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1- A consumer who starts (i.e. has an endowment) at point B, and has preferences shown by IC1, will want to borrow.
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- I JUST WANT THE DIAGRAM FOR EACH PART. PLEASE DRAW THE DIAGRAMS, DONT TYPE IT!!!!!! WRONG ANSWERS WILL BE REPORTED. Consider the representative consumer who decides consumption and leisure. The preference is given by U (C,L) = αln C + (1 −α) ln L. Assume h = 1, i.e., the time endowment is one day. Suppose the non-wage income π −T increases while the wage rate w falls at the same time. The size of the changes can be different. Determine the effects on consumption demand and labour supply (i.e., leisure demand). Use the indifference map to explain your results in terms of income and substitution effects for the following cases: (i) The increase in π −T exactly cancels out the drop in w, i.e., |∆ (π −T)|= |∆w|. (ii) The increase in π −T is greater than the drop in w, i.e., |∆ (π −T)|> |∆w|. (iii) The increase in π −T is smaller than the drop in w, i.e., |∆ (π −T)|< |∆w|.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.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.
- Consider a model in which individuals live for two periods and have utility functions of the form U = In(C1) + In(C2). They earn income of $100 in the first period and save S to finance consumption in the second period. The interest rate, r, is 10%. 1. Set up the individual's lifetime utility maximization problem. Solve for the optimal C1, C2, and S. (Hint: Rewrite C2 in terms of income, C1, and r.) Draw a graph showing the opportunity set. (5 marks) 2. The government imposes a 20% tax on labor income. Solve for the new optimal levels of C1, C2, and S. Explain any differences between the new level of savings and the level in part (a), paying attention to any income and substitution effects. 3. Instead of the labor income tax, the government imposes a 20% tax on interest income. Solve for the new optimal levels of C1, C2, and S. (Hint: What is the new after tax interest rate?) Explain any differences between the new level of savings and the level in a, paying attention to any income…In a two-good market, a consumer starts with an initial endowment of (x₁, x2) = (15.00, 5.00), while the market prices for these goods are given by (P1, P2) = (7.00, 3.00). The consumer has the following utility function: U 0.52 0.48 - Given this information, what will this consumer's final choice of quantity for each good be? x1 = x2 =question ii
- Solve all this question......you will not solve all questions then I will give you down?? upvote...A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.Suppose an individual makes consumption and savings decisions in two time periods (1 and 2). Its utility function is given by: U = In addition, the prices and income of said individual and the interest rate he faces are known: P1 = 1, P2=3; M1 = 100, M2 = 200 r=0.23 Determine: a) The budget constraint and plot b) Optimal demand functions c) The savings supply function d) In equilibrium, will the individual be a lender or a borrower?
- Fred is planning his consumption over two time periods. Fred's preferences for consumption in period and two can be represented by the following utility function: U(c,,c,) = C +(1+p) C" , where pis the subjective discount rate, and c;,c, is consumption in the first and second period. Fred's income in the first period is y, and grows by g % from the first period to the second period. Fred has access to perfect financial markets. The rate of interest is r>0. (a) Derive Fred's demand functions for consumption in the two periods as functions of p,r , y and g. (b) Derive Fred's demand for borrowing/saving as a function of p,r, y and g. (c) Give a condition involving the relationship between r and g for when Fred will borrow and when he will save.A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.If your utility function is the following form: U(c) = c1 + B c2, where c1 is the consumption in period 1, c2 is the consumption in period 2, the time-preference parameter, B= 1 and period l's endowments el= 500 and period 2's endowments e2 = 400, what is the optimal consumption in each period if (a) the interest rate (r) is zero, and (b) the interest rate (r) is positive? %3D
