National income, gdp, inflation

Document Preview: Econ 304 Summer 2012 Problem Set #2 Due by...

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National income, gdp, inflation
	
Document Preview: Econ 304 Summer 2012 Problem Set #2 Due by 11:59 PM MDT June 22(Note that the points only add up to 49. You get one free point on this assignment)NAME:________________________1. (3 points each)Consider the following Cobb-Douglas Production function: Y=K1/2L1/2=KLa.Compute the value of Y for K = 100 and L = 25b.Define the term constant returns to scale.c.Now show that the production function for this problem has constant returns to scale by completing the following table:KLY=K^(1/2)* L^(1/2)=vKL10025 20050 2,500625 d.Using the original values of K and L (100 and 25), compute the marginal product of labor by calculating how much output would rise if an additional worker were employed. This can be done by substituting L = 26 and K = 100 in the production function and noting the increase in Y.e. If firms had decided to employ 25 workers (L = 25) what would the equilibrium wage be?2. ( 4 points each)Consider an economy described by the following equations:Y = C + I + GY = 5,000G = 1,000T = 1,000C = XXXXXXXXXXY - T)I = 1,000 - 50ra.In this economy, compute private saving, public saving, and national savingb.Find the equilibrium interest ratec.Now suppose that G rises to 1,250. Compute private saving, public saving, and national savingd.Find the new equilibrium interest rate3. ( 3 points each)Suppose that the money demand function takes the form (MP)d=Li,Y=Y/5ia.If output grows at rate g, at what rate will the demand for real balances grow (assuming constant nominal interest rates)?b.What is the velocity of money in this economy?c.If inflation and nominal interest rates are constant, at what rate, if any, will velocity grow?d.How will a permanent (once-and-for-all) increase in the level of interest rates affect the level of velocity? How will it affect the subsequent growth rate of velocity?4. (3 points each)a.What is the inflation tax?b.In what ways is the inflation tax a tax, and in...

Robert · Accepted Answer

Solution 
1) Y = K
1/2
L
1/2
 
a) When K = 100 and L = 25, 
     Y= (100)
1/2
* (25)
1/2 
            
= 10*5 
        = 50 
             b) When all the inputs used in the production process are increased in the same 
proportion and output also increases by the same proportion (as inputs are increased), then it is 
called constant returns to scale. Returns to scale is a long run concept (all inputs are varied). 
Here, in this question, the two inputs used in production are capital and labour. 
           c)
           In the given production function, when both K and L are doubled, Y also doubles. When 
both initial K and L are multiplied by 25, then Y also gets multiplied by 25. Hence, the given 
production function exhibits constant returns to scale. 
        d) When K = 100 and L= 25, Y= 50. 
             When K= 100 and L= 26, Y comes out to be 10* (26)
1/2
 = 50.99 
             Marginal product of labour = (change in Y)/ (change in L)    [note: capital is constant] 
           Here MPL = 50.99-50 
                           = 0.99 
K L 
Y=K^(1/2)* 
L^(1/2)=√KL 
100 25 
 Y= (100)1/2*(25)1/2 = 
50 
200 50  Y= (200*50)1/2 = 100 
2,500 625 
 Y= (2500)1/2*(625)1/2 
= 1250 
e) If the firm decides to employ 25 workers, then the equilibrium real wage will be equal to the 
marginal product of 25
th
 worker. 
When K=100 and L = 24, 
Y is equal to (100)
1/2
(24)
1/2
 or 48.9 
Therefore, MPL of 25
th
 worker= 50-48.9= 1.1 approx 
The equilibrium real wage rate is 1.1approx. And equilibrium nominal wage rate is 1.1* price 
level. Price level is not given here.
2) Y = C + I + G 
Y = 5,000 
G = 1,000 
T = 1,

National income, gdp, inflation Document Preview: Econ 304 Summer 2012 Problem Set #2 Due by 11:59 PM MDT June 22 (Note that the points only add up to 49. You get one free point on this assignment)...

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