Intermediate Microeconomics,Spring2016Instructor:Siwei Chen,Yang YangAssignment1(due date:March8/March10)a.Assignments should be submitted at the beginning of next week’s te submissions will not be accepted.b.Discussion with classmates is encouraged.But you should write up answers independently.c.If the case of identical answers is found,all the students involved in verbatim copying will receive a score of zero.Budget Constraint1.Suppose that Ming has$60to spend on either CDs or video rentals.For each of the situations described below,draw Ming’s budget line.Put“CDs”on the x-axis,and“video rentals”on the y-axis.Provide coordinates of all special points on the graph.(Treat CDs and video rentals as CONTINUOUS goods,which can be con-sumed in non-integer amounts.)(a)CDs are$10each and video rentals are$6each.(b)The prices are the same as in(a).The government imposes a20%value tax on CDs.(c)Video-rentals are$6each.CDs are$10each for thefirst three,and$6each for additional ones.(For example,the cost for two CDs is10*2=20;The cost forfive CDs is10*3+6*2=$42.)(d)The prices are the same as in(a).However,there is an on-going promotion of CDs,a bundle of four CDs for$30.(For example,the cost offive CDs is30+10=40;The cost of eight CDs is 30+30=60.)(e)The prices are the same as in(a).However,there is an on-going promotion of video rentals. Ming can buy a member card for$36,which allows him to rent up to10videos.(f)The prices are the same as in(a).The government imposes a$30lump-sum tax on Ming,but compensates him with a member card which allows him to rent up to10videos.(g)The prices are the same as in(a).The government imposes a50%value subsidy on CDs. However,Ming can buy at most8CDs.2.Jenny wants to intake royal jelly and pollen for health,and she has$60to spend on drinksevery month.There are two types of drinks on the market containing royal jelly and pollen, Popsi and Cela,each with a different formula.Each100ml of Popsi contains10ml of royal jelly and20g of pollen.Each100ml of Cela contains20ml of royal jelly and25g of pollen.The prices of Popsi and Cela are,respectively,$10and$15for each100ml.(a)Put the amount of royal jelly on the x-axis and the amount of pollen on the y-axis.Draw Jenny’s two extreme consumption bundles on the graph when she spends all the budget on Popsi,or Cela.(b)What is Jenny’s budget set?Mark it out by shadow on the graph you’ve plotted in(a).Preferences3.Prof.Goodheart gives two midterms in his communications class.He only uses the higher of the two scores that a student gets on the midterms when calculating the course grade.Nancy is taking Prof.Goodheart’s course and wants to maximize her grade.Let x1be her score on the first midterm,and x2be her score on the second midterm.(a)Which combination would Nancy prefer,x1=30and x2=70,or x1=60and x2=60?(b)Draw the indifference curve going through(30,70),and the indifference curve going through (60,60).(c)Does Nancy have monotonic preferences?Does Nancy have convex preferences?(d)Suppose that Prof.Goodheart changes his policy.He uses the lower of the two scores that a student gets on the midterms when calculating the course grade.Re-answer parts(a)-(c). (e)Suppose that Prof.Goodheart uses the average of the two scores that a student gets on the midterms when calculating the course grade.Re-answer parts(a)-(c).4.Consider the following two goods:concerts and movies.Draw indifference curves that rep-resent the preferences of each of the following people.Put“concerts per month”on the x-axis, and“movies per month”on the y-axis.For each graph,label the direction of increasing welfare with an arrow.(a)YoYo Ma likes concerts,but does not care whether or not he watches movies.(b)Ruth like movies,but dislikes concerts.(c)Carlos dislikes both movies and concerts.He dislikes each additional movie more,as he watches more movies.He dislikes each concert the same,no matter how many he goes to.(d)Sanjay also dislikes both movies and concerts.He dislikes each concert the same,no matter how many concerts he goes to.However,unlike Carlos,he dislikes each additional movie less, as he watches more movies.(e)Marie likes concerts up to three per month,and then starts to dislike extra ones.However, she likes movies no matter how many she watches.(f)Andrea likes it best when she watches three movies and goes to two concerts each month. If she deviates from this optimal consumption bundle,she would be dissatisfied.The further away she deviates from the optimal bundle,the more dissatisfied she is.Utility5.Calculate the marginal utility of x1,the marginal utility of x2,and the marginal rate of sub-stitution,for the following utility functions:(a)2x1+3x2(b)ln x1+x2(c)x a1x b2(d)(x1+2)(x2+1)6.Assume that t>0.Is each of the following functions a monotonic transformation?(a)f(t)=t2(b)f(t)=t−2(c)f(t)=(ln t)27.Apply the three transformations from Question6to the utility function u(x1,x2)=x a1x b2. Write down the three new utility functions.Calculate the marginal rate of substitution for each of them.Do they represent the same preference relation as u(x1,x2)=x a1x b2?。