Autarky and Economics Questions and Answers

Autarky and Economics Questions and AnswersQuestion 1(a). Write shovel in the problem of an broker that maximizes ex-ante utility in autocracy. Find the conditions that characterise the parceling in autarky. apologise how the in allocation changes with .Autarky is a situation where no trading takes place between agents. Each agent needs to bring home the bacon for his admit needs in an autarky, ie he independently chooses the keep down of I that he wants to come in in the tenacious run technology. The inconvenience of liquidity insurance arises here.Every agent wants to maximise his ex-ante utility still the problem is that at time t=0 he does non know about his type whether he wants to consume early at t=1 or late at t=2 topicing in asymmetric information. Hence, there is a stake that much than is best may be invested.The conditions that characterise the allocation in autarky be move by the bashfulnesss of C1 and C2. If agent decides to consume early, he pass on stop savings (1-I) and liquidated enthronization (I).C1 = 1 I + I = 1 I (1-)If agent decides to consume late, he depart father savings (1-I) and returns from investment (RI).C2 = 1 I + RI = 1 + I(R-1)Agent pull up stakes choose his consumer write (C1, C2) that volition maximise his ex-ante utility U based on the supra controls.However, the allocation is non efficient in autarky as shown in the next part of the question.Max U(C1,C2) = u(C1) + u(C2) = 1 I + I+ 1 I + RI= 2+ I + RI We set up the lagrangian rule to explain the allocation changes in where the constraint in the below comparability is the upper limit utility.L = u(C1) + (1-)u(C2) + 2+ I + RI = + I = 0 = (1- ) + RI = 0 = 2+ I + RI = 0Complementary neglect Condition *2+ I + RI = 0If time values were given for the vari fits, we could even slang work out and get the value of . If a value confining to nothing is obtained for , it elbow room agent is impatient anda value close to one indicates that ag ent is patient.This wrinkle is further supported by the marginal post of reversal concept where = R. If =0, no returns obtained as the agent wants to consume immediately. If =1, returns go forth result for the patient agent. Hence, it shows that the push aside factor provide not change the base results of the model.(b) Write down the conditions that characterise the P arto-optimal allocation. Show that autarky is not efficient. Explain how the allocation changes with .The conditions that characterise the allocation in autarky atomic number 18 bounded by the constraints of C1 and C2.1C1 = 1 I = C1 = (1-)C2= RI = C2 = The constraints piece of tail be combined in a single one.1C1 + (1-)= 1The key result is that allocation is wasteful in autarky as shown belowRecall in autarky C1 = 1 I + I = 1 I (1-) C2 = 1 I + RI = 1 + I(R-1)If C1 1 (un slight I = 0) and C2 R (unless I = 1), then combination these two facts we obtain1C1 + 2 1 which differentiates that efficiency is not reached. It is square(a) as less money and fewer resources exist in an autarky than in Pareto optimal allocation as no trade occurs. Therefore, usance level is lower in autarky.Max U(C1,C2) = u(C1) + u(C2) = + We set up the lagrangian method to explain the allocation changes in where the constraint in the below equation is the maximum utility.L = u(C1) + (1-)u(C2) + + = + = 0 = (1- ) + = 0 = + = 0Complementary thoughtlessness Condition * + = 0If values were given for the variables, we could even crap solved and get the value of . If a value close to cypher is obtained for , it doer agent is impatient anda value close to one indicates that agent is patient.The argument of marginal rate of substitution is also applicable here where = R. If =0, no returns obtained as the agent wants to consume immediately. If =1, returns will result for the patient agent. Hence, it shows that the discount factor will not change the basic results of the model.(c) Assume the a gents are now infinitely risk- loath(predicate). That is U(c1,c2) = minc1,c2. What is the Pareto-optimal allocation?Pareto optimal is an allocation of resources where it is unaccepted to distribute resources without making at least one consumer worst off. Pareto optimal is the best outcome that could result in an economy with trade taking place and thus there is broad(prenominal)er spending level. It is like a desired state where assets are increased for patient people and purpose is increased for impatient people.The Pareto optimal allocation for risk neutral agents satisfies the pursuit first order conditionU(C1) / U(C2) = Rwhich means that agents would like to equate the marginal rate of substitution between consumption levels at t=1 and t=2 with the returns on the long run technology.When U(c1,c2) = minc1,c2, it shows agents attitude to risk aversion.The pareto optimal allocation for the risk averse agent is u(C1) + u(C2G) + (1-)u(C2B) where the superscripts G and B denote good and deadly state respectively.L = u(C1) + u(C2G) + (1-)u(C2B) + u(C1)The concaved utility function states that agents p preserve to consume more to less and shows how consumption is smoothed out over time and across states in the future. The agent is risk averse in the sense that he does not want consumption in the bad state at t=2 to be too much different from consumption at t=1.Question 2(a) Write down the bonus constraint of the cashbox. How does verificatory aect the repayment R the bank can promise? Banks, regarded as information sharing coalitions, can easily cover the problem of asymmetric information of investors. It is assumed that banks will drill the mansion tool to invest in high select abides which will return the investors. Banks are evaluate to be check in such a guidance that will maximise investors interest.The firm chooses the good bemuse ifpH(y-Ru-Rm) pL(y-Ru-Rm) + b = Ru + Rm y- The bank must also be pushd to observe the cipherpHRm C pLRm = Rm The bank will relieve completely least contingent amount from banks as bank finance is more expensive than invest finance.Im = Im () = where denotes expected rate of return.The bank will nail get the stay finance Iu = from uninformed investors. Hence, the banks incentive constraint binds.Using the incentive constraints we have Ru y- which states Iu y indicating that the meet will only be financed ifA + Iu + Im 1 = A (,r) 1 Im() y Other constraints would include a lack of supervise from the bank giving rise to the opportunity of non- reminder pL and the inability to dispose the collateral, ie if the collateral appreciates, the bank will not be able to lot it until bestow to investors has been repaid.The collateral, usually in the form of assets, plays the role of a guarantee that banks give to investors as a security in case of sorrow of the go for. Collateral is also seen as an alternative to monitoring as it saves efforts and reduces the risk of the bank. (0,1) can be interpreted as if K is close to one, bank will be able to refund the money to investors whereas if K is close to zero, bank will be unable to repay keep going the loan.A better collateral equals better chance of getting money back as the bank will prefer to behave or else it will lose the collateral.If the calculate is successful with expected probability p, the bank will gain returns X which will be used to refund the loan to investors and claim back the collateral. The higher the returns from the project, the bank will be able to distribute partly between the investors and keep partly as its own winnings.In case of failure of the project, the bank will obtain zero returns and is then unable to repay R to the investors. The latter will snaffle the collateral and will liquidate it to gain maximum money from it as refund of their investment in the unsuccessful project.(b) Suppose investors have all the bargaining power. Write down their objective, find the optimal cut off and their chemical proportionality profits. If investors have all the bargaining power, they will be able to go the project financing process significantly and dictate their terms. The objective of investors is to obtain maximum returns X from the project. They will want to have full lucubrate about the project to ensure that the bank is choosing a high quality project () rather than making an adverse selection. Investors delegate the monitoring of the project to the bank as the latter has comparative advantage in monitoring activities hence monitoring be will be reduced. Investors will use monitoring and auditing as tools to be free from asymmetric information and to reform efficiency. They will expect close monitoring and continuous feedback on the project from the bank.The optimal contract for investors will be where lending will be most profitable and the below equation is taken from the Diamond flummox (1984)Ey 1 + r + C = Ey 1 + 1 + C = Ey 2+ Cw here Ey = Returns from investmentr = risk free rate, equal to 1 in the questionC = monitoring costThe optimal contract is bounded by the break-even constraint of uninformed investors implying an upper bound on IupHRu (1 + r) = Iu y Equilibrium profits of the investors will be at a executable break-even point, usually where demand equals to supplyA + Iu + Im 1 = A (,r) 1 Im() y (c) For which value of K can the bank borrow and invest?The value of the collateral must be either equal or more or less higher than the investment in project (I) and monitoring be (C) to encourage investors to finance the project as a lower value of the collateral will not attract them.K = I + C or K I + CIdeally if K I + C, this will attract more investors to finance the project and in turn banks will be able to borrow from them and invest in the project.Question 3(a) If A A3, the firm issues high-quality world debt (public debt that has a high probability of world re-paid) We will dis cuss mickle when the enterpriser can issue high quality public debtWell- neatised firms A can issue direct debt as they receive high capital.Low credit risk eminent quality public debt refers that the entrepreneur is likely to meet payment obligations. This type of public debt is an piquant investment vehicle as it has a low risk of default.High dilution costGood reputed firms can issue direct debt only if s where s is the probability of repayment at t=2, conditionally on success at t=0 and given all firms are monitored at t=0.It is assumed that monitoring cost c is miniature such that in the credit mart at equilibrium. The entrepreneur has incentive to issue high quality public debt at a rate of when as the latter equation means high probability of success. The stinting interpretation is when project is successful, returns (R) are obtained. The entrepreneur cannot ask for more than R as the firm will also keep some profits for itself. Every party in the transaction is happy and is in equilibrium when a good project is undertaken.(b) If A3 A A2, the firm borrows from a monitor (and from uninformed investors) We will analyse circumstances when the firm borrows from a monitor and uninformed investorsFirms with medium capital (,r) A borrow from banks.Firms borrow from banks when they fulfil from high credit risk and high dilution costs because banks can yield efficient renegotiation in case of default and can limit dilution costs though there will be an intermediation cost involved. unenlightened investors are ready to invest Iu in exchange of return Ru upon successful project. Firms must be advance to choose good project pH(y Ru) pL (y- Ru) + B Ru y When the firm falls short of capital to issue a direct debt, it can borrow Im from banks (with return Rm if project succeeds) and Iu from uninformed investors (with return Ru if project succeeds).The firm chooses the good project ifpH(y-Ru-Rm) pL(y-Ru-Rm) + b = Ru + Rm y- The bank must also be encouraged to monitor the projectpHRm C pLRm = Rm The bank will borrow only least possible amount from banks as bank finance is more expensive than direct finance.Im = Im () = where denotes expected rate of return.The bank will collect get the remaining finance Iu = from uninformed investorsHence, the banks incentive constraint binds. devil conditions are necessary for bank lending to be in equilibrium in credit market(i) Monitoring cost must be less than the returns of the good projectpH G 1 c(ii) Direct lending which is cheaper must be impossible.pHRc 1Firm should borrow from a monitor (for example a bank) and from uninformed investors at liaise probability of success when pH at a rate of R = .(c) If A2 A A1, the firm issues junk bonds (public debt that has a low probability of success) We will discuss circumstances when the firm issues junk bondsIt is possible that firms with medium capital (,r) A issue junk bonds.High credit risk- Junk bonds refer to bon ds with low credit quality and high default risk. They are taking to risk seeker investors due to their high yielding returns.Low dilution costs as it limits exposure to bad firms but involves inefficient bankruptcy costs for good firms.The zero profit condition for investors is1 = pR + (1- p) AThis nominal return R is feasible (R y) if py + (1- p) A 1 and the expected profit of good firms is thenB = p (y- R)+ pyBy substituting R, we will obtain B = 2py 1 + (1- p) AWhen the monitoring fragment c is added, the monitor can reduce the entrepreneurs private benefit of misbehaving from B to b.pH c (pH pL) RpH If R Rc, the firm will issue junk bonds with low probability of success. This states that the firm is indebted and have too much risk associated with it. The economic interpretation out of it is that the entrepreneur will ask for higher returns but the firm will not afford to provide it. This will lead the entrepreneur to choose the bad project and disequilibrium occurs. He nce, such a combination is not feasible because the maximum repayment is K.(d) If A1 A, the firm does not investWe will analyse circumstances when the firm cannot investFirms with low capital A (,r) can neither invest nor borrow. Venture capitalists are the only solution for such firms.When monitoring costs are added, if pH it means there is a small probability of success. The equilibrium consists of no trade taking place and the credit market collapses because good projects cannot be funded and bad projects have a negative salary present value. Hence, the firm should not invest as there is no trade equilibrium.ReferencesFrexias X. and Rochet J-C., (2006) Microeconomics of Banking, 2nd Edition