Give clear answers.
6. Write down consumption per worker, G, as a function of k, and the savings rate. Determine the Golden Rule level of the savings rate in this economy. (6 points) Solution. C = (1-8) kp. At the steady state, we have c* = (1 -8) 8 + gN Taking log: In c' = -7 1 - a - In (8 + gN ) + In (1 - s) + 1-a In s. Differentiating it w.r.t. s gives the following first order condition, 1 0 = - So s = 0. 7. Using a Solow diagram, show how the accumulation of capital per worker would change if there were an increase in the population growth rate, g. Provide the intuition. In another diagram, draw the evolution of consumption per worker over time after this change. (8 points) Solution. The increase in gy would shift up the required investment curve, resulting in a lower level of ke and ye in the steady state. Intuitively, the original level of investment is no longer sufficient to keep up with the growing population so capital per worker would fall. Since a = (1 - s) ye, it suffices to study the evolution of y. y = ky was at its steady state level and will change to its new steady state level which is lower. Hence, the evolution of consumption per worker decreases from (1 - s) (k*)" to (1 - s) (k*)". Make sure that the rate of change becomes slower and slower in your graph.Consider once again an economy in which there are two goods, 1 and 2, whose prices are p > 0 and py > 0, respectively. The two goods can only be consumed in non-negative amounts r, and r2, respectively. A consumer has preferences over R, which are represented by the utility function 1 : R- - R, (21, 12) - 4(21, 12) := (or, ' + 812 ?) where a and 8 are strictly positive real numbers. The consumer's income is I > 0. (Note: This is an example of CES utility function) 2 (a) Formulate the consumer's utility maximization problem, find the first- order conditions for utility maximization, and find the Marshallian de- mand functions ,(p1, p2, /) and ra(p1, p2, /) for goods 1 and 2, respec- tively. (Note: Use the Lagrangian method. Assume that the budget con- straint holds with equality and that the solution is interior (i.e. r] > 0 and x2 > 0), thus disregarding the non-negativity constraints on a and 12. Do not check second order conditions.) (b) Find the price elasticity of demand for good 1. Is demand for this good elastic or inelastic? (c) Find the derivative of the quantity of good 2 demanded with respect to the price of good 1. Use this to indicate whether goods 1 and 2 are substitutes or complements. Now consider a consumer whose preferences over R4 are represented by the CES utility function 1 : R. - R. (11, 12) - 4(21, x2) := (arf + Brzo)/e, (1) where p, a and S are real numbers such that 0 # p 0 and # > 0) The consumer's income is / > 0. (d) Why does the utility function U: R -R. (21, 12) 4 0(21.12) :=0 represent the same preferences over R. as the function u in (1)? Now forget about the previous utility functions. For the next question, con- sider generic Marshallian demand functions for goods 1 and 2, z,(p1, p2, !) and r2(pi, p2, I), resulting from a consumer's utility maximization problem. Assume that Marshallian demands are differentiable functions of prices.05 Question (3 points) ' See page 38? A mail-marketing company combines two inputs, pre-stamped envelopes (input 1} and printed marketing campaign material (input 2). Every envelope can be stuffed with three pieces of paper. That is, the number of marketing mailers is determined by the following production function: y= minixl. '5'} where _y stands for the number of mal Iers. .u stands for the number of pre-stamped envelopes, and JEStBFIdS for the number of sheets of paper. v ist attempt Part 1 {1 point} 0 See Hint If the unit cost of Envelopes is an, and the unit cost of printing a sheet of mailing materials Is my. the conditional factor demands for envelopes and sheets are, respectively Choose one: Part2 {1 point} 0 See Hint Considering your ndings from Part 1, which of the following statements are correct? Choose one or more: Q AThe conditional input demand for envelopes {x1} is independent of the price the firm charges for producing each mailer [the price of . ' B.The conditional input demand for envelopes {x1} depends positively on the number of mailers iyi the firm wants to produce. E.The conditional input demand for envelopes {x11 depends negatively on the per-unit cost of printed sheets of mailer material (aid. ' ' D.The conditional input demand for envelopes {x1} depends negatively on the per-unit cost of envelopes (mi). E.The conditional input demand for envelopes {x1} depends positively on the per-unit cost of envelopes (on). F. The conditional input demand for envelopes {x1} depends positively on the per-unit cost of printed sheets of mailer material (033. V. How have the numbers and living standards of the retired changed since 1940? A. When did companies start in mass offering private pensions? How did the post-WWII generation fund their retirements? B. Why does Gordon call the 1970's the "Golden Age" of Pensions? Why does he highlight the importance of ERISA and what did it do? C. How do typical retirees spend their time? Why does Gordon present that number? D. What policy issue does Gordon identify with the "progressive growth of the elderly population"? Why might their consump- tion " needs be greater"?Reading Questions - Ch. 33: The Literature Research Essay 1) In discussing the three approaches that you can take in examining a piece of literature, the author of your book refers to these as "contexts" to consider: "critical contexts," "biographical contexts," and "historical and cultural contexts." Explain what is being considered in each one and how this can be helpful for making sense of a work of literature. 2) When you write a research essay about a literary text, the point of the essay is to report what others have said about that text. True or false? Explain briefly. 3) When do you need to provide a citation of a secondary source? See pp. 1954, 1959. 4) What makes a secondary source "academic" or "scholarly" such that you could actually use it in a research essay? See pp. 1956-1957
