Solve the following questions ,as indicated below.
translates into a greater increase in the capital stock. (Note: another way to interpret q, is as the inverse of the relative price between machinery and output: when q, is high, machinery is relatively cheaper). (a) Transform the model (the production function, the equations for consumption and investment, and the capital accumulation equation) in per-worker form. Be careful, this is the model with population growth, so your per-worker capital accumulation equation will have terms involving both k, and kit on the right-hand side. (b) Use your capital accumulation equation from part (a) to explain why there is no steady-state in this model. (Hint:draw a graph with the typical investment and depreciation curves). (c) Suppose that capital per worker k, grows at a constant rate (we do not know that yet, but we will make a guess). Divide the capital accumulation equation by , and use this assumption to prove that q,k, has to be constant over time. (d) Use the fact that the growth rate of be equals (o - 1)4% together with the result from part (c) to derive an expression for the growth rate of capital k It as a function of y and o only. How does the growth rate of investment-specific technology y affect the accumulation of capital? (e) Use the growth accounting equation: 2M =04* to derive the growth rate of output per worker How about the growth rates of consumption and investment per worker? Is there balanced growth in this economy? (f) In class we noted that in the data the ratio ~ is constant over time. Show that this fact is violated in this model. Is this a problem? (Hint: In the real world we measure capital and output in the same units (dollar values). The value of capital in terms of output in this model is : - show that this value grows at the same rate as output Y?).9.)The Mumfords had the following expenditures for 2019: Courtney's contributions to her traditional IRA $6000 Net gamabling loss 1000 Life insurance premiums 2700 Medical and dental expenses not covered by insurance 16612 Taxes: Ad valorem taxes on personal residence 4100 State and local sales taxes from receipts 2800 6900 Interest on home mortgage reported on form 1098 4000 Cash contributions: Feeding south dakota (EIN 36-3293534) 1750 South dakota governor's election campaign fund 300 2050 The $1,000 net gambling loss for 2019 is the difference between the Mumfords' gambling winnings of $1,200 and losses of $2,200. The life insurance premiums relate to the universal life insurance policies that Matthew and Courtney own. The first beneficiary on both policies is the other spouse, with the second beneficiaries being the children. Included in the medical expenses are $1,200 incurred in 2018, which were paid in early February 2019. While South Dakota does not impose income taxes on individuals, it does impose sales taxes. The Mumfords can substantiate the $2,800 in sales taxes paid based on their purchase receipts for the year. The local sales tax rate in Sioux Falls is 2%. (Hint: Be sure to check to see if the Optional Sales Tax Tables provide the Mumfords with a greater deduction.) Courtney contributed to the governor's campaign fund because she thinks her influence was key in getting the Minnehaha County land rezoned for commercial use (see item 4 above). 10.]The Mumfords maintain a household that includes their two children, Nickolas (age 16) and Kaleigh (age 19). Nickolas is a junior in high school and a talented wrestler. In hopes of competing at the state tournament, all of his free time is consumed with weight training and wrestling practices. Kaleigh graduated from high school on June 7, 2018, and is undecided about college. She is an accomplished vocalist and during 2019 earned $7,200 performing at various events (e.g., weddings, funerals). Kaleigh placed most of her earnings in a savings account for future use and kept only a small amount to spend on herself. 11.)Matthew's Form W-2 from The Pour House shows $15,800 withheld for Federal income tax. The Mumfords also made estimated tax payments to the IRS totaling $5,000 for 2019.1 Theory Questions (100%) 1. Consider an agent who lives for two periods. The agent has to units of income in the rst period and no income in the second period. The agent can save for the second period at the interest rate r. The agent's preferences are given by: 1 1 Cl 0' + 62 IT 1 cr 1 or Here, a > [J is a parameter and {J <: :3 is the subjective discount factor. agent faces two period budget constrains: c1 s="ml" and c2="(1" r here represents second assets savings. find optimal consumption savings decision of this agent. how do change with interest rate consider basic twcrperiod labor supply an that only works in rst period. let her be denoted by suppose time normalized to so has preferences over e given by: hence gets utility from leisure l times constraints: cl wage1 lending borrowing a tax pay. problem solow growth model points very consisting following three equations: production function: y ak-ni- investment rule: i law motion for capital: k="(1-5)K," where n denote respectively gdp output or income capital at all periods f="0,1," ... constant total factor productivity parameter also constant. economy starts stock k. assume closed net exports are zero. moreover government purchases then equals sum c i. rule fraction invested it follows rest consumed. is. finally tells us new undepreciated old plus depreciation replaced every due wear tear comes age use. we initially values: what using equations above keep finding periods. you may want use excel. show evolution graph on horizontal axis vertical axis. happens long run i.e. there sustained does converge steady state if much>
