4. Consider the standard Ramsey model where the planner chooses time paths for the representativeagent's consumption c(t) and capital k(t) to solvefe-mu(c(t))dtsubject to k(t) = Aƒ(k(t), L) — c(t)k(0) > 0 given, L> 0 givenmaximisewhere f(,) exhibits diminishing returns to capital, u() satisfies standard assumptions, A is a multiplicativetechnology parameter, and L is the labour supply.(a) At date 0 information is revealed that there will be a (temporary) increase A at date t₁, andthat at t₂ (where t2 > t₁ > 0 ) A will be decreased to its initial level and will remain there forever. Analysethe economy's response regarding consumption, capital accumulation, GDP, and capital's marginal product(equal to the competitive equilibrium interest rate) over time under the following two conditions:Initially, at date 0, the capital stock is at its steady state level.Initially, at date 0, the capital stock is larger than its steady state level.(b) Discuss the differences in the economy's response between the above two parts.

In the given Ramsey model, the planner aims to maximize the discounted utility of consumption over…

(a) At date 0 information is revealed that there will be a (temporary) increase in A at date t₁, and that at t₂ (where t₂ > t₁ > 0) A will be decreased to its initial level and will remain there forever. Analyse the economy's response regarding consumption, capital accumulation, GDP, and capital's marginal product (equal to the competitive equilibrium interest rate) over time under the following two conditions: Initially, at date 0, the capital stock is at its steady state level. Initially, at date 0, the capital stock is larger than its steady state level. (b) Discuss the differences in the economy's response between the above two parts.

(a) At date 0 information is revealed that there will be a (temporary) increase in A at date t₁, and that at t₂ (where t₂ > t₁ > 0) A will be decreased to its initial level and will remain there forever. Analyse the economy's response regarding consumption, capital accumulation, GDP, and capital's marginal product (equal to the competitive equilibrium interest rate) over time under the following two conditions: Initially, at date 0, the capital stock is at its steady state level. Initially, at date 0, the capital stock is larger than its steady state level. (b) Discuss the differences in the economy's response between the above two parts.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

4. Consider the standard Ramsey model where the planner chooses time paths for the representative agent's consumption c(t) and capital k(t) to solve Love- e-ptu(c(t))dt subject to k(t) = Aƒ (k(t), L) — c(t) k(0) > 0 given, L> 0 given maximise where f(,) exhibits diminishing returns to capital, u() satisfies standard assumptions, A is a multiplicative technology parameter, and L is the labour supply. (a) At date 0 information is revealed that there will be a (temporary) increase in A at date t₁, and that at t2 (where t2 > t₁ > 0 ) A will be decreased to its initial level and will remain there forever. Analyse the economy's response regarding consumption, capital accumulation, GDP, and capital's marginal product (equal to the competitive equilibrium interest rate) over time under the following two conditions: Initially, at date 0, the capital stock is at its steady state level. Initially, at date 0, the capital stock is larger than its steady state level. (b) Discuss the differences in…
2. Mr. A has the following utility function and budget constraints: Max 0.1Ln(C1) + 0.7Ln(C2) Subject to S1 + C1 = 100 C2 + S2 = (1 + r)S1 where C1 and C2 are consumption level at young and that at old respectively. Likewise, S1 and S2 are saving at young and saving at old respectively. a) Find out Mr. A’s optimal consumption levels (i.e. C1*, C2*) and optimal savings (i.e. S1*, S2*) in terms of interest rate r. b) Show clearly the results in part a) in a suitable diagram (with C1 as x-axis and C2 as y-axis). c) Is Mr. A a saver ? or a borrower ? d) If r is equal to 0 (i.e. saving gives no returns), will Mr. A still choose to save when he is young (i.e. is S1 still bigger than 0) ? Why ? e) Suppose that Mr. A is not allowed to save (i.e. S1 = 0). What are his optimal consumption levels ? Show his optimal consumption levels in the same diagram you prepare for part a) (with a suitable indifference curve). f) If r increases,…
Let's incorporate the labor-leisure trade-off and capital income taxes in the two-period model. Let c₁, c₂ be consumption in two periods, I the number of hours worked, Te Te the proportional taxes on consumption in 2 periods, s the saving rate, w the wage rate, b pension in the 2nd period, and 7, the tax on savings (capital income tax). The household's maximization problem in this case is: given by maxe₁,e2,8,1-1 log(c₁) + log (1-1)+5log (c₂) such that (1+T₂) C₁+8 = (1-7)wl and (1+T₂)C₂ = [1+r(1-Ts)]s+b, where measures how the household values leisure vis-a-vis consumption.
Anna has endowment 1500 now and 500 later. Internet rate is 2.0%. She prefers smooth consumption to time (i.e., u0=u1=u). a. Assume utility function, u(c)= log c. What are the optimal consumption c0and c1if Anna's beta=1, and she wants to maximize her utility? b. Now assume that the utility function, u(c)=c0.5. If everything else remains the same as Problem 1(a), what are the optimal consumption c0and c1if Anna wants to maximize her utility?
a)Based on the given Lagrangian, compute the representative consumer's first-order conditions with respect to consumption and with respect to labor. Clearly present the important steps and logic of your analysis..
3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.
Answer the following questions using the following information. Columns 1 and 2 in the table below show the marginal utility that Cody gets by purchasing products A and B. Column 3 shows the marginal utility Cody gets from saving Assume that the price of A is $13 the price of B is $10, and Cody has an income of $129. a) Find the following series of MU/$ for each column. Note: Keep as much precision as possible during your calculations. Your final answer should be accurate to at least two decimal places Column 1 Column 2 Column 3 Units of A MU MU/S Units of B MU MU/$ Number of $ saved MU MU/S 68 6.8 1 80 6.15 1. 13 0. 2 71 5.46 2 63 6.3 2 10 0. 3 66 5.08 3 56 5.6 3 7 4 61 4.69 4. 46 46 0. 54 4.15 40 4 45 3.46 31 3.1 6. 1 39 3 22 2.2 0. 29 2.23 8 17 1.7 8 b) What quantities of A and B will Cody purchase in maximizing his utility? Quantity of A: 0 Quantity of B: 0 c) How many dollars will Cody save? Dollars Saved = $0 SAVE AND CLOSE
The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per %3D week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume A bags of candy.
f) i) Find the degree of homogeneity of the following functions and comment on their returns to scale i. Q = K² + 5KL – 4L² ii. Q = 13KSL ii. A consumer has the following utility function a. U = Ax“yf Find the MU, and MU, iii. Given the following consumption function C = 70 + 0.85Y Find the corresponding savings function and marginal propensity to save
In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/4b³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is T. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume = 0.5. Knowing that bad weather…
In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/46³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is π. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume π = 0.5. Knowing that bad weather…
A consumer is maximising her utility function: U(r. y) = (r05 +y0.5)2, subject to the budget constraint 4x + 2y = 108. (a) Set up the Lagrangian function of this utility maximisation problem and first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the multiplier. (c) What are the utility maximising amounts of x and y if the budget constrain to x+ 2y = 36? How would change? Explain your reasoning. (Hint: Yc need to calculate A, rather comment on how it would change and why.)