Suppose that • y =100 (income today) y' = 150 (income tomorrow) • r = 10% (interest rate on bonds) • t = 10 (taxes today) • t' = 10 (taxes tomorrow) What is the lifetime budget constraint for the consumer? c + c'/1.1 = 250 %3D c + c'/1.1 = 230 %3D C + c' = 217.27 c + c'/1.1 = 217.27
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- In this hypothetical economy, there are two consumers living over two periods of life. Ann's incomes are $50,000 in both periods. Meanwhile, Bob earns nothing in the first period but $105,000 in the second period. Both of them can borrow or lend at the interest rate r. For simplicity, assume that there are no taxes. a)Assume that both Ann and Bob consume $50,000 in the first period and $50,000 in the second period. Write down the lifetime budget constraint for each consumer then calculate the interest rate r. Describe the economic behaviour of each consumer. b) Suppose the interest rate increases. What will happen to Ann's consumption in the first period? Is Ann better off or worse off than before the interest rate rises? Explain your answer using an appropriate diagram c) What will happen to Bob's consumption in the first period when the interest rate increases? Is Bob better off or worse off than before the interest rate increases? Explain your answer using an appropriate diagram.The rules of politics are not always the same as the rules of economics. In discussions of setting budgets for government agencies, there is a strategy called “closing the Washington Monument.” When an agency faces the unwelcome prospect of a budget cut, it may decide to close a high-visibility attraction enjoyed by many people (like the Washington Monument). Is this strategy economically efficient? In other words, does it minimize the utility loss from a budget cut? Explain. If this strategy is not economically efficient, what is the incentive to pursue such a strategy?Suppose that the economy of country 1 is characterized by the following behavioral equations: Variable Equation Consumption C=1234 +0.5 YD Investments I=1000 + 0.1 Y Government expenditures G= 100 Net exports Nx= 300-0.2 Y Where Y denotes the real GDP and YD denotes the disposable income (YD= Y-T). Suppose that the output gap in country is measured as -15000. What should be increase in government expenditure in order to close the gap and make the economy to reach its potential level of GDP?.
- If BC2 is the relevant budget constraint, which of the identified bundles (combinations of X and Y goods) can this consumer afford? A. A. B. B. C. C. D. D. E. E. F. F. G. G. H. H. I. I. J. J.1- A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow. Select one: True False 2-Assuming a mix of present and future consumption is preferred, ANY consumer who starts (i.e. has an endowment) at point A will gain utility from a rise in interest rates. Select one: True False 3-A consumer who starts at point B will want to borrow, but as little as possible in order to minimise the cost of interest. Select one: True False 4-If a consumer starts at point A, and then receives extra income in the present, this would appear as an outward shift of the budget constraint. Select one: True FalseAn investor with an initial endowment of $ 16,000 is confronted with the following productivity curve: C1= 240 (16,000 - C0)^0.5 where C0 denotes consumption at present, and C1 consumption in the future. Assume the interest rate (for borrowing and lending) is 20%. The investor's utility function, from which it is possible to derive his indifference curves, is defined as: U(C0,C1) =C0C1 How much will the investor invest in production? A)$16,000 B)$0 C)$10,000 D)$12,000
- 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.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.)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.
- Question 3 Consider the utility function of the form: ?=?1?1?2?2 Given the budget constraint: ?1?1+?2?2=? Show that the implied Marshallian demand curves are: ?1=?1(?1+?2)??1 ?1=?2(?1+?2)??2Given f(x,y) = 2x2 - 5xy + 5y2, and Px= 7, Py= 6 and income, I = 169. 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) (d) Based on the value of the Bordered Hessian, comment whether the obejective function is maximised or minimised.There are two candidates in an election that compete only on the education budget they will enact if elected. The budget can be any integer from $1 to $8 and the distribution of voters’ preferences over these outcomes is given below. For example, there are 2 voters that prefer a budget of $1, 4 voters that prefer a budget of $2, and so on. Furthermore, all voters have single-peaked preferences. Assume the candidates’ sole objective is to receive as many votes as possible. (Image Attached) a) Find a proposed budget for each candidate that constitutes an equilibrium. Explain.
