Name Date 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 1 The production technology of a firm is given by the following equation 5 Y 15 K N 5 Assume K initially equals 25 a Fill in the first blank column below showing what the output is per different number of workers Round the nearest two decimal places Number of workers 0 1 2 3 4 5 6 7 Units of output MPN MRPN P 6 b 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 c Find the marginal product of labor MPN for each level of employment fill in the third column of table above 1 d Assume that the price of a unit of output is 6 Calculate the MRPN for each worker and add it to the table above e Calculate the number of workers that will be hired if the nominal wage rate 140 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 90 Please show your work If W 140 N If W 110 N If W 90 N f Why exactly does the firm s behavior change when the nominal wage fall like it did all else constant In particular explain exactly why the firm changes their labor input when nominal wages fall from 140 to 110 all else constant Make sure you refer to the profit maximizing condition when answering this question 2 Assume that an event makes the new production function equal to Y 20 K 5 N 5 g Fill in the table below Number of workers 0 1 2 3 4 5 6 7 Units of output 0 MPN h List and explain two real life examples of events that could cause this change to the production function 3 2 Consider an economy with the following characteristics MPN 500 3 N N s 24 14 w 3 T where w is the real wage and T is a lump sum tax levied on individuals Suppose that initially T 38 a Compute equilibrium values for the real wage and employment Round your answer to two decimal places 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 4 c Now this economy passes a law and pays a minimum wage equal to 5 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 of people willing to work w 5 of people willing to be hired w 5 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 5 e Was this change in the number of people employed due to a shift or a movement along the demand curve circle your answer Shift Movement Along f Intuition Why does the profit maximizing level of labor input change with the living wage program make sure you write out the profit maximizing condition and explain why it has changed i e why does the hiring company rationally change their quantity demanded of labor the way they did g Intuition We also experience a movement along the labor supply curve Explain the intuition here as in why are more people are willing to work using and explaining the substitution and income effects associated with labor supply Which effect dominates and what has happened to the price of leisure given the living wage program 6 Suppose now that there is a new marginal product of labor equals MPN 629 3 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 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 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 7 3 An economy s aggregate production function is given by Y A K N N2 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 w N Y 8 b Draw a production function and labor demand curve vertically as we did in the videos many times and label these initial equilibrium points as A 9 c Suppose that a new innovation 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 fullemployment level of output for this economy and label on your diagrams as point B Round everything to 2 decimal places Note it is OK to have fractions of workers or fraction of output w N Y d List and explain two reasons as to why A could have changed like this 10 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 18 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 Round everything to 2 decimal places Note it is OK to have fractions of workers or fraction of output w N Y f List and explain two reasons as to why K could have changed like this 11 g Instead of a change to A or a change in K impacting the economy we are back to point A suppose that there is a change in the supply of labor such that we have NS 3 w All else remains as in part a In particular …