1)   a. (5) Briefly describe the “tit-for-tat” strategy? Suppose two players play the    prisoners’ dilemma game a finite number of times, both players are rational, and the game is played with complete information, is a tit-for-tat strategy optimal in this case? Explain using your own words.

A player following a tit-for-tat strategy will cooperate as long as his or her           opponent is cooperating and will switch to a noncooperative action ifthe             opponent stops cooperating. Since cooperation will unravel from the last period  back to the first period, the tit-for-tat strategy is not optimal when there is a finite number of periods and both players anticipate the competitor’s response in every period. Given that there is no response possible in the period after the last period for action in the last period, cooperation breaks down in the last period. Then,     knowing that there is no cooperation in the last period, players should maximize their self-interest by not cooperating in the second-to-last period, and so on back to the first period. This unraveling occurs because both players assume that the    other player has considered all consequences in all periods.

b. (5) Using your own words, explain the backward bending labor supply curve?

A backward-bending supply curve for labor may occur when the income effect of an increase in the wage rate dominates the substitution effect. Individuals make    labor supply decisions by choosing the most satisfying combination of income      (with which to consume goods and services) and leisure. With a larger wage, the  individual can afford to work fewer hours: the income effect. But as the wage rate increases, the value of leisure time (the opportunity cost of leisure) increases, thus inducing the individual to consume less leisure and work longer hours: the            substitution effect. Because the two effects work in opposite directions, the labor  supply curve is backward bending if the income effect triggered by a higher wage is greater than the substitution effect of the higher wage.

c. (5) Using your own words, explain the production contract curve. What is the relationship between the production contract curve and the production                possibilities frontier? Explain using your own words.

When constructing an Edgeworth box for the production of two goods with two  inputs, each point in the box represents an allocation of the two inputs between    the two production processes. With production, each point can be ordered            according to the total output. These points lie on isoquants instead of on               indifference curves. Since each point simultaneously represents the allocation of inputs to two production processes, it lies on two isoquants, one for each              production process. The production contract curve represents all combinations of inputs that are technically efficient. Thus there would be no way to increase the   output of one good without decreasing the output of the other good.

We can graph the quantities of each good produced (each point in the Edgeworth box) on a graph, where the vertical axis represents the output of one good and the horizontal axis represents the output of the other good. The production contract    curve is represented in this graph as the production possibilities frontier. It is        analogous to the utility possibilities frontier for consumers. Points inside the        frontier are feasible but inefficient; points outside the frontier are infeasible and   attainable only when more inputs become available or technological change         increases productivity. Points on the production possibilities frontier are the same as those on the production contract curve. The difference is that the production    contract curve measures inputs on the axes and the production possibilities           frontier measures outputs on the axes.

d. (5) You graduate from UCI with a 3.8 GPA. Is your GPA a strong signal to future employers that you will be a productive worker? Explain why or           why not?

Yes, for the most part a high grade point average is a strong signal to the               employer that the employee will perform at an above-average level. Regardless of what he actually learned, it indicates that you are able to outperform the majority  of students. On the other hand, you could have padded your schedule with easy     classes, and/or classes taught by easy professors.

2. Suppose an economy is given by the following equations:

C = 150 + 0.25Yd

I = 150 +0.25Y − 1000i

G = 250

T = 200

(M/P) = 1400

Y L(i) = 2Y − 8000i

Yn (Natural level of output) = 1200

Using the above information, answer the following.

(a) (5) Derive the IS and LM equations.

(b) (5) Find equilibrium Y and equilibrium i. Is the economy in a recession or a boom?

a. Y=C+I+G=150+.25(Y-200)+150+.25Y- 1000i+250

Y=1000-2000i

M/P=1400=2Y-8000i

i=Y/4000- 1400/8000

b. Substituting from part (a) gives Y=900, i=5%, C=325; I=325; G=250; C+I+G=900 . The economy is in a recession.

C = 500 + 0.75 (Y-T)

I = 1000 - 50r

M/P = Y-200r

G = 1000

T = 1000

M = 6000

P =2

a. (5) Derive the IS and the LM equations. Calculate the equilibrium interest rate and level of income.

b. (5) Suppose that taxes are cut by 20% and the money supply is held constant. What are the new equilibrium interest rate and level of income?

c. (5) Now suppose that the Federal Reserve changes the money supply to hold the interest rate constant. What is the new level of income? What must the new money supply be?

d. (5) Now suppose that the Federal Reserve changes money supply to hold the level of   income constant. What is the new equilibrium interest rate? What must the money supply be?

The IS curve is given by:

Y = C(Y – T) + I(r) + G.

We can plug in the consumption and investment functions and values for G and T as given in the question and then rearrange to solve for the IS curve for this economy:  Y = 500 + 0.75(Y – 1,000) + 1,000 – 50r + 1,000

Y – 0.75Y = 1,750 – 50r

(1 – 0.75)Y = 1,750 – 50r

Y = (1/0.25) (1,750 – 50r)

Y = 7,000 – 200r.

The LM curve is determined by equating the demand for and supply of real money balances. The

supply of real balances is 6,000/2 = 3,000. Setting this equal to money demand, we find: 3,000 = Y – 200r.

Y = 3,000 + 200r.

Equating the IS and LM equations, we can solve for r:

7,000 – 200r = 3,000 + 200r

4,000 = 400r

r = 10.

Now that we know r, we can solve for Y by substituting it into either the IS or the LM equation.

We find:

Y = 5,000.

Therefore, the equilibrium interest rate is 10 percent and the equilibrium level of output is 5,000.

b. If taxes fall by 20% then taxes are now equal to 800 and we can recalculate the IS curve equation:

Y = 500 + 0.75(Y – 800) + 1,000 – 50r + 1,000

Y – 0.75Y = 1,900 – 50r

(1 – 0.75)Y = 1,900 – 50r

Y = (1/0.25) (1,900 – 50r)

Y = 7,600 – 200r.

Equating the new IS and old LM equations, we can solve for r:

7,600 – 200r = 3,000 + 200r

4,600 = 400r

r = 11.5.

Now that we know r, we can solve for Y by substituting it into either the IS or the LM equation.

We find:

Y = 5,300.

Therefore, the equilibrium interest rate is 11.5 percent and the equilibrium level of output is 5,300.

The decrease in taxes will shift the IS curve to the right. The new equilibrium point is       labeled as point b in Figure 12- 17 in part e below. The tax multiplier measures the change in equilibrium output divided by the change in taxes, or 300/-200 = - 1.5.

c. To find the value of the money supply that will keep the interest rate at the original     level of 10 percent after the tax cut, rewrite the LM curve equation so that it is a function of M:

M/2 = Y – 200r

Y = M/2 + 200r.

Now we can equate this new equation for the LM curve with the new IS curve, plug in the value of

10 for the interest rate r and solve for the money supply M:

7,600 – 200r = M/2 + 200r

7,600 – 200(10) = M/2 + 200(10)

M = 7,200.

If the money supply has a value of 7,200 then the level of output is 5,600. The increase in the money supply will shift the LM curve to the right.

d. To find the value of the money supply that will keep output at the original level of  5,000 after the tax cut, rewrite the LM curve equation so that it is a function of M, and solve for r:

M/2 = Y – 200r

200r = Y – M/2

r = Y/200 – M/400.

Rewrite the IS curve equation so that r is defined as a function of Y:

Y = 7,600 – 200r

200r = 7,600 – Y

r = 7,600/200 – Y/200.

Now we can equate these new equations for the IS and LM curves, plug in the value of 5,000 for the level of output Y and solve for the money supply M:

7,600/200 – Y/200 = Y/200 – M/400

7,600 – Y = Y – M/2

Common land is likely to be overgrazed since each individual will consider only their     own private cost and not the total social cost of grazing. The social cost of grazing is       likely to be higher than any one individual’s private cost because no one individual has   an incentive to take into account how his grazing affects the opportunities of others. As a result, conservation efforts by individuals are pointless.

For example, one individual could decide to graze only in certain areas during certain      times of the year, while preserving other areas for other times of the year. However, the   individual will not do this if the resource is common property as any other grazer can       come along and freely disrupt the preservation system that the individual has set up.         Selling annual permits may help, but an annual permit will exclude only those grazers     whose total benefits are less than the price of the permit. Anyone who buys the permit     will still have the same incentive to overgraze the commons. Selling the land outright is a better solution to the overgrazing problem. If an individual purchases the land she will     then have an incentive to consider all of the costs associated with using the land, and as a result will use it in such a way that the resource is preserved, since she alone captures all of the benefits of preserving the resource. Another possibility would be to charge users    based on the amount of grazing their cows do. If the grazing fee were set correctly, the    efficient amount of grazing could be induced. However, it might be difficult to determine the correct fee, and the village would have to keep track of each resident’s grazing and    bill him or her accordingly.

6)  (20) A small town is studying the proposal to build a new hotel. The impact of the hotel on the surrounding community is both negative and positive.

a.   (5) The hotel will increase traffic which has a cost to the community equal to $5 per hotel guest night. What kind of externality is this? Explain.

b.   (5) The hotel will operate late at night which improves the safety of the            community with an estimated benefit of $2 per hotel guest night. What kind of externality is this? Explain.

c.   (5) Given the market for hotel guest nights in the presence of these two         externalities, is the market equilibrium level of hotel guest nights going to be larger or smaller than the efficient level of hotel guest nights? Explain.

d.   (5) Suggest a government policy that would result in an efficient outcome. Explain.

a. Because there is a cost to the community from the extra traffic, it is a negative consumption externality.

C = 100 + 0.75Yd

I = 125 − 5i

G = 100

T = 100

(M/P) = 50

Y L(i) = 0. 1Y − 2i

Yn = 525                     (Yn is the natural level of output)

Using the above information, answer the following.

(a) (5) Derive the IS and LM curves.

IS: Y = 100+0.75Y-0.75T+125-5i+100,

LM: 50=0. 1Y-2i,

i=50-0.05Y

i=0.05Y-25

C = c0  + c1YD

YD  = Y − T

I = b0  + b1 Y

a.   (2.5) Government spending and taxes are constant. Suppose that consumers  decide to consume less (and therefore to save more) for any given amount of disposable income. Specifically assume that consumer confidence ( c0 ) falls. What will happen to output?

b.   (2.5) As a result of the effect on output you determined in part (a), what will

happen to investment? What will happen to public saving? What will happen to private saving? Explain. What is the effect on consumption?

c.   (2.5) Suppose that consumers had decided to increase consumption expenditure,  so that c0   had increased. What would have been the effect on output, investment, and private saving in this case? Explain. What would have been the effect on       consumption?

d.   (2.5) Comment on the following logic: “when output is too low, what is needed is an increase in demand for goods and services. Investment is one component of    demand, and saving equals investment. Therefore if the government could just     convince households to attempt to save more then investment, and output, would increase.

a

b

9)  (10 pts) Suppose the economy begins with output equal to its natural level. Then there is a decrease in consumer confidence, as households attempt to increase     their saving, for a given level of disposable income. What happens to output and the interest rate in the short run? What happens to consumption, investment, and private saving in the short run? Is it possible that the decline in consumer            confidence will actually lead to a fall in private saving in the short run?

10) (10) The room for policy to help output return to its natural level is limited in two ways: Monetary policy is limited by the presence of a liquidity trap. Fiscal policy is limited by the presence of a high level of public debt. Explain.

11) (10) The demand for labor by an industry is given buy the curve L = 1200-   10w, where L is the labor demanded per day and w is the wage rate. The supply curve is given by L = 20w.

a. (5) What is the wage rate and quantity of labor hired?

b. (5) What is the economic rent earned by workers?

a.   By setting the quantity of labor supplied to the quantity of labor demanded we   find the wage rate is equal to $40 and the quantity of labor hired is equal to 800.

b.   Economic rent earned by workers is the area above the supply curve below the wage rate. Economic rent is 0.5*40*800 = 16,000.

12) (10) Suppose that there are two types of drivers: reckless and safe. Reckless         drivers have a higher probability of accidents with an expected loss to the             insurance company of $5000. Safe drivers have a lower probability of accidents   with an expected loss to the insurance company of $1000. Insurer cannot              distinguish between reckless and safe drivers but know that reckless drivers make up “β” proportion of all drivers. What single premium should the risk-neutral       insurer charge? Assume that the insurance market is perfectly competitive. Is the above mentioned problem an example of Adverse Selection or Moral Hazard?      Explain.

If the insurance market is perfectly competitive, the insurance premium will be driven down to where the expected profits are zero.

Insurer is overcharging safe drivers to cover the losses from reckless drivers. If insurance is not required then safe drivers would not want to get it.

The above mentioned problem is an example of Adverse Selection. Adverse Selection is  a form of market failure resulting when products of different qualities are sold at a single price because of asymmetric information, so that too much of the low-quality product and too little of the high-quality product are sold.

13) (15) Defendo has decided to introduce a revolutionary video game. As the      first firm in the market, it will have a monopoly position for at least some      time. In deciding what type of manufacturing plant to build, it has the choice of two technologies. Technology A is publicly available and will result in        annual costs of

CA(q) = 10 + 8q

Technology B is a proprietary technology developed in Defendo’s research labs. It involves a higher fixed cost of production but lower marginal costs:

CB(q) = 60 + 2q

Defendo must decide which technology to adopt. Market demand for the new product is

P = 20 − Q, where Q is total industry output.

a.   (5) Suppose Defendo were certain that it would maintain its monopoly  position in the market for the entire product lifespan (about five years) without threat of entry. Which technology would you advise Defendo to adopt? What would be Defendo’s profit given this choice?

Defendo has two choices: Technology A with a marginal cost of 8 and               Technology B with a marginal cost of 2. Given the inverse demand curve is P = 20 − Q, total revenue, PQ, is equal to 20Q − Q2 for both technologies. Marginal revenue is 20 − 2Q. To determine the profits for each technology, equate           marginal revenue and marginal cost:

20 − 2QA = 8, or QA = 6,  and

20 − 2QB = 2, or QB = 9.

Substituting the profit-maximizing quantities into the demand equation to determine the profit-maximizing prices, we find:

PA = 20 − 6 = $14, and

PB = 20 − 9 = $11.

To determine the profits for each technology, subtract total cost from total revenue:

A = (14)(6) − (10 + (8)(6)) = $26, and

B = (11)(9) − (60 + (2)(9)) = $21.

To maximize profits, Defendo should choose Technology A, the publicly available option.

b.   (7.5) Suppose Defendo expects its archrival, Offendo, to consider entering the        market shortly after Defendo introduces its new product. Offendo will have access only to Technology A.

If Offendo does enter the market, the two firms will play a Cournot game (in quantities) and arrive at the Cournot-Nash equilibrium.

i.    (2.5) If Defendo adopts Technology A and Offendo enters the market, what will be the profit of each firm? Would Offendo choose to enter the market given      these profits?

If both firms play Cournot, each will choose its best output, taking the other’s        strategy as given. Letting D = Defendo and O = Offendo, the demand function will be

P = 20 − QD −QO .

Profit for Defendo will be

D  = (20− QD  − QO )QD  − (10+ 8QD ),orD  = 12QD  − QD(2)  − QDQO  −10

To determine the profit-maximizing quantity, set the first derivative of profits with respect to QD equal to zero and solve for QD :

This is Defendo’s reaction function. Because both firms use the same technology, Offendo’s reaction function is analogous:

QO = 6 − 0.5QD .

Substituting Offendo’s reaction function into Defendo’s reaction function and solving for QD :

QD = 6 − (0.5)(6 − 0.5QD), or QD = 4.

Substituting into Defendo’s reaction function and solving for QO :

QO = 6 − (0.5)(4) = 4.

Total industry output is therefore 8 video games. To determine price, substitute QD and QO into the demand function:

P = 20 − 4 − 4 = $12.

The profits for each firm are equal to total revenue minus total costs:

D = (12)(4) − (10 + (8)(4)) = $6, and

O = (12)(4) − (10 + (8)(4)) = $6.

Therefore, Offendo would enter the market because it would make positive economic profits.

ii.    (2.5) If Defendo adopts Technology B and Offendo enters the market,  what will be the profit of each firm? Would Offendo choose to enter the market given these profits?

Profit for Defendo will be

D  = (20− QD  − QO )QD  − (60+ 2QD ),orD  = 18QD  − QD(2)  − QDQO  − 60.

The change in profit with respect to QD is

To determine the profit-maximizing quantity, set this derivative to zero and solve for QD :

18 − 2QD − QO = 0, or QD = 9 − 0.5QO .

This is Defendo’s reaction function. Substituting Offendo’s reaction function (from part i above) into Defendo’s reaction function and solving for QD :

QD = 9 − 0.5(6 − 0.5QD), or QD = 8.

Substituting QD into Offendo’s reaction function yields

QO = 6 − (0.5)(8), or QO = 2.

To determine the industry price, substitute the profit-maximizing quantities for Defendo and Offendo into the demand function:

P = 20 − 8 − 2 = $10.

The profit for each firm is equal to total revenue minus total cost, or: D = (10)(8) − (60 + (2)(8)) = $4, and

O = (10)(2) − (10 + (8)(2)) = −$6.

With negative profit, Offendo would not enter the industry.

iii.  (2.5) Which technology would you advise Defendo to adopt given the threat of possible entry? What will be Defendo’s profit given this      choice? What will be consumer surplus given this choice?

With Technology A and Offendo’s entry, Defendo’s profit would be $6. With Technology B and no entry by Offendo, Defendo’s profit would be $4. I        would advise Defendo to stick with Technology A and let Offendo enter the   market. Under this advice, total output is 8 and price is $12. Consumer           surplus is

(0.5)(8)(20 − 12) = $32.

c.   (2.5) What happens to social welfare (the sum of consumer surplus and producer profit) as a result of the threat of entry in this market? What happens to equilibrium price? What might this imply about the role of potential competition in limiting market power?

From part a we know that, under monopoly, Q = 6, P = $14, and profit is $26. Consumer

surplus is

(0.5)(6)(20 − 14) = $18.

Social welfare is defined here as the sum of consumer surplus plus profits, or $18 + 26 = $44.

With entry, Q = 8, P = $12, and profits sum to $12. Consumer surplus is

(0.5)(8)(20 − 12) = $32.

Social welfare is $44 – equal to $32 (consumer surplus) plus $12 (industry profit).  Social welfare does not change with entry, but entry shifts surplus from producers to