economy to answer parts a-d. You may use graphical versions of this model to answer parts e and f.
(1) Labor Demand: Ld = n0 - n1*(W/P) + n2*K
(2) Labor Supply: Ls = s0 + s1*(W/P) - s2*to
(3) Labor Market Position: U = (Ls - Ld)/Ls + U*
(4) Production: Y = Tech*Ld.7 *K.3
(5) Consumption: C = co + c1*Yd
(6) Investment: I = d - e*r + f*Y
(7) Net Exports: X = go - g1*Yd - g2*r +g3*Yf
(8) Disposable Income Yd = Y - T
(9) Taxes: T = to + t1*Y
(10) Aggregate Expenditure: AD = C + I + G + X
(11) Goods Market Equilibrium: Y = AD
(12) Money Demand: Md - P = h1*Y - h2*i
(13) Money Supply: M = m0 + m1*i + m2*(Yp - Y)
(14) Money Market Equilibrium: Md = M
(15) Nominal Interest Rate: i = r + ?e
Endogenous Variables Exogenous Variables
Ld,P,U,Ls,Y,C,Yd,T,r W,K,U*, Tech, Yf, Yp, ?e and
I,X,AD,Md,M,i various autonomous terms (e.g., no, so, and to)
(8) a. Derive the IS Curve.
(6) b. Derive the LM Curve.
(6) c. Derive the Aggregate Demand Curve and indicate its slope.
(5) d. Derive the Aggregate Supply Curve and determine the sign of its slope.
(10) e. Determine the effect of an increase in expected inflation (?e) on output, prices, real interest rates, and employment. Show graphics.
(10) f. Show how an increase in the capital stock (K) affects output, prices, real interest rates, and employment. Show graphics.
2. (30 points) Consider the following version of model 5. McCallum's Rule has replaced Taylor's Rule. Except where indicated, variables are expressed in current year terms thus the "t" subscript has been suppressed.
IS Curve: Y = Yp - α(r - ρ) + ?
Fisher Equation: r = i - πe
Phillips Curve: π = πe + φ(Y - Yp) + v
Inflation Expectations: πe = π-1
McCallum's Rule: M = M-1 + β1*(π* - π) + β2*(Yp-Y)
Money Demand: Md = k*Y - h*i
Money Market Equilibrium: M = Md
Endogenous variables: Y, r, π, πe, M, Md, i Exogenous variables: Yp, ρ, ?, v, π*
(4) a. Derive the LM curve.
(6) b. Derive the dynamic aggregate demand curve. Indicate its slope.
(4) c. Determine the dynamic aggregate supply curve and indicate its slope.
(8) d. Indicate the effects of a change in the potential GDP (Yp) on the paths of output and inflation.
(8) e. Indicate the effects of a negative supply shock (v >0) on the paths of output and inflation.
Part II (15 points each) Answer four of the following questions. Indicate any noteworthy assumptions.
1. Evaluate the quotation at the beginning of the exam. If you believe that it is true, provide evidence to support your assertion. If you believe that it is false, how would you change the statement to make it true? Provide evidence to support your claim.
2. a. What is Okun's Law?
b. How have macroeconomic policy makers used it to determine how much stimulation should be provided by monetary and fiscal policy?
c. In what ways might Okun's Law be a misleading guide to appropriate policy?
3. Expectations and Credibility
a. Distinguish between forward and backward looking formulations of expectations regarding the inflation rate.
b. How does this distinction matter in terms of macroeconomic stabilization policy?
c. Whose credibility matters in terms of part b? Why does it matter?
4. The effects of macroeconomic stabilization policy depend on a number of factors.
a. Clearly illustrate and discuss how the specification of the Aggregate Supply curve matters for determining the effects of stabilization policy on output and prices.
b. Clearly explain one set of circumstances under which money would be neutral; that is, changes in the stock of money would not affect real variables?
5. The Natural Rate of Unemployment and the Phillips Curve
a. What is meant by the term "natural rate of unemployment"?
b. What is the Phillips Curve and how do some policy makers use it?
c. What's the relationship between the natural rate of unemployment and the Phillips Curve?
d. What can the character and stability of the Phillips Curve tell us about the Sacrifice Ratio?
6. The Iron Triangle or Impossible Trilogy
a. Is monetary or fiscal policy more potent under fixed exchange rates? Explain why.
b. In terms of policy making regarding openness of the economy, what three policy options must be jointly considered by macroeconomic policy makers? Explain why the third policy depends upon the choice of the first two.
c. In light of the Iron Triangle, why might large countries and small countries make different policy choices?
"There are two and only two ways to grow an economy in real terms. You can grow your working population or you can increase your productivity. That's it. - John Mauldin
Part I. (40 points)
1. Use the following algebraic model of an economy to answer parts a-d. You may use graphical versions of this model to answer parts e and f.
(1) Labor Demand: Ld = n0 - n1*(W/P) + n2*K + n3*RM
(2) Labor Supply: Ls = s0 + s1*(W/P)
(3) Labor Market Position: U = (Ls - Ld)/Ls + U*
(4) Production: Y = Tech*Ld.6 *K.3*RM.1
(5) Consumption: C = co + c1*Yd +c2*NW - c3*P (NW = net worth)
(6) Investment: I = d - e*r
(7) Governmental Expenditures G = G0 + f*(Yp - Y)
(8) Net Exports: X = go - g1*Yd - g2*r
(9) Disposable Income Yd = Y - T
(10) Taxes: T = to + t1*Y
(11) Aggregate Expenditure: AD = C + I + G + X
(12) Goods Market Equilibrium: Y = AD
(13) Money Demand: Md - P = h1*Y - h2*i
(14) Money Supply: M = m0 + m1*i
(15) Money Market Equilibrium: Md = M
(16) Nominal Interest Rate: i = r + πe
Endogenous Variables Exogenous Variables
Ld,P,U,Ls,Y,C,G,Yd,T,r W,K,RM, U*, Tech, NW, Yp, πe and
I,X,AD,Md,M,i various autonomous terms (e.g., n0, s0, t0)
(6) a. Derive the IS Curve.
(4) b. Derive the LM Curve.
(6) c. Derive the Aggregate Demand Curve and indicate its slope.
(6) d. Derive the Aggregate Supply Curve and determine the sign of its slope.
(9) e. Determine the effect of an increase in potential GDP (Yp) on output, prices, real interest rates, and employment. Show graphics based on the above model.
(9) f. Show how an increase in the raw materials (RM) affects output, prices, real interest rates, and employment. Show graphics based on the above model.
2. (24 points) Consider the following version of model 5. Except where indicated, variables are expressed in current year terms thus the "t" subscript has been suppressed. Be sure to show your work for all parts.
IS Curve: Y = Yp - α(r - ρ) + NX+ ?
Net Exports NX = x0 - x1*E
Fisher Equation: r = i - πe
Phillips Curve: π = πe + φ(Y - Yp) + v
Inflation Expectations: πe = π-1
Monetary Rule: i= π + ρ + β*(π - π*) + (1- β )*(Y-Yp) 0 < β < 1
Endogenous variables: Y, r, NX, π, πe, i Exogenous variables: Yp, ρ, ?, E, x0,v, π*
(6) a. Derive the dynamic aggregate demand curve. Indicate its slope.
(3) b. Determine the dynamic aggregate supply curve and indicate its slope.
(8) c. Paul Krugman, Olivier Blanchard and others have suggested that the inflation target (π*) be raised to 4%. What would happen to the paths for output and inflation if monetary policy reflected this new inflation target?
(7) d. How would the results in d change if inflation expectations were rational?
Part II (12 points each) Answer three of the following questions. Indicate any noteworthy assumptions.
1. Evaluate the quotation at the beginning of the exam. If you believe that it is true, provide evidence to support your assertion. If you believe that it is false, how would you change the statement to make it true? Provide evidence to support your claim.
2. Use Model 4 to determine the effect of an exogenous increase in net exports on GDP, P, L, U, W/P and r. Assume Y < Yp . Provide graphics to support your claim.
3. Use Model 5 to determine the paths of output and inflation if there is a positive aggregate supply shock in period t (i.e., vt < 0). Provide graphics to support your claim.
4. The Iron Triangle or Impossible Trilogy
a. In terms of policy making regarding openness of the economy, what three policy options must be jointly considered by macroeconomic policy makers? Explain why the third policy depends upon the choice of the first two.
b. In light of the Iron Triangle, why might large countries and small countries make different policy choices?
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A solitary decent is created by n firms.
The expense to firm I of creating qi units of the great is Ci(qi), where Ci is an expanding capacity (more result is all the more exorbitant to deliver).
All the result is sold at a, not set in stone by the interest for a long term benefit and the organizations' all out yield.
In particular, in the event that the organizations' all out yield is Q, the market cost is P(Q); P is known as the "converse interest work". Accept that P is a diminishing capacity when it is positive: on the off chance that the organizations' absolute result expands, the cost diminishes (except if it is as of now zero). In the event that the result of each firm I is qi, the cost is P(q1 + · · · + qn), so that firm I's income is qiP(q1 + · · · + qn). Consequently firm I's benefit, equivalent to its income short its expense, is
πi(q1,...,qn) = qiP(q1 +···+qn)−Ci(qi). (54.1) Cournot proposed that the business be demonstrated as the accompanying key
game, which I allude to as Cournot's oligopoly game.
Step-by-step explanation
A solitary decent is created by n firms.
The expense to firm I of creating qi units of the great is Ci(qi), where Ci is an expanding capacity (more result is all the more exorbitant to deliver).
All the result is sold at a, not set in stone by the interest for a long term benefit and the organizations' all out yield.
In particular, in the event that the organizations' all out yield is Q, the market cost is P(Q); P is known as the "converse interest work". Accept that P is a diminishing capacity when it is positive: on the off chance that the organizations' absolute result expands, the cost diminishes (except if it is as of now zero). In the event that the result of each firm I is qi, the cost is P(q1 + · · · + qn), so that firm I's income is qiP(q1 + · · · + qn). Consequently firm I's benefit, equivalent to its income short its expense, is
πi(q1,...,qn) = qiP(q1 +···+qn)−Ci(qi). (54.1) Cournot proposed that the business be demonstrated as the accompanying key
game, which I allude to as Cournot's oligopoly game.
Players The organizations.
Activities Each company's arrangement of activities is the arrangement of its potential results (nonnegative numbers).
Inclinations Each company's inclinations are addressed by its benefit, yielded (54.1). 3.1.3 Example: duopoly with steady unit cost and direct opposite request work
For explicit types of the capacities Ci and P we can figure a Nash harmony of Cournot's down. Assume there are two firms (the business is a "duopoly"), each company's expense work is something similar, given by Ci(qi) = cqi for all qi ("unit cost" is consistent, equivalent to c), and the reverse interest work is straight where it is positive, given by
P(Q)=????α−Q ifQ≤α (54.2) 0 if Q > α,
where α > 0 and c ≥ 0 are constants. This backwards request work is displayed in Figure 55.1. (Note that the value P(Q) can't be equivalent to α − Q for all upsides of Q, for then it would be negative for Q > α.) Assume that c < α, so there is some worth of absolute result Q for which the market value P(Q) is more noteworthy than the organizations' normal unit cost c. (If c somehow managed to surpass α, there would be no result for the organizations at which they could create any gain, on the grounds that the market cost never surpasses α.)
To observe the Nash equilibria in this model, we can utilize the methodology in view of the organizations' best reaction capacities (Section 2.8.3). First we really want to track down the organizations' settlements (benefits). On the off chance that the organizations' results are q1 and q2, the market value P(q1 + q2) is α − q1 − q2 if q1 + q2 ≤ α and zero if q1 + q2 > α. Hence firm 1's benefit is
π(q,q)=q????(P(q +q)−c) 112112
q1(α−c−q1−q2) ifq1+q2 ≤α −cq1 if q1 + q2 > α.
To find firm 1's best reaction to some random result q2 of firm 2, we really want to study
firm 1's benefit as an element of its result q1 for given upsides of q2. In the event that q2 = 0,
firm 1's benefit is π1(q1, 0) = q1(α − c − q1) for q1 ≤ α, a quadratic capacity that
is zero when q1 = 0 and when q1 = α−c. This capacity is the dark bend in
Figure 56.1. Given the evenness of quadratic capacities (Section 17.3), the result
q1 of firm 1 that boosts its benefit is q1 = 1 (α − c). (Assuming you know math, 2
you can arrive at a similar resolution by setting the subordinate of firm 1's benefit with
regard to q1 equivalent to nothing and tackling for q1.) Thus firm 1's best reaction to an
outputofzeroforfirm2isb1(0)= 1(α−c). 2
As the result q2 of firm 2 expands, the benefit firm 1 can acquire at some random result diminishes, on the grounds that more result of firm 2 methods a lower cost. The dim curveinFigure56.1isanexampleofπ1(q1,q2)forq2 > 0andq2 < α−c. Again this capacity is a quadratic up to the result q1 = α − q2 that prompts a cost of nothing. In particular, the quadratic is π1(q1, q2) = q1(α − c − q2 − q1), which is zero when q1 = 0 and when q1 = α − c − q2. From the balance of quadratic capacities (or some math) we presume that the result that expands π1(q1, q2) is q1 =
1(α−c−q2). (Whenq2 = 0,thisisequalto 1(α−c),thebestresponsetoanoutput 22
of zero that we found in the past section.)
Whenq2 > α−c,thevalueofα−c−q2 isnegative. Thusforsuchavalueof
q2, we have q1(α − c − q2 − q1) < 0 for generally certain upsides of q1: firm 1's benefit is negative for any sure result, so that its best reaction is to deliver the result of nothing.
We reason that the best reaction of firm 1 to the result q2 of firm 2 depends onthevalueofq2:ifq2 ≤α−cthenfirm1'sbestresponseis1(α−c−q2),whereas
2
in the event that q2 > α − c, firm 1's best reaction is 0. Or on the other hand, more minimally,
????1(α−c−q2) ifq2≤α−c b1(q2)= 2
0 if q2 > α − c.
Since firm 2's expense work is equivalent to firm 1's, its best reaction work b2 is likewise something very similar: for any number q, we have b2(q) = b1(q). Obviously,
