Kent State University Intermediate Macroeconomics Written Problem Set 1 Due at 1158PM in Blackboard on the Date Indicated in the Syllabus There are 100pm'nk and two pagfar this assignment Show your work for full credit! For the following problems, consider an economy made up of a representative household, a government that spends and finances it by collecting lump sum taxes. There is no trade nor investment in this economy. The price of consumption is equal to one (p=1)r Suppose the representative household in the economy has the following utility function and MRS: u(C,L) = 4ln(C) +l3ln(L) which implies that the MRS he = 13CI4L where C is consumption and L is leisure hours of the 800 hours available Firms have the following technology where Y is the economy's goods and services with 900 units of physical capital (K) and N being labor used with the capital share of income and Total Factor Productivity given as (a = 133; z = 9.6): Y=zK"N\""') which implies that MPH = (l-u)zK\"N\"\"'. l) [6 Points] For this question, suppose wages are 11, prot is 89 and taxes are 441 a) [3 Points] What is the most leisure that can be taken? Show your work. h) [3 Points] What is the most consumption that can be taken? Show your work. [19 Points] Household Choices. Prot, taxes and government spending are unknown for this question. Do not assume they are zero but assume that the economy is in equilibrium. a) [8 Points] Would the household above prefer (45 C, 35 L) or (35 C, 45 L)? Would the household prefer (35 C, 45 L) or (19 C, 60 L)? ex. (5 C, 3 L) means 0:5 and L=3 b) [6 Points] Suppose the household above chose leisure to be 536, how many hours of labor would the household provide to the market? What would the value of wages be in this case? c) [5 Points] Suppose for this part of this question (onlyl), we know nothing about the rms but we know households spend half their time in leisure and wages are 8. Find the level of consumption taken by the household. 3) [15 Points] Firm Choices. Consider a rm with production as follows: QuantityofLabor l0 1 l2 3 M. 5 butpucoraevenue I0 101 km 338 339 mo Suppose wages are 43, provide the following for each quantity of labor: a) [5 Points] Show the marginal product of each worker. Do not use MPN = (Ia)zK' M" b) [5 Points] Provide the total cost incurred by the rm for each quantity of labor. b) [5 Points] Provide the prot for the rm for each quantity of labor. Do not use Y=zK'N'"" Page I of l