Download Economics 304WD -- Homework - Lesson 3 – The Factors of Production, The Labor Market, and and more Exams Economics in PDF only on Docsity!
Name Yash Parikh Date 09/11/2016 last 4 PSU ID _______ Economics 304WD -- Homework - Lesson 3 – The Factors of Production, The Labor Market, and Aggregate Supply -- 130 points (5 points per part)
- The production technology of a firm is given in the table below. Table 1 : Production Technology of a Firm Number of workers Units of output MPN MRPN (P=10) 0 0 0 0 1 35 35 350 2 65 30 300 3 85 20 200 4 100 15 150 5 112 12 120 6 120 8 80 7 125 5 50 a. Define the marginal product of labor and explain how it relates to the production function (with N on horizontal axis and Y on vertical axis). b. Find the marginal product of labor (MPN) for each level of employment (fill in the third column of table above). Marginal Product of labor is essentially the additional output yielded by adding an extra unit of labor. Marginal Product of Labor is the slope of the curve that is drawn with Y on vertical axis and number of labor(N) on horizontal axis
c. Assume that the price of a unit of output is $10. Calculate the MRPN for each worker and add it to the table above. d. Calculate the number of workers that will be hired if the nominal wage rate = $160. Calculate the number of workers the firm will hire if the nominal wage is $110. Calculate the number of workers that the firm will hire if the nominal wage is $80. Please show your work. The equilibrium, Nominal Wage Rate = MRPN W = 160 N = 3 as MPRN is 200 at that but if N= 4, MPRN = 150 which is less than 160 If W = 110 N = 5 as MPRN is 120 at that but if N = 6, MPRN = 80 which is less than 110 If W = 80 N = 6 as MPRN is 80 at that which is equal to Nominal Wage = 80
If W = $160, N =
If W = $110, N =
If W = $80, N =
3 5 6
- Consider an economy with the following characteristics: MPN = 700 − 2 N N s = 22 + 14 w + 3 T where w is the real wage, and T is a lump-sum tax levied on individuals. Suppose that initially T = 32. a) Compute equilibrium values for the real wage and employment. Round your answer to two decimal places At equilibrium, MPN = w w = MPN = 700 – 2N and N = 22+14w + w = 700 – 2(118+14w) w = 700 – 236 – 28w 29w = 464 w = 16 N = (700-16)/2 = 342
w = employment (N) =
b) Illustrate this equilibrium on a labor market diagram. Please be sure you label the diagram completely and label this initial equilibrium point as point A.
w N = 118+14w C D B A w = 816-2N w = 700-2N N
c) Now this economy passes a law and pays a minimum wage equal to $20. Compare the number of people willing to work (label as point B on your diagram) vs. the number of people willing to be hirer (label as point C on your diagram) under this living wage program. Ns^ = 22 + 14(20)+3(32) = 398
of people willing to work w = 20:
20 = 700 – (2N) N = 340
of people willing to be hired w = 20:
d) Compare the number of people willing to work (label as point B) vs. the number of people willing to be hired (label as point C) under this living wage program. What is the value and what do we call this difference? Also, what value represents the number of people who are employed? Difference: It’s called:
of people employed:
58 Unemployment
Suppose now that there is a new marginal product of labor equals MPN = 816 − 2 N. h) List and explain two real-life examples that could cause the MPN to change like this. i) Find the equilibrium ‘market’ clearing wage and level of employment. Please show all work below. w = MPN = 816-2N and N = 118 + 14w w = 816 – 2(118+14w) w = 580 – 28w w = 20 and N = 398
w = employment =
j) Please depict this new development on your original diagram labeling this new equilibrium point as point D in your diagram in part b. Point B and D are the same. k) Intuition: Compare the welfare of the workers under the two scenarios: 1) the living wage program vs. 2) no living wage program but the productivity shock as in part g. In other words, are workers better off in part b) or are they better off in part g)? Be sure to explain.
- An increase in technology could lead to increase in marginal product of labor.
- An increase in vaccination program to cure diseases could lead to increase in marginal product of labor
The wage in both the case is 20 but the workers are better of in the scenario (2) as in that case the employment is 100% and 398 which is 58 more than the previous one.
- An economy’s aggregate production function is given by Y = A·K·N – N^2. The marginal product of labor for this production function is MPN = A·K – 2N. a) Assume that A = 3 and K = 16. Suppose that the labor supply function for this economy is given by NS = 4 + w. Find the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy. Round everything to 2 decimal places. Note: it is OK to have fractions of workers or fraction of output. MPN = 48 – 2N and Ns = 4+ w At equilibrium, w = MPN = 48 – 2N w = 48-2(4+w) = 40 – 2w w = 20, N = 24 y = 48N – N^2 =960 – 400 = 560 w = N = Y =
c) Suppose that a computer virus leads to a decrease in total factor productivity so that A decreases to 2.5. Everything else remains as in part a). Find the equilibrium real wage rate, the full employment level of employment, and the full- employment level of output for this economy and label on your diagrams as point B. MPN = 40 – 2N N = 4+w=(40-w)/ N = 8 , w= 24 Y = 320- N = 480- w = N = Y = d) List and explain two reasons as to why A could have changed like this.
Productivity factor can decrease because of disease outbreak or natural disaster. As both of them lead to decrease in amount of efficiency by workers.
e) Let’s go back to our initial conditions (point A). Instead of a change to A impacting the economy, assume that K is now equal to 20. Everything else is as it was in part a). (In particular, A = 3.) Find the new levels of the equilibrium real wage rate, the full employment level of employment, and the full-employment level of output for this economy and label (on both diagrams) as point C. MPN = 60-2N N = 4+w = (60-w)/ w = 17. N = 21. Y = (21.3360)-(21.3321.33) w = N = Y = f) List and explain two reasons as to why K could have changed like this.
K could have changed because of increase in amount of capital spent on the workers by company because of increased profits or because of increase in tax benefits by the govt.
