6) According to the graph below, at which point is the consumer choosing to borrow in the first period in order to consume exclusively in that period?: * Consumer's Budget Constraint Second-period consumption C2 (1+)Y1 + Y2 Y2 Y2 v1 +v2/(1+r) First-period consumption C1 A) Point A O B) Point B OC) Point C O D) Point D 7) According to New Keynesian theory, economic shocks can arise as a result of:* O A) Microeconomic imperfection O B) Lack of government spending on durable goods OC) Monetary neutrality ORIEXcess monetary reserves
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A: Answer -
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A: c*= 1+r2+r×we
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- . On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according to thefunctionU (c, b) = 20c - c2 +18b- 3b2.How many cigars and glasses of brandy does he consume during an evening? (Cost is no objectto J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum of glasses ofbrandy and cigars consumed to 5. How many glasses of brandy and cigars will he consumeunder these circumstances?Suppose a consumer has $1500 in the current time period and $1100 in the future time period.Suppose also that the consumer can borrow and lend freely and, unless otherwise specified, borrowing and lending interest rates are the same. (a) If the interest rate between time periods is 50%, what is the budget constraint between consumption in the present and consumption in the future? (B) If the interest rate at which the consumer can borrow is 75% but the rate at which she can lend is25%, what is the budget constraint? (C) Suppose the interest rate is 50%. If the consumer has to pay a fee of 10% of the loan amount in order to borrow money, what is the budget constraint?Question 4 A consumer is maximising her utility function: U (x, y) = (205 + y05)², subject to the budget constraint 4x + 2y 108. (a) Set up the Lagrangian function of this utility maximisation problem and derive the first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the Lagrange multiplier. (c) What are the utility maximising amounts of x and y if the budget constraint changes to x + 2y = 36? How would A change? Explain your reasoning. (Hint: You do not need to calculate A, rather comment on how it would change and why.)
- Task 5: Consumption as young and consumption as old Now suppose Mary is thinking about her retirement and wants to understand how much to save. Today she can either con- sume or save for retirement. During her young, working life she will make 100.000 euros. Thus, her current budget constraint is Cy + S = 100.000. In her retirement she has no income, only the amount she saved as young. She can save at a rate of (1+r). So, her budget constraint as old is Co = (1+r)S. (a) Write Mary's lifetime budget constraint as plot it in a graph. Tip: Solve for savings while old and substitute in the young budget constraint. (b) Mary's utility from consumption as young and consumption as old is U(Cy,Co) = 1-0 Solve Mary's maximization problem. What is the MRS and the MRT? (c) Suppose Mary wins the lottery while young. What is the effect on her optimal decision for consumption as young and as old? (d) The local bank decided to increase the interest rate on savings. Discuss the effect of this increase…2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.Suppose a consumer has a monthly income of m = 100 which she spendson two commodities: french fries (x1) and beef jerky (x2). The price offrench fries is p1 = 2 and the price of beef jerky is p2 = 5.(a) Write down the consumer’s budget constraint (equation).(b) What is the maximal consumption of french fries (this is calledthe real income in french fries).(c) Find the maximal consumption of beef jerky (real income interms of beef jerky).
- 12) Melquiades is worried about his grades from the microeconomics course, according to the rules for grading, the final grade is obtained as the minimum between the grade for the midterm test (x) and the final test (y). The utility function of Melquiades will depend on the grades obtained from those two tests Now, Melquiades has researched that the average student needs to study 24 minutes an additional point in each test (tests are graded from 0 to 100) obtain a) If Melquiades has 20 hours to study for both tests (x and y), how much time would he employ for each test? Figure out the grade that Melquiades will obtain in each test and his final grade in microeconomics. Elaborate a graph. b) How much additional study time would Melquiades require to increase his final grade by 10 points. Elaborate a graph. c) Suppose the difficulty of the final test increases in such a way that now each additional point would require 26 minutes of study. What would be the total cost (in minutes)…5. Suppose the representative consumer has the (quasilinear) utility function: U(x, y) = ax + In(v) where x,y are consumption goods. Denominated in US dollars, the prices of x and y Pi and pz, respectively. (a) What does the term quasilinear mean? Is consumption of x independent of y? (b) Assume the consumer has a budget of C dollars at his/her disposal. What is the maximum utility the consumer may achieve with this budget? (c) What is the minimum expenditure if the consumer wants to derive U,units of utility?How would you demonstrate part b) diagramatically 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.
- Q 1 5. Refer to the following intertemporal budget constraint of a respective consumer: a. How would this budget constraint change if individual becomes more presented oriented (he discounts future heavily)? b. How would this budget constraint change if individual faces a borrowing constraint in second period?2. An economist is interested in the variation of the price of a single product. It is observed that a high price for the product in the market attracts more suppliers. However, increasing the quantity of the product supplied tends to drive the price down. Over time, there is an interaction between the price and supply. The economist has proposed the following mode, where Pn represents the price of the product at year n, and Qn the quantity: (a) Explain the significance of the constants 500 and 100 in the proposed equation. (b) Explain the significance of the signs of the constants -0.1 and 0.2. (c) Simulate the system using the following initial conditions (plot the trajectories) and predict the long term behavior of the dynamical system. Po 100 and Qo= 500 • Po= 200 and Qo = 500 ● Po 100 and Qo = 600 Po 90 and Qo = 400 [Pn+1 = Pn -0.1 (Qn - 500) [Qn+1 =Qn +0.2 (Pn - 100) ●Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h) = c-3h¹+, where 3 > 0 and p > 0 are parameters. 1+p