Calculate the natural rate of unemployment

Reference no: EM131195594

Problem 1: Consider the following equations that describe the labor market:

- (The PS equation) P = (1 + µ)W where P , W , and µ are the price level, nominal wage, and the firms's markup over costs, respectively.

- (The WS equation) W = P^e(b - u), where P^e, b and u are the expected price level, unemployment benefits, and the unemployment rate, respectively.

(1) Suppose that P = P^e, the markup of prices over costs is 0.1, and the amount of unem- ployment benefits is 1 (b = 1).

(i) Calculate the real wage as determined by the price-setting equation.

(ii) Calculate the natural rate of unemployment?

(2) Suppose that P = P^e, the markup of prices over costs is 0.1, but the amount of unem- ployment benefits increases to 1.1 (b = 1.1). Calculate the new level of the natural rate of unemployment associated with this higher level of unemployment benefits.

Problem 2: The AS relation in year t is given as P_t = P_t^e(0.8 + Y_t/1000) where P_t, P_e, and Y_tare the price level in year t, the expected price level in year t and the output level in year t, respectively. The AD relation in year t is given by Y_t = 1300 - 1000Pt. Suppose that 2007 = 1.

(1) Using this information, calculate the natural level of output Yn (Hint: To get Y_n, you have to use the condition that P_t = P_e.)

(2) Draw the AS relation in 2007. Clearly indicate the value of Yn and the value of P_e in your diagram.

(3) Carefully add the AD relation to your diagram.

(4) Find the short-run equilibrium level of output in 2007 (Y₂₀₀₇). What is the corresponding level of price in 2007 (P^e₂₀₀₇)? Clearly indicate the values of Y₂₀₀₇ and P₂₀₀₇ in the diagram you drew in (2).

(5) Is P2007 higher or lower than P^e₂₀₀₇? Assuming that P^e_(t+1) = P_t, what will the expected price level in 2008 be? Briefly explain.

(6) Add the AS relation in 2008 to the diagram.

(7) Illustrate the MR equilibrium and indicate the medium-run level of price as P_MR. Then calculate PMR.

Problem 3 Start by drawing a typical AS/AD diagram. Suppose that the economy is initially in a medium run equilibrium. In your diagram, clearly label the natural level of output "Y_n", the initial level of actual output "Y₀" and the expected price level "P₀^e".

(1) Illustrate the short-run effects of a tax cut on the AD and AS curves in your diagram. What effects will the tax cut have on output and price in the short run? Label the short-run level of output "Y₁" and the short-run level of price "P₁" in your diagram.

(2) Illustrate the new medium run equilibrium which will result from the tax policy in your diagram. What effects will the tax cut have on output and price in the medium run? Label the new medium run equilibrium level of price "PMR" in your diagram.

(3) In the short run, will consumption increase or decrease? In the new medium run equilibrium, will the level of consumption be higher or lower than that at the initial medium run equilibrium? Explain your answers.

(4) In the short run, will investment increase or decrease? In the new medium run equilib- rium, will the level of investment be higher or lower than that at the initial medium run equilibrium? Explain your answers.

Problem 4 Answer the questions based on the diagram provided below. Please reproduce it in your paper and add any new curve(s) according to the instructions in the following questions.

(1) Suppose that the U.S. economy is initially experiencing a trade deficit. Carefully draw a NX line that describes this situation.

(2) Further assume that government officials would like to eliminate the trade deficit and adjusting tt is the only option they can use. Should they increase or decrease tt to eliminate the trade deficit? What effect would this policy have on output? Illustrate your answers in the diagram provided below.

Problem 5 Consider the following model.

C = 100 + 0.6(Y - T ) (consumption)

I = 80 (investment)

G = 130 (government spending)

T = 100 (taxes)

X = 0.1Y* - 50∈ (exports)

IM/∈ = 0.1Y + 50∈ + 50 (imports)

Y* = 3000 (foreign income)

∈ = 2 (real exchange rate)

(1) Solve for equilibrium real output Find the equilibrium value of NX. Is this economy running a trade deficit or surplus?

Let us consider four separate scenarios described by (2)-(5) below.

(2) Suppose that government wants neither trade deficit nor trade surplus and the only policy tool to achieve this goal is to adjust its spending tt. Should it increase or decrease its spending tt? What value of tt should the government choose?

(3) Suppose that the economy needs Y = 800 in order to achieve full employment, the government wants to accomplish this full employment level of output and the only policy tool to achieve this goal is to adjust its spending tt. Should it increase or decrease its spending tt? What value of tt should the government choose? If it pursues this policy, what would be the level of net exports?

(4) Suppose that the level of foreign income increased from 3000 to 4000. Solve for equilib- rium real output and the equilibrium value of NX. output and the equilibrium value of NX.

Reference no: EM131195594

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