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Suppose that there are three states of the world, a, b, and c. The probabilities of the three states are 1 = 0.25, 2 = 0.5, and 3 = 0.25. Let A, B, and C denote the Arrow-Debreu securities that pay $1 in states a, b, and c, respectively. That is, A = (1,0,0), B = (0,1,0) and C = (0,0,1). Let pA = 0.4, pB = 0.5 and pC = 0.2 denote the prices of A, B, and C.

Consider a security X which is worth $2 in state a, $3 in state b, and $1 in state c. If there are liquid markets for A, B, C and X, what is the price of X?

Suppose we are planning power system operations for 4 hours. Demand in the four hours is 350, 480, 460, and 380 MW, respectively. We have a collection of zero-cost variable resources with output of 0, 80, 40, and 0 MW in the four hours. We also have a collection of thermal assets with a cost function f(x) = .05x 2 (e.g., it costs $500 to produce 100 MW for an hour and $2000 to produce 200 MW for an hour). As in Problem 2, we can also curtail load at a cost of $10,000/MWh. Construct a model in Excel describing this system and solve to determine an optimal production schedule for the three resources (variable, thermal, and demand). Since the problem is nonlinear, you will need to choose the GRG Nonlinear solving method rather than Simplex LP.

surplus, borrow, decrease

deficit, borrow, increase

d) As a result of the US shock, Canada - a small country with no shocks - will have a current account __, ___ abroad, and ____ their holdings of the international currency H.

surplus, lend, decrease

deficit, lend, increase

surplus, borrow, decrease

deficit, borrow, increase

e) Now consider the same type of shocks in the gold standard model. Fixed exchange rates are assumed and the US is assumed to be 50% of the world. There are no shocks elsewhere. Presume that the US's Y1 increases by 3% while its Y2 increases by 5%. The result is that the US increases its ___, and runs a current account ___.

next exports, could be either deficit/surplus

net imports, deficit

net imports, neither a deficit or surplus

net exports, surplus

f) Given the above numbers, prices initially change by _ in the US; world prices change by _. Countries other than the US are net _____ of gold.

-2%, -2%, suppliers

-2%, -1%, recipients

2%, 2%, suppliers

2%, 1%, recipients

g) Now suppose the US wished to maintain its prices after the shock - by sterilization. If successful, world prices would change by __ and countries other than the US would ___ more gold than in the original problem. The US gold reserve would ____.

2%, lose, decrease

1%, gain, increase

2%, gain, decrease

0%, lose, increase

h) In a 2-country version of this problem, where US is the 'large' foreign country and Canada is the small domestic economy, the adjustment to the US shock is of the form:

ABA

ABD

ABC

i) If we assumed flexible exchange rates in this setting, the Canadian dollar would __.

appreciate

remain constant

depreciate

Subject: Economics $14.00 Default user avatar

a) Suppose that the US is currently in a balance of payments equilibrium and receives shocks that reduce both Y1 and Y2 by 3%. In the intertemporal model, the US balance of payments moves into ___ and world prices P* ___.

deficit, rise

surplus, rise

does not change, rise

deficit, fall

b) In the gold standard model, two large economies have negative correlation in their business cycles. D sustains a 1% increase in output in Y1, and 2% decrease in Y2. F has the opposite, output decreasing by 2% for Y1, and increasing by 1% for Y2. Under flexible exchange rates, the domestic currency should _____:

appreciate by 6%

appreciate by 3%

depreciate by 6%

depreciate by 2%

Consider the full version of the Solow model with both population growth and technology: Yt = F(Kt,LtEt). We will extend this version of Solow to also explicitly include the government. The national income accounts identity becomes: Yt = Ct + It + Gt where Gt is government spending in period t. In order to fund its spending the government collects a tax Tt. Suppose for simplicity that the government runs a balanced budget Gt = Tt and that the tax collected is a constant fraction of output: Gt = Tt = Yt. The remaining disposable income for households each period is (1 )Yt. As in Solow we still assume that households save/invest a constant fraction s of their (now disposable) income. The population growth rate is n, techonology grows at g, and the depreciation rate is . (a) Assume for now that there is only private and no public investment (i.e all government purchases are spent on consumer goods and none of Gt is used to invest in capital). Write down the standard system - the equations for output, consumption, investment, and the capital accumulation equation. Define: yt = Yt/EtLt,

kt = Kt/EtLt,

it = It/EtLt,

ct = Ct/EtLt,

gt = Gt/EtLt.

(b) Transform the model from part (a) in per- effective worker form and derive the steady-state equation for capital per effective worker. Draw a graph depicting the steady state.

(c) What is the effect of higher tax rate on the steady state? Show the effect on your graph and explain the intuition for your answer.

d) Now suppose that, in addition to the case in part (a), a fraction of Tt is also invested in the capital stock, i.e. public investment equals Tt = Yt. What is total investment equal to now? Similarly to part (b) derive the steady-state equation for capital per worker and depict your answer on a graph.

(e) Show that if is sufficiently high (i.e. you will need to find a specific threshold value), then the steady state capital per effective worker will increase as a result of higher taxation.