Review Questions – Chapters 4 and 5. ECON 500 – Spring 2004. Chapter #4 (“The Market Forces of Supply and Demand”): Questions for Review: 4, 5, 8, 9, and 10. Problems and Applications: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Additional Questions: 1) Consider a market in which demand is given by ppD 2100)(−= and supply is given by ppS 4)( = . Illustrate each function graphically. Does the “Law of Demand” appear to be satisfied; does the “Law of Supply” appear to be satisfied? Explain. 2) Consider a market in which demand is given by 2100,8)(ppD = and supply is given by 2100)( ppS = . Determine the functional forms of inverse demand and inverse supply. 3) Consider a market with a total of n consumers, half of which have individual demand characterized by ppDi210)(−= and half of which have individual demand characterized by ppDi440)(−=. Determine the corresponding market demand function. Graphically illustrate the market demand function. As n increases, will demand increase or decrease? Is this consistent with our discussion in lecture? Explain. 4) Suppose 2108)(qqPD= and qqPS21)(=. Is there excess demand, excess supply, or neither: at a price of 2=p , at a price of 3=p , at a price of 6=p ? Explain. 5) Suppose 21200)( ppD −= and 22)( ppS = . Determine the equilibrium price and quantity in this market. 6) Consider a market in which bppD−=100)( and kppS=)( (with 0>b and 0>k ). Would an “increase in k ” correspond to an increase in supply or decrease in supply? Clearly explain. Would an “increase in b ” correspond to an increase in demand or decrease in demand? Clearly explain. Based upon your insights thus far (that is, without doing any “calculations”) how would you expect the equilibrium price and equilibrium quantity to behave if k and b increase simultaneously? Determine the equilibrium price and equilibrium quantity, eachas a function of k and b . Argue that the general insights that you made (before doing any calculations) were correct. Chapter #5 (“Utility and Choice”): Review Questions: 1, 5, and 6. Problems: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, and 2.7. Additional Questions: 1) Consider a consumer with 21)( xxXU = . a. Rank the following bundles in “order of preference,” from “least preferred” to “most preferred”: )1,1(=A , )10,10(=B , )4,16(=C , )18,2(=D , and )10,7(=E . b. Suppose the price of commodity one is 51=p , the price of commodity two is 22=p , and the income of the consumer is 80=I . Which of the bundles from part (1.a.) are affordable? Explain. Could any of the bundles from part (1.a.) be optimal for this consumer? Explain. 2) Consider an individual with 321)( xxXU = . For this individual, 321xMU = and 22123 xxMU = . a. Specify 2,1MRS as a function of 1x and 2x . b. Determine the utility maximizing consumption bundle for this consumer (that is, the optimal levels of 1x and 2x , each as a function of prices and income). Determine the level of utility (as a function of prices and income) that this individual realizes as a result of consuming this optimal bundle. 3) Consider an individual with 2152)( xxXU+=. For this individual, 21=MU and 52=MU . a. Argue that in order to maximize utility, this consumer will either “spend all income on commodity one” (that is, consume = 0,1pIY) or “spend all income on commodity two” (that is, consume =2,0pIZ). b. If 41=p and 92=p , will the consumer wish to purchase Y or Z? Clearly explain. If 21=p and 62=p , will the consumer wish to purchase Y or Z? Clearly explain. c. From here, argue that the consumer will wish to purchase Y when 2152pp < and will wish to purchase Z when 1225pp < .4) Consider a consumer with {}213,2min)( xxXU=. a. Graphically illustrate the indifference curve map for this consumer. b. Graphically illustrate the solution to the utility maximization problem for this consumer. c. This consumer will always want to choose 1x and 2x so that 2132 xx = . From here, argue that the optimal levels of 1x and 2x (as functions of prices and income) are 21*1233ppIx+= and 21*2232ppIx+= . Determine the level of utility (as a function of prices and income) that this individual realizes as a result of consuming this optimal bundle. 5) Suppose you are told that a consumer has “monotonic preferences” (and you know nothing else about the preferences of the consumer). Given a choice between )5,8(=A and )8,12(=B , which will the consumer prefer? Explain. Given a choice between )8,12(=B and )7,15(=C , which will the consumer prefer?
View Full Document
Unlocking...