Autarky and Economics Questions and Answers

Question 1

(a). Jot down the condition of an agent that maximizes ex-ante utility in autarky. Find the conditions that characterise the allocation in autarky. Explain how the allocation changes with β.

Autarky is a predicament where no trading takes place between real estate agents. Each agent needs to give his own needs in an autarky, ie he individually chooses the amount of I that he wants to invest in the long term technology. The issue of liquidity insurance occurs here.

Every agent needs to maximise his ex-ante utility but the situation is the fact that at time t=0 he does not know about his type whether he needs to consume early on at t=1 or late at t=2 leading to asymmetric information. Hence, there's a risk that more than is optimal may be invested.

The conditions that characterise the allocation in autarky are bounded by the constraints of C1 and C2. If agent decides to consume early on, he will get cost savings (1-I) and liquidated investment (ÉI).

C1 = 1 - I + ÉI = 1 - I (1-É)

If agent chooses to consume later, he will obtain cost savings (1-I) and dividends from investment (RI).

C2 = 1 - I + RI = 1 + I(R-1)

Agent will choose his consumer account (C1, C2) that will maximise his ex-ante utility U based on the above mentioned constraints.

However, the allocation is not successful in autarky as shown in the next area of the question.

Max U(C1, C2) = u(C1) + βu(C2) = [1 - I + ÉI]+ [1 - I + RI]= 2+ ÉI + RI

We setup the lagrangian method to describe the allocation changes in β where in fact the constraint in the below equation is the maximum utility.

L = πu(C1) + (1-π)βu(C2) + λ[2+ ÉI + βRI]

= π + λÉI = 0

= (1- π)β + λRI = 0

= 2+ ÉI + βRI = 0

Complementary Slackness Condition: λ*[2+ ÉI + βRI] = 0

If values received for the parameters, we could have even solved and get the value of β. If the value near to zero is obtained for β, it means agent is impatient anda value near to one signifies that agent is patient.

This argument is further supported by the marginal rate of substitution strategy where = R. If β=0, no results obtained as the agent would like to take immediately. If β=1, profits will effect for the patient agent. Hence, it implies that the discount factor β won't change the basic results of the model.

(b) Jot down the conditions that characterise the Pareto-optimal allocation. Show that autarky is not successful. Explain how the allocation changes with β.

The conditions that characterise the allocation in autarky are bounded by the constraints of C1 and C2.

π1C1 = 1 - I => C1 =

(1-π)C2= RI => C2 =

The constraints can be mixed in one one.

π1C1 + (1-π)= 1

The key effect is the fact that allocation is inefficient in autarky as shown below

Recall in autarky: C1 = 1 - I + ÉI = 1 - I (1-É)

C2 = 1 - I + RI = 1 + I(R-1)

If C1 < 1 (unless I = 0) and C2 < R (unless I = 1), then merging these two facts we obtain

π1C1 + π2 < 1 which states that efficiency is not come to. It really is true as less overall and fewer resources can be found in an autarky than in Pareto optimal allocation as no trade occurs. Therefore, usage level is leaner in autarky.

Max U(C1, C2) = u(C1) + βu(C2) = + β

We create the lagrangian solution to make clear the allocation changes in β where in fact the constraint in the below formula is the utmost utility.

L = πu(C1) + (1-π)βu(C2) + λ[ + β ]

= π + λ = 0

= (1- π)β + λ β = 0

= + β = 0

Complementary Slackness Condition: λ*[ + β ] = 0

If values received for the variables, we could have even resolved and get the worthiness of β. If a value near zero is obtained for β, it means agent is impatient anda value close to one implies that agent is patient.

The debate of marginal rate of substitution is also relevant here where = R. If β=0, no comes back obtained as the agent wants to consume immediately. If β=1, returns will direct result for the patient agent. Hence, it implies that the discount factor β will not change the basic results of the model.

(c) Presume the agents are actually infinitely risk-averse. That is U(c1, c2) = minc1, c2. What is the Pareto-optimal allocation?

Pareto optimal can be an allocation of resources where it is impossible to deliver resources without making at least one consumer most detrimental off. Pareto optimal is the better outcome that can result in an current economic climate with trade occurring and thus there is higher intake level. It is like a desired point out where belongings are increased for patient people and intake is increased for impatient people.

The Pareto optimal allocation for risk natural agents satisfies the following first order condition

Uʹ(C1) / Uʹ(C2) = R

which means that real estate agents wish to equate the marginal rate of substitution between consumption levels at t=1 and t=2 with the results on the long run technology.

When U(c1, c2) = min[c1, c2], it shows agents' attitude to associated risk aversion.

The pareto optimal allocation for the chance averse agent is u(C1) + πβu(C2G) + (1-π)βu(C2B) where the superscripts G and B denote good and bad talk about respectively.

L = u(C1) + πβu(C2G) + (1-π)βu(C2B) + λ[u(C1)]

The concaved electricity function says that agents favor to take more to less and shows how utilization is smoothed out over time and across state governments in the foreseeable future. The agent is risk averse in the sense that he will not want intake in the bad state at t=2 to be too much not the same as use at t=1.

Question 2

(a) Write down the incentive constraint of the lender. How does guarantee aïect the repayment R the bank can assure?

Banks, thought to be information sharing coalitions, may easily overcome the problem of asymmetric information of traders. It is assumed that banks use the signaling tool to purchase high quality projects which will advantage the investors. Finance institutions are anticipated to behave so that will maximise shareholders' interest.

The firm chooses the good job if

pH(y-Ru-Rm) > pL(y-Ru-Rm) + b => Ru + Rm < y-

The bank must also be motivated to keep an eye on the job

pHRm- C > pLRm => Rm >

The bank or investment company will acquire only least possible amount from banking institutions as bank fund is more costly than direct funding.

Im = Im (β) ≡ = where β denotes expected rate of go back.

The loan provider will acquire get the rest of the fund Iu = from uninformed traders. Hence, the bank's motivation constraint binds.

Using the incentive constraints we've: Ru < y- which claims: Iu < [y - ] indicating that the task is only going to be financed if

A + Iu + Im > 1 => A > (β, r) ≡ 1 - Im(β) - [y - ]

Other constraints would include a insufficient monitoring from the lender giving rise to the probability of non-monitoring pL and the shortcoming to dispose the guarantee, ie if the security appreciates, the bank will not be able to sell it until loan to buyers has been repaid.

The guarantee, usually by means of assets, plays the role of a guarantee that banks give to traders as a security in case of inability of the task. Collateral is also viewed as an alternative solution to monitoring as it helps you to save initiatives and reduces the risk of the lender. Ï ∈ (0, 1) can be interpreted as though K is near to one, bank can refund the money to shareholders whereas if K is near to zero, loan company will be unable to repay again the loan.

A better guarantee equals better chance of getting cash back as the lender will want to behave if not it will lose the collateral.

If the project is successful with expected possibility p, the bank will gain dividends X which will be used to refund the loan to traders and claim back again the collateral. The higher the results from the task, the bank will be able to distribute partly between the investors and keep partially as its profits.

In case of failure of the job, the lender will obtain zero comes back and is then struggling to repay R to the traders. The latter will seize the guarantee and will liquidate it to gain maximum money from it as refund with their investment in the unsuccessful project.

(b) Suppose traders have all the bargaining ability. Write down their aim, find the perfect deal and their equilibrium revenue.

If shareholders have all the bargaining electricity, they will be able to influence the project funding process significantly and dictate their terms. The objective of investors is to acquire maximum returns X from the task. They will want to have full information regarding the project to ensure that the bank is choosing a high quality project (θ) rather than making a detrimental selection. Traders delegate the monitoring of the task to the lender as the latter has comparative gain in monitoring activities hence monitoring costs will be reduced. Shareholders will use monitoring and auditing as tools to be free from asymmetric information and improve efficiency. They'll expect close monitoring and constant opinions on the task from the lender.

The optimal agreement for buyers will be where financing will be most profitable and the below formula is taken from the Gemstone Model (1984)

E[y] > 1 + r + C = E[y] > 1 + 1 + C = E[y] > 2+ C

where E[y] = Dividends from investment

r = risk free rate, equal to 1 in the question

C = monitoring costs

The optimal agreement is bounded by the break-even constraint of uninformed shareholders implying an higher bound on Iu

pHRu > (1 + r) => Iu < < [y - ]

Equilibrium earnings of the shareholders will be at a possible break-even point, usually where demand equals to provide

A + Iu + Im > 1 => A > (β, r) ≡ 1 - Im(β) - [y - ]

(c) For which value of K can the bank borrow and invest?

The value of the collateral must be either similar or slightly higher than the investment in task (I) and monitoring costs (C) to encourage investors to funding the task as a lesser value of the collateral will not draw in them.

K = I + C or K > I + C

Ideally if K > I + C, this will draw in more investors to finance the job and subsequently banks will be able to borrow from them and invest in the project.

Question 3

(a) WHEN A ≥ A3, the strong issues high-quality general public debt (open public debt that has a high probability to be re-paid)

We will discuss circumstances when the business owner can issue high quality general public debt
  • Well-capitalised companies [A > ] can issue direct debt as they own high capital.
  • Low credit risk - Top quality public debt pertains that the businessperson will probably meet payment obligations. This type of public debt can be an attractive investment vehicle as it offers a low threat of default.
  • High dilution costs
  • Good reputed businesses can issue direct debt only when πs > where πs 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 small in a way that in the credit market at equilibrium. The businessperson has motivation to issue high quality open public debt at a level of when as the latter equation means big probability of success. The economic interpretation is when project is successful, results (R) are obtained. The businessman cannot ask for more than R as the organization will also keep some revenue for itself. Every get together in the transaction is happy which is in equilibrium whenever a good project is performed.

(b) If A3 > A ≥ A2, the firm borrows from a keep an eye on (and from uninformed traders)

We will analyse circumstances when the organization borrows from a monitor and uninformed buyers
  • Firms with medium capital [(β, r) < A < ] borrow from banks.
  • Firms acquire from bankers when they have problems with high credit risk and high dilution costs because lenders can provide effective renegotiation in case there is default and can limit dilution costs though you will see an intermediation cost involved.
  • Uninformed investors will be ready to invest Iu in trade of go back Ru upon successful project. Businesses must be urged to choose good job pH(y - Ru) > pL (y- Ru) + B <==> Ru < y -
  • When the firm falls lacking capital to concern a direct arrears, it can acquire Im from banking institutions (with return Rm if task succeeds) and Iu from uninformed traders (with come back Ru if task succeeds).

The firm decides the good task if

pH(y-Ru-Rm) > pL(y-Ru-Rm) + b => Ru + Rm < y-

The bank must be urged to keep an eye on the job

pHRm- C > pLRm => Rm >

The bank or investment company will acquire only least possible amount from finance institutions as bank money is more costly than direct financing.

Im = Im (β) ≡ = where β denotes expected rate of go back.

The standard bank will accumulate get the rest of the financing Iu = from uninformed investors

Hence, the bank's motivation constraint binds.

  • Two conditions are essential for bank financing to maintain equilibrium in credit market:

(i) Monitoring cost must be less than the results of the good project

pH G - 1 > c

(ii) Direct financing which is cheaper must be impossible.

pHRc < 1

Firm should borrow from a monitor (for example a bank or investment company) and from uninformed traders at intermediate probability of success when pH ] at a level of R =.

(c) If A2 > A ≥ A1, the company issues junk bonds (open public debt which has a low possibility of success)

We will discuss circumstances when the firm issues junk bonds
  • It can be done that organizations with medium capital [(β, r) < A < ] concern junk bonds.
  • High credit risk- Junk bonds refer to bonds with low credit quality and high default risk. They are simply attractive to associated risk seeker investors due to their high yielding comes back.
  • Low dilution costs as it limits contact with bad organizations but entails inefficient bankruptcy charges for good firms.
  • The zero earnings condition for buyers is:

1 = pR + (1- p) A

This nominal come back R is possible (R < y) if py + (1- p) A > 1 and the expected profit of good businesses is then

πB = p (y- R)+ py

By substituting R, we will obtain: πB = 2py - 1 + (1- p) A

  • When the monitoring element c is added, the keep an eye on can reduce the entrepreneur's private benefit of misbehaving from B to b.

pH > c >(pH −pL) R−pH

If R > Rc, the firm will issue rubbish bonds with low possibility of success. This areas that the organization is indebted and have too much risk associated with it. The financial interpretation out of it would be that the entrepreneur will require higher returns however the firm won't manage to provide it. This will likely lead the business owner to choose the bad job and disequilibrium occurs. Hence, such a combo is not feasible because the maximum repayment is K.

(d) If A1 > A, the company will not invest

We will analyse circumstances when the company cannot invest
  • Firms with low capital [A < (β, r)] can neither invest nor borrow. Venture capitalists will be the only solution for such firms.
  • When monitoring costs are added, if pH < this means there is a little possibility of success. The equilibrium includes no trade occurring and the credit market collapses because good assignments can't be funded and bad tasks have a negative net present value. Hence, the organization should not invest as there is absolutely no trade equilibrium.


Frexias X. and Rochet J-C. , (2006) Microeconomics of Banking, 2nd Edition

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