Long Question 1: Animal Spirits [26 pts.] Consider the following quote on investment from The General Theory of Employment, Interest and Money, the seminal book written by John Maynard Keynes

Long Question 1: Animal Spirits [26 pts.] Consider the following quote on investment from The General Theory of Employment, Interest and Money, the seminal book written by John Maynard Keynes in 1936: “[…] most […] of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits – of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities. Enterprise only pretends to itself to be mainly actuated by the statements in its own prospectus, however candid and sincere […] if the animal spirits are dimmed and the spontaneous optimism falters, leaving us to depend on nothing but a mathematical expectation, enterprise will fade and die […].” For the purpose of this test, we assume that what Keynes meant by “animal spirits” was really “business confidence”. This implies that investment I does not only depend on interest rate and income, but on “business confidence” as well. In light of this fact: 1. How does this affect the shape of aggregate demand? Starting from the investment curve and moving to the IS-LM model, graphically derive both an optimistic AD (i.e. an AD curve which embeds high business confidence) as well as a pessimistic AD (i.e. an AD curve which embeds low business confidence). [13 pts.] 2. If animal spirits (business confidence) do indeed play a role in the economy, what does their presence imply about the potential tools policymakers have at their disposal for affecting output in the short run? Apart from monetary and fiscal policy, suggest a new type of policy that could be used for increasing or decreasing output in the short run (be specific in how the policy would affect output). [13 pts.] Long Question 2: Fire at Will [46 pts.] 1. Starting from the wage setting relation and the price setting relation, derive an expression for aggregate supply. Make sure you clearly explain each steps in the derivation. [11 pts.] Italy’s Prime Minister, Mr. Mario Monti, has presented to the Italian parliament a proposal to change labor laws. The Italian government claims that the new measures would “create a dynamic, flexible and inclusive labor market, one able to […] create good working conditions […]”. We interpret these proposals as a decrease in firing and hiring costs, i.e. a decrease in the variable z, the parameter in the wage setting relation. 2. Using the wage setting relation and the price setting relation you derived in part 1, predict what will happen to the unemployment rate in the medium run un if these labor proposals are approved by parliament. [6pts.] 3. How will the change predicted in part 2 affect the AS-AD equilibrium? Show using the AS/AD graph. Let E be the initial medium rum equilibrium. Let the first short-run equilibrium the economy transitions to be labeled as E” and the new medium run equilibrium as E””. [6 pts.] We now assume that these new labor market measures do pass in Italy’s parliament. We also assume that Italy has complete monetary autonomy, and that the objective of the central bank is to maintain a constant price level, P = PE (note that this is equivalent to a zero inflation target). 4. kind of monetary policy should the Bank of Italy choose to achieve its goal? Explain your answer, describe the mechanics through which the economy goes from the initial medium run equilibrium to the new one and use an AS/AD graph to trace the effect of the appropriate monetary policy on the medium run equilibrium. [6pts.] 5. Assume that the Italian economy is characterised by the following dynamics: ut − ut−1 = − (gy,t − 3%) 3 2 πt − πt−1 = − (ut − 5%) 3 gy,t = gm,t − πt where ut is the unemployment rate at time t, gy,t is the output growth rate at time t and gm,t the nominal money supply growth rate at time t. Further assume that the length of the transition to the new medium run equilibrium is 1 year, and the absolute value of the change in unemployment needed to implement the Bank of Italy’s objective is |Δut| = 1% (note that this means 100 basis points, not 1% of 5%!). should the nominal money growth rate gm,t be to achieve a constant price level (i.e. zero inflation)? Show your calculations. [11 pts.] 6. Italian GDP in 2011 was 2.3 trillion dollars. By how much is output (measured in dollars) going to change after the central bank has implemented its policy? Is Italian tax revenue going to increase or decrease after these measures are implemented? By how much? Assume that the aggregate tax rate is 30%. [6 pts.] (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
gallon gasoline shot espresso
31 4076
British Literature – fcSU18-DCISP2783 v
Calculus – fcFA19-DCISP2797
Introduction to Differential Equations and Euler’s Meth
est Questions
of 1 –
Question 4 of 10
10 Points
Use Euler’s method to find the approximate solution. Find y(2) when
y’ = 1 – y, y(0) = 0, and n = 4.
A. 0.9375
OB. 15
OC. 7.5
OD. 4.0625
Reset Selection
MacBook Air Use Differentials to approximate v/ 99.5
Round your anwer to 2 decimal places.
Turn in calculus work for this problem at the end of the test Instructions. This is an open-book exam. You can use the results in the notes and the answers to the
problem sets without proof, but you need to invoke them explicitly. You have 80 minutes. Each question is
25 points. Good Luck!
1. Ann is an expected utility maximizer. She is to submit a bid b in an auction to buy an object. The
resulting price for the object is p, which is uniformly distributed on 0, 1), independent of &. Ann gets
the object at price p if the price turns out to be less than or equal to b. The value of the object for
Ann is e e [0. 1). Ann does not know , but by expending effort c 2 0 she can obtain an estimate
" for u where Var (0) = c, E = 1/2, and E [ole] = e. The von Neumann and Morgenstern utility
function of Ann is
u (up, b, c) = up- ifb2p
The price p is stochastically independent from a and e.
(a) Compute Ann’s optimal bid as a function of o and c.
(b) Compute the optimal e for Ann.
2. Consider a finite state space S with at least two elements and a set C = [0, 1] of consequences. The
decision maker is risk-neutral and ambiguity averse, i.e.,
f z g = min f (:) > ming (8)
for any two acts f : 5 – C and g : S – C. Which of the postulates Pl and P2 of Savage are satisfied
by >? (Show your work.)
3. For each of the pairs X and Y below, check whether X necessarily stochastically dominates Y’; check
for both first- and second-order dominance. (It suffices to give an example to show that X does not
necessarily dominate V.)
(a) X = (Y + 2) /2 where Y’ and Z are iid.
(b) X = # + 1 and Y = 0 + 62 where 8 ~ N (0, 1), 21 ~ N (1, 1), and 22 ~ N (0, 1).
4. Ann has initial wealth W and an asset X that pays a with probability 1/2 and -r with probability
1/2, where r E [z, a] and W 2 W for some 2. 5, IL with 0 < 1 58 5 W.
(a) Assume that she is an expected utility maximizer with utility function u (2) = VE. Compute the
highest premium P (x, W) she is willing to pay in order to get rid of X. When do we have the
highest "profit margin" P (z, W) /x?
(b) Answer the above question assuming instead that Ann is as in the prospect theory where the
reference point is W, the payoff function for changes is
* (1) =
if y 2 0
-2v-y ify <0,
and the probability weighting function is w (p) = p.
(c) Briefly compare and discuss your findings above. The work for this problem should be uploaded at the end of the exam.
You need to show me the calculus process used to answer the question
4×3 + 2x-7
Find lim,- -co
Round answer to 2 decimal places.

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