代做Problem Set 3代做回归

Problem Set 3

(Due Monday, November 11th, by 10AM, in Canvas. You can work in groups with up to three members. If you do so, write down the group members in the first page.)

1 Credit Markets and Inequality

Consider the following simple version of the model discussed in lectures 15 and 16. In particular, consider a small open economy with 3 types of individuals: workers, unproductive entrepreneurs, and productive entrepreneurs. The total population is N, with half of the population being workers N/2, and the rest entrepreneurs, N/4 of which are low productivity and N/4 high productivity. Types are fixed, i.e., perfectly persistent (in terms of the notation in the lecture notes, we assume that γ = 1). This economy can borrow or lend at a fixed world interest rate r. Labor is inmovil (i.e., there is no migration in and out of this economy, while capital can freely flow).

Workers supply inelastically a unit of labor and save a fraction s of their available resources. Their net-worth evolves according to the following law of motion

Entrepreneurs with productivity zi , i = 1, 2, produce output yi using capital ki and labor li using a technology described by the following Cobb-Douglas production function

The amount of capital that they can invest is limited by the following collateral constraint

ki,t+1 ≤ λni,t+1

(to simplify the analysis, we take the leverage λ as given. See lecture 15 for a derivation of the equilibrium leverage in terms of more fundamental parameters). The law of motion of the net-worth of entrepreneurs with productivity zi evolves according to the following law of motion

where profits

are payments to the talent of entrepreneurs zi .

1.1 Perfect Credit Benchmark

Assume that the leverage is sufficiently high, so that entrepreneurs can invest the optimal amount of capital irrespective of their net-worth. In this case, the equilibrium wage w and the profits of entrepreneurs of productivity zi , πi , are independent of the distribution of net-worth and equal to

and

where aggregate output

and

L = N/2.

To further simplify the analysis, in the rest of this exercise we are going to assume that the unproductive entrepreneurs are extremely bad, i.e., they can’t produce, i.e., z1 = 0 < z2.

1. (15 points) Graph the Lorenz curve of non-capital income (labor income for workers and profits for entrepreneurs) in this economy under the as-sumption that (1 − α − θ) 2 > θ. Interpret this condition.

2. (15 points) Solve for the steady state net-worth of workers and entrepreneurs under the assumption that s (1 + r) < 1.

3. (15 points) Graph the Lorenz curve of net-worth in this economy under the assumption that (1 − α − θ) 2 > θ and s (1 + r) < 1. Compare the Lorenz curves of income and wealth.

1.2 Imperfect Credit

Assume that the leverage is sufficiently low so that productive entrepreneur are constrained. As before, assume that the productivity of the unproductive entrepreneur is zero, z1 = 0. In this case, the equilibrium wage wt and the profits of productive entrepreneurs π2t and aggregate output Yt are a function of the net-worth of productive entrepreneurs and equal to

and

To further simplify the analysis, assume the following parameter values: λ = 1 (no credit), θ = 0.4, α = 0.3, z2 = 10, s = .1, r = 0.02, and δ = 0.06.

1. (10 points) Graph the Lorenz curve of non-capital income in this economy. How does the curve changes with ?

2. (10 points) Solve for the steady state net-worth of workers and entrepreneurs.

3. (10 points) Graph the Lorenz curve of net-worth in this economy. Compare your answer with that of exercise 1.1, using the same parameter values (other than the value of λ).

4. (10 points) Calculate the Gini coefficient of non-capital income and net-worth in the steady state of the two economies, i.e., the one with perfect credit market (exercise 1.1) and the one with λ = 1 (exercise 1.2), using the same parameter values (other than the value of λ).

5. (15 points) Calculate the GDP in the steady state of the two economies, i.e., the one with perfect credit market (exercise 1.1) and the one with λ = 1 (exercise 1.2), using the same parameter values (other than the value of λ).






热门主题

课程名

mktg2509 csci 2600 38170 lng302 csse3010 phas3226 77938 arch1162 engn4536/engn6536 acx5903 comp151101 phl245 cse12 comp9312 stat3016/6016 phas0038 comp2140 6qqmb312 xjco3011 rest0005 ematm0051 5qqmn219 lubs5062m eee8155 cege0100 eap033 artd1109 mat246 etc3430 ecmm462 mis102 inft6800 ddes9903 comp6521 comp9517 comp3331/9331 comp4337 comp6008 comp9414 bu.231.790.81 man00150m csb352h math1041 eengm4100 isys1002 08 6057cem mktg3504 mthm036 mtrx1701 mth3241 eeee3086 cmp-7038b cmp-7000a ints4010 econ2151 infs5710 fins5516 fin3309 fins5510 gsoe9340 math2007 math2036 soee5010 mark3088 infs3605 elec9714 comp2271 ma214 comp2211 infs3604 600426 sit254 acct3091 bbt405 msin0116 com107/com113 mark5826 sit120 comp9021 eco2101 eeen40700 cs253 ece3114 ecmm447 chns3000 math377 itd102 comp9444 comp(2041|9044) econ0060 econ7230 mgt001371 ecs-323 cs6250 mgdi60012 mdia2012 comm221001 comm5000 ma1008 engl642 econ241 com333 math367 mis201 nbs-7041x meek16104 econ2003 comm1190 mbas902 comp-1027 dpst1091 comp7315 eppd1033 m06 ee3025 msci231 bb113/bbs1063 fc709 comp3425 comp9417 econ42915 cb9101 math1102e chme0017 fc307 mkt60104 5522usst litr1-uc6201.200 ee1102 cosc2803 math39512 omp9727 int2067/int5051 bsb151 mgt253 fc021 babs2202 mis2002s phya21 18-213 cege0012 mdia1002 math38032 mech5125 07 cisc102 mgx3110 cs240 11175 fin3020s eco3420 ictten622 comp9727 cpt111 de114102d mgm320h5s bafi1019 math21112 efim20036 mn-3503 fins5568 110.807 bcpm000028 info6030 bma0092 bcpm0054 math20212 ce335 cs365 cenv6141 ftec5580 math2010 ec3450 comm1170 ecmt1010 csci-ua.0480-003 econ12-200 ib3960 ectb60h3f cs247—assignment tk3163 ics3u ib3j80 comp20008 comp9334 eppd1063 acct2343 cct109 isys1055/3412 math350-real math2014 eec180 stat141b econ2101 msinm014/msing014/msing014b fit2004 comp643 bu1002 cm2030
联系我们
EMail: 99515681@qq.com
QQ: 99515681
留学生作业帮-留学生的知心伴侣!
工作时间:08:00-21:00
python代写
微信客服:codinghelp
站长地图