A. Consider an economy with a production function given by Y = . The depreciation rate is  = 0.1, the population growth rate is n = 0.02 and the technological growth rate is g = 0.03. The economy’s current savings rate is s = 0.3 and the current level of capital per effective worker  = 1. Answer the following questions.

  1. What is the consumption per effective worker in the current year () ?
  2. What is the capital per effective worker in the next period () ?
  3. What is the steady state level of output per effective worker (y*) ?
  4. Find the golden rule level of output per-effective worker () ?
  5. Compare the economy’s savings rate with the golden-rule savings rate. Is the economy saving less ?

B. Consider an economy in which the consumption, investment and production functions are as follows

C = 10 + 0.8(Y – T)

I = 40 – 2.5r

F(K,L) = 

Suppose government spending is 20, taxes equal 25 and the supply of factors is  =  = 125. Answer the following questions.

  1. What is the equilibrium level of real GDP.?
  2. What is the equilibrium real interest rate?
  3. Find the level of national savings. How much of that savings is from the private agents?
  4. Find the level of investment in equilibrium.
  5. Suppose taxes increase to 35. What is its effect on private savings? (Give numerical answer) 
 
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