5. Use an IS-LM graph to show the impact of an increase in the supply of

money (M ) on output. What happens to investment? (5 points)

Long Question 2: A Modification of the Diamond-

Dybvig model (30 points)

Consider the standard version of the Diamond-Dybvig model discussed in class.

A bank has access to two investment technologies. There is a short term

technology which yields 1 in period t = 1 for every unit invested in period t = 0.

There is also a long term technology which yields R > 1 in period t = 2 for

every unit invested. The bank can choose to liquidate its long term investment

in t = 1, in which case it gets L

Each consumer has 1 unit of endowment and the total size of the population

is normalized to 1. In period t = 0 consumers do not know if they will be

impatient or patient. In period t = 1, a fraction 1 ? ? of consumers realise that

they are impatient, which means they only get utility from consuming their

endowment immediately, in $t=1$. A fraction ? of consumers find out that

they are patient, which means that they only enjoy consuming at t = 2. ? ? The bank offers a contract which gives right to withdrawals of size (c1, c )2

in period t = 1 and t = 2 respectively to consumers who in t = 0 deposit their

endowment at the bank.

? ? 1. Assume c1 > 1. What is the maximum amount c2 that a bank could

promise to patient consumers under the assumption that only impatient ? consumers will withdraw c1 at t = 1? (5 p

2. How much should the bank invest in each technology to fulfill its promise ? ? of (c1, c2)? (5 points)

Now we change our assumptions.

We assume that instead of the bank there is a firm which has access to

exactly the same two technologies as the bank. The only difference is that

instead of the deposit contract, for each dollar invested in the firm, the

firm offers a share. A "share" is the right to receive a payment D1 at

t = 1 and D2 at t = 2 independent of whether who owns the share is

patient or impatient. In t = 1, consumers can sell or buy the shares of the

firm, only after receiving D1 and finding out whether they are impatient

or patient.

The sequence of events is as follows:

In t = 0 people give their one unit of endowment to the firm.

In t = 1 the firm pays D1. After D1 has been paid and consumers find

out whether they are patient or impatient, consumers can sell or buy the

shares of the firm.

In t = 2 the firm pays D2 = R(1 ? D1), since we are assuming that the

firm makes zero profit.

3. Let us first assume the price of the shares is such that patient consumers

can buy all of the shares of impatient consumers by giving them their D1 ? dividends. Show that if D1 = (1??)c1 then impatient consumers consume ? ? c1 and patient consumers consume c2. (5 points)

(2.81 - Calculus of Variations) Given y = sin(x) and by = -0.5 + 0.2x2 a. Compare d d d dx (y toy) - dx (y) with dx (by) a. Compare - 3 3 3 (y + dy)dx - ()dx with (Sy)dx 0 0 07. (14 marks). Dr. Poincaire teaches both calculus and introductory differential equations, often to the same (a) (I!) (C) (d) (at students. Passing the calculus course was a prerequisite to taking the differential equations course. Dr. Puincaire was curious as to whether the calculus grade could be used to predict the differential equations grade in some way. He randomly selected 12 former students who had taken both courses from him and created the following table (grades for both course are out of 100). Student I 2 3 4 5 6 7 8 9 ID 1 l 12 Grade in calculus 1' 81 63 T5 33 70 55 67 T4 74 96 89 70 Grade in differential equations 3: 91 75 92 39 75 65 32 TD 72 95 90 61 The following summary shows the sums required to perform linear regression analysis. 293,. = 397 2 y,- = 957 23:: = 68447 Z 3;? = 77795 Zrtyi = 72510 (5 marks). Show explicitly the calculations to nd E, E, S\2. Uncertainty [20 points] An economy has two agents. Bill and Bob. Bill has $110. and Bob has $200. Utility of agents in this economy is characterized by the following function of income: logEy ll} if y s: l g if y 3 iii- U=ulsl={ The minimum level of income possible in this economy is ll. Each agent is about to choose a new business venture. and has a choice between project A and project 13. Neither project requires any investment up front. Project A yields revenues of EU with probability % and revenues of -1C| with probability a Project H yields revenues of 4 with probability onehalf and revenues of 5 with probability onehalf. Throughout this problem. assume that fractional income is possible. [a] [5 points] Which project would each agent choose? Provide intuition for your answer. (i) There is a government election in this society and there are two candidates: a Rawlsian and an Utilitarian government candidates. Claim: In a democratic election (majority win election) a Utilitarian candidate will be elected since more individuals in this society prefer the Utilitarian candidate. (f) (8 points) Jon spends his entire budget on espresso and gasoline. You have the fol- lowing data on his choices: Table 1: Jon's budget Price Price, Gallons Shots Total gallon gasoline shot espresso purchased purchased income February 2 9 22 March 5/2 3/4 10 31 April 3 1/2 8 14 3161 1. Notice that MRC breaks out to the right of the supply curve and is much steeper; this is due to the pricing policy the monopolist can employ. Also the wage and employment levels in the monopsony are much lower than in a competitive labor market. 4. Control of Monopsony: a. minimum wages has been one approach to the control of monopsony. 1. minimum wages under competition "Minimum Wage Pe . . . ..... Qd Qe Qs 2. The minimum wage acts the same as an effectiv 72 / 248 that it creates a surplus of labor -- unemployment. between Qd and Qe is the number of workers who lost jobs, and the distance between Qe and Qs is the number of workers attracted to this market that cannot find employment. 3. Minimum wage opponents argue that the minimum wage does two things that are bad for the economy (and these arguments are based on the competitive model) b. The working poor can very easily become the unemployed poor if the competitive model's predictions are correct. c. Again, the government interferes with the freedom of management to operate its firm -- thereby reducing economic freedom and increasing costs of doing business. 62 1. minimum wages in a monopsony MRC Supply Demand - MRC Quantity of Labor 2. In a monopsony the wage increases with the establishment of a minimum wage, but if the employer is rationale so too does the employment level. 3. If the monopsony model is accurate then the conservative argument does not hold water. Recent research results seem to suggest the monopsony predictions are correct. 5. Unions have also be an effective response to monopsony: a. craft union (exclusive union): 1. AFL Affiliated, organizes one skill class of employees (i.e., IBEW)