Mind helping in these

Human lCapital Model: Fieinterpretthe human capital growth model as follows: Suppose there are two groups of people in a country, the lowskilled and the highskilled, where the lowskilled have less human capital per person initially than the highskilled. Each type of worker produces output independently from the other, using efficiency units of labor and total factor productivity, 2, which is assumed to be common across groups. Each individual in this economy accumulates human capital on their own,1 and each has one unit of time to split between human capital accumulation and work. Assume that the high skilled have initially higher efficiency of learning: bh :> bl , and that uh 6: ul . {a} In all developed countries, there has been an increase in the socailed skill premium, the gap between the wages of highskilled workers and lowskilled workers, over the last 3G years. Determine how this model can explain this observation. Human Capital: Our textbook points out that human capital is not included in the simple model of production but that it could be an important factor in explaining why the marginal product of capital differs among countries. 1. Consider a Cobb-Douglas production function with three inputs: Y = KiLiHi, (1) where K is capital, L is labor, and H is human capital. What is the marginal product of capital (MPK) implied by this production function? 2. Is MPK increasing in human capital or decreasing? 3. Use this model to explain why capital may flow from poor to rich countries. 4. Is the return to education higher or lower in countries with scarce capital?EXERCISE Question 1 (Three-period Model - Appendix to Ch. 4) A consumer lives three periods - the learning period, the working period, and the retirement period. Her income is 100 during the learning period, 1000 during the working period, and 400 during the retirement period. The real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime. 1) Assuming no borrowing constraint, what are the consumption and saving in each period? Period Desired Consumption Desired Saving Learning Period Working Period Retirement Period 2) Assuming that the consumer faces a borrowing constraint that prevents her from borrowing, what is the consumption in each period? Period Desired Consumption with Borrowing Constraint Learning Period Working Period Retirement Period Question 2 (Two-period Model on Budget Line and Indifference Curve - Appendix to Ch. 4) Part I - Constructing Budget Line and the Changes in Interest Rate and Asset Suppose Alice earns $10,000 today and expects to earn $18,000 tomorrow. The real interest rate is 20%. 1) With current and future consumption on horizontal and vertical axes, respectively, draw Alice's budget line. Precisely calculate the intercepts and denote the no-borrowing-no-lending point. Write down the budget constraint equation. 2) Suppose the real interest rate is 100%, repeat 1). 3) Suppose, instead of the increase in real interest rate, Alice finds $10,000 in her attic today. Draw her new budget line. Part II - Finding Optimal Consumption Plan 4) From Part I, assuming no borrowing constraint. Suppose Alice desires perfectly smooth consumption over her lifetime, give the method on how to find her optimal consumption plans. 5) "When interest rate decreases, a borrower will not become a saver, but a saver may become a borrower." Use the budget lines and indifference curves to show the optimal consumption plans that correspond to the statement. Part III - Substitution Effect and Income Effect 6) Draw the budget lines and indifference curves that corresponds to both cases of borrowing and lending consumer facing a decrease in interest rate. Decompose the substitution and income effects.EXERCISE Question 1 ( Small Open Economy and Current Account Balance - Chapter 5) Consider a small open economy with zero net unilateral transfers and zero net factor payments. In each of the following cases, what is the result (increase/decreaseo effect ) on the current account balance? Draw the diagrams to show the answers. 1) A temporary favorable supply shock 2) A decrease in the expected future marginal product of capital 3) A temporary increase in the government purchases 4) A temporary decrease in tax today, holding the government purchases constant Question 2 (Two-Large-Country Model - Chapter 5) Consider a world with two large open economies, which are designeted the Home Country (H) and the Foreign Country (F). You are given the following information about savings and investments in each country. Home Country Foreign Country Saving 5y = 1.5+0.5re SF= r Investment | 7 =9-r IF = 7.5 - 0.5r 1) What is the equilibrium value of the world real interest rate and the current account balance in each country? Draw the diagrams for each country and the world saving-investment to show your answers. 2) Suppose the Foreign Country's desired saving rises by 3 at each level of the world real interest rate. What is the new equilibrium world interest rate and the current account balance in each country? Illustrate the changes to the diagrams drawn in 1). Question 3 ( Solow Growth Model: Introduction) This question walks you through the underlying basics of Solow growth model. 1) Consider the usual constant return to scale production function at time f given by It = F (K,, L,). Write down and draw the per-worker production function. 2) Population save constant saving rate s of the output. Write down and draw the per-worker saving function st at time f. 3) Gross investment must at least replace the worn out capital (dk, ) and must expand the capital stock as population grows (nk:). The gross investment at time t is therefore given by It = (d + n) Kr. Write down and draw the per-worker gross investment. 4) Steady-state level of capital corresponds to the situation where saving equals to gross investment. Denote such point on the diagram drawn. 5) Denote the per-worker consumption at the steady-state level of per-worker capital. 6) Suppose the economy starts with the level of per-worker capital below the steady-state level, this leads to positive net investment and the economy accumulates capital. Explain in a diagram with saving and gross investment. 7) The golden-rule level of consumption corresponds to a particular saving rate such that, at the steady-state, the steady-state level of capital leads to the highest level of consumption. Explain the golden-rule level of consumption. Consider three saving rates: below, above and the golden-rule saving rates