Steve has the utility function U(ci, c2) = c2 + 2c2where ci is his consumption in period 1 and ci is his consumption in period 2. He will earn 100 units of the consumption good in period 1 and 100 units of the consumption good in period 2. He can borrow or lend at an interest rate of 10%. Write an equation that describes Steve's budget constraint and explain how you find it. If Steve neither borrows nor lends, what will be his marginal rate of substitution between current and future consumption? Show your calculation. If Steve does the optimal amount of borrowing or saving, what will be the ratio of his period 2 consumption to his period 1 consumption? Explain your answer.

Steve has the utility function U(ci, c2) = c2 + 2c2where ci is his consumption in period 1 and ci is his consumption in period 2. He will earn 100 units of the consumption good in period 1 and 100 units of the consumption good in period 2. He can borrow or lend at an interest rate of 10%. Write an equation that describes Steve's budget constraint and explain how you find it. If Steve neither borrows nor lends, what will be his marginal rate of substitution between current and future consumption? Show your calculation. If Steve does the optimal amount of borrowing or saving, what will be the ratio of his period 2 consumption to his period 1 consumption? Explain your answer.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.6P

See similar textbooks

Similar questions

Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + βu(C2) 1. Assume this consumer cannot borrow. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility curve. 2. Assume that now the consumer is allowed to save or borrow. Write down the new budget constraint. What is the consumption in period 1 and period 2? Display graphically. Could the consumer be worse off? Could the consumer be better off? Draw budget constraints such that for one of them consumer prefers to borrow and for the other - prefers to save. 3. Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin t r a d e s a t P1 > 0 in the first period…
Consider an overtime rule that requires that workers get paid double for any weekly hours over 40. Draw a picture that shows how a worker decides how much to work. Label everything in your picture and explain what is happening. Consider an investment that costs $100 and pays back $10 each year as long as the person making the investment is alive. Construct an equation for the net present value of the investment. An individual has a utility function, U = AX1 X2 where X1 and X2 are consumption of goods 1 and 2. The individual also faces a budget constraint. Show mathematically how an increase in Aa§ects the individualís decisions about consumption of each good.
Q83 Suppose Jillian spends $250 on books per year when her income is zero. As her income rises, she spends 8 percent of each additional dollar of income on books. The correct mathematical equation that describes the functional relation between her spending on books (B) and her income (Y) is... a. B = 250 + 8Y b. B = 250 + 0.02Y c. Y = 250 + 0.08B d. Y = 250 - 8Y e. B = 250 + 0.08Y Clear my choice
Suppose your current income is $90,000 and your future income is $110,000. The interest rate is 10%. a. Suppose your optimal bundle is to live “paycheck by paycheck”, draw the intertemporal budget constraint and optimal bundle in a graph, and mark the optimal bundle and maximum C1, C2.b. What if your MRTP is 1.05, how should you change your consumption? c. What if your MRTP is 1.2, how should you change your consumption?d. If the interest rate decreases to 5%, how should you change your consumption? If the interest rate increase to 15%, how should you change your consumption?
If preferences for pizza increase and the price of labor to produce pizza decreases, the equilibrium quantity of pizza will ____ and the equilibrium price of pizza will _____ . increase, increase decrease, be indeerminate increase, be indeterminate increase, decrease Assume an intertemporal budget constraint that shows how consumption can be traded off between two periods, t and t+1. Assume the consumer can save and borrow at the same interest rate of 10%. Assume the consumer collects income of $100 in each period. To gain an extra $10 dollars in period t+1, what must the consumer give up in period t? $11 $9.10 $1 $10 A convex indifference curve implies what type of behavior? diminishing marginal utility complementary goods perfect substitutes inferior goods
Which of the following two effects of a decrease in the tax rate on saving would raise savings? a. the income effect and the substitution effect b. the income effect but not the substitution effect c. the substitution effect but not the income effect d. neither the substitution effect nor the income effect
Ruby has the following utility function: U(X, Y) = X^3/4 , Y^1/4, where X is her consumption of food items, with a price of $10, and Y is her consumption of clothing items, with a price of $30. She plans to spend $360 on food and clothing over the next week. Using the Lagrange multiplier technique, determine the number of food and clothing items that will maximize Ruby's utility.
Given f(x,y) = 2x2 - 6xy + 9y2, and Px= 7, Py= 5 and income, I = 175. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) unanswered d. Based on the value of the Bordered Hessian, comment whether the objective function is maximized or minimized. Answer in one word.
You are given the following utility function: ? = ?? The budget is K100 and the price of X is K2 while the price of Y is K5. a) Derive the demand for X and Y by the Lagrange multiplier method. b) What will be the demand when all the prices are doubled and the income is doubled? c) What is the utility when the budget is increased by K1?
given f(x,y) = 9x2 - 2xy + 8y2, and Px= 12, Py= 1 and income, I = 165. Construct the budget contraint and Lagrange function and solve for the equilibrium values of x and y. (a) What is the equilibrium value of x? (Give your answer to two decimal places, if required) (b) What is the equilibrium value of y? (Give your answer to two decimal places, if required) (c) What is the value of the determinant of the bordered Hessian matrix? (Give your answer to two decimal places, if required) Question #2 Based on the value of the Bordered Hessian, comment whether the obejective function is maximised or minimised.
Empirical evidence suggests that many consumers tend to spend all of their current disposable income immediately. Is this irrational?
Suppose we wanted to investigate the saving and borrowing behavior of consumers. It’s not that difficult to extend our basic model. We can use the same framework as before, but define our two goods as “consumption in period 1” (horizontal axis) and “consumption in period 2” (vertical axis). a. Construct a budget constraint for a consumer who earns $100 in income in period 1 and $300 of income in period 2. Label this point E for the “Endowment” point. Assume that he can choose to save some income in period 1 to be used in period 2, or to borrow some income from period 2 to use in period 1. (Let’s imagine the consumer saves the money by putting it in a piggy bank and can borrow money from his parents, who don’t charge interest.)