Problem 4 - Costless Magical MacGuffin
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)
Assume this consumer cannot borrow.
1. What is the consumption in period 1 and period 2? Display graphically. Show the corresponding utility
curve.
Assume that now the consumer is allowed to save or borrow.
2. 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.
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 MacGuffins trade at P1 > 0 in the first period, and is expected to trade at P2$ in the second period.
3. Write down the new budget constraint.
4. Under what conditions would a consumer borrow and then sell a MacGuffin? Would they be better
off with this option?
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- Problem 4 - Costless Magical MacGuffin Consider a consumer that lives only for two periods. He works in period 1 (and gets income ₁) and moves up the corporate ladder in period 2 (and gets income ₁ 0 in the first period, and is expected to trade at P₂ in the second period. 3. Write down the new budget constraint. 4. Under what conditions on P₂ would a consumer borrow and then sell a MacGuffin? Would they be better off with this option?arrow_forwardConsider an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J a) Plot an Edgeworth box and mark the initial endowment point. b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments. c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box. d) Suppose Gillian and Joana can “trade” consumption in both periods at pricesp1,p2. Find the competitive equilibrium (6 numbers) and depict the equilibrium allocation in the Edgeworth box. e) Using the MRS condition from part b),…arrow_forwardHow does savings change with changes in y2? Provide some intuition behind this result.arrow_forward
- Please *provide and *recheck *clear and complete *step-by-step solutions in *scanned handwriting or *computerized output. Thanks.arrow_forward2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?arrow_forwardHandwritten solution not required correct answer will get instant upvote.arrow_forward
- 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.arrow_forwardConsider a consumer who can borrow or lend freely at an interest rate of 100% per period of time (think of the period as being, say, 30 years, a bit like with a mortgage). So r = 1.0, or 100%. The consumer's two-period utility function is: U = In(ct) + (1/2)In(Ct+1) The consumer earn Y=100 each period, so Y₁=100 and Yt+1 also equals 100. If this consumer is behaving optimally, trying to maximize her lifetime utility subject to the IBC, what's her consumption in period t?arrow_forward6. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmicarrow_forward
- 2nd attempt See Hint A consumer faces a tradeoff between labor (L) and leisure (R). She consumes a composite good (C). When the consumer works, she earns an hourly wage of $15.00, and she spends a maximum of 24 hours on labor and leisure, but she chooses to work 10.00 hours. Whatever time she does not spend working, she spends on leisure. She starts with an initial endowment of 11.00 units of the composite good, which she can buy and sell freely at a market price of $4.00. Given this information, what is the consumer's real wage? $ 194arrow_forward1. Consider a two-period model in which you work and save in the initial period (period 0) and live off savings and the interest from savings in retirement (period 1). Suppose that income in period 0 is $250,000, income in period 1 is $0, and the interest rate is 50%. a. Draw the budget line. b. Draw an indifference curve consistent with a person whose preferences causes them to equalize their consumption in period 0 and period 1. c. Savings are $_ d. Draw the after-tax budget line if a personal income tax is introduced with a marginal tax rate of t= 40%. e. Suppose that preferences are such that after tax consumption is equalized in period 0 and period 1. On the diagram show after-tax savings. Сі ($x 1,000) 450 400 350 300 250 200 150 100 50 25 50 75 100 125 150 175 200 225 250 275 300 325 350 Со ($ x 1,000)arrow_forwardFred 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.arrow_forward
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