Consumption, Savings, and Financing Constraints. Because consumption expenditures that occur later in an individual's lifetiinc are typically on \"bigger-ticket items\" (e.g., cars, refrigerators, etc.} and thus more eitpensive, an individual oen has to begin planning for hisr'her future consumption expenditures well in advance of their actual purchase and use. In contrast, consumption eXpenditurcs during the earlier years of an individual's life are predominantly on \"smaller'I items {e.g., movies, food. entertainment, etc.) and thus might not require as much \"advance planning.\" We can analyze this idea in a two-period representative consumer framework. As always, suppose the representative consumer has a lifetime utility function of period-1 consurnption and period-2 consumption given by \"(CM-'1)- Period 1 is the \"early stage\" of an individual's economic life, and period 2 is the \"later stage\" of an individual's economic life. Suppose the fmancial assets that individuals have at their disposal are \"stocks\" {exactly as studied in Chapter 8}. The rePresentativc consumer begins period 1 with zem stock holdings (i.e., an = 0]. The period-1 and period-2 budget constraints of the reprensntative consumer are 3'] + Slat = YL and Pics +3232 = 1"2 +032 +D23a1' The notation is standard: P denotes the per-Unit nominal price of a consumption good (in a given time peiiod], Ydenotes the nominal income the consumer earns (in a given time period}, 3 denotes the nominal price of each share of stock (in a given time period), and D denotes the per-unit nominal dividend each share of stock pays (in a given time period). Because period-2 goods are weighted more towards \"big-ticket items,\" consumers typically have to borrow to purchase them. This means that asymmetric information issues may be a factor in lenders being willing to extend credit to consumers for their period-2 purchases. Suppose the nancing constraint (aka credit constraint) that has evolved in markets to deal with tltese information issues is Pact =R'Sial- The interpretation of this constraint is that the market value of assets accrunulated during period 1 of the individual's life forms the basis (along with a government-mandated regulatory policy captured in the R 2] term) for period-2 consumption. Just as in class, dene the \"nominal interest rate on stock\" as mm\" =3=+D= Sr -SI'DCK l + I dene the \"real intemst rate on stock\" as 1+ r570\" = . Finally, because this is a two- l+ 9:2 period framework, we know or: = D. a. Construct the smgng'gt L goggle for the representative consumer's utility maximization problem starting from the beginning of period 1. Several hints and notes might be useful here: i} Do not substitute the nancing constraint directly into any of the other constraints; it will be most informative to conduct the analysis with the nancing constraint as a separate constraint ii) Use the multiplier p (the Greek letter ' u\") for the nancing constraint iii) Be extremely careful about the setup of the Lagrange function because it is the basis for virtually all of the analysis that follows b. Based on the sequential Lagrange function in part a, compute the rst-order conditions with respect to cl, :2, and or. c. If there were no nancing constraint on consumers' purchases of period-2 consumption, the value of the Lagrange multiplier p could be thought of as being equal to what numerical value? Be as precise as possible, and briefly explain the economic interpretation. (Note: You can answer this part even if you were unable to get all the way through part a and part b.) smelt: .smcx = 32 +192 1 + ' d. Using the denitions 1+1 and l+rsm = I 3] 1+ 1'32 order conditions obtained in part b above to derive the consumption-savings optimality condition. The nal expression should be written as , rearrange the three rst- \"q (cl Dcz) : "52(819 c1} ".1 in which the term in ellipsis [\"..."') on the right-hand side is for you to determine. Clearly and carefully provide important algebraic stepsogic that leads to the solution. (Note: It is ne if the nal expression contains the multiplier p.) e. (Harder) Based on the consumption-savings optimality condition obtained in part d, does the financing constraint PC, = R . S a "matter" for consumer's consumption and savings decisions over time? In other words, does the "standard" consumption-savings optimality condition studied in Chapter 3 and 4 get altered by the presence of this financing constraint? If so, explain the economic intuition behind why; if not, explain the economic intuition behind why not