Q1. Consider the following two-period model of consumption and saving: Utility = C1^0.5 + B*C2^0.5 C1 + C2/(1+r) = Y1 + Y2/(1+r) where Y1 = 4, Y2 = 1, r = 0.17 and B = 0.5. Find a numerical solution for period 1 consumption, C1.
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Q1. Consider the following two-period model of consumption and saving:
Utility = C1^0.5 + B*C2^0.5
C1 + C2/(1+r) = Y1 + Y2/(1+r)
where Y1 = 4, Y2 = 1, r = 0.17 and B = 0.5.
Find a numerical solution for period 1 consumption, C1.
(State your answer to 2 decimal places.)
Step by step
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- Explain the term random walk in consumption. Under what conditions will consumption follow such a behavior? Aggregate consumption varies less than GDP and aggregate investment varies more. Can you reconcile these observations with assumption that consumption and investment decisions are taken by rational forward-looking agents? How do changes in r affect expected consumption growth? Interpret the effect of r on expected consumption in the light of precautionary saving.In a two-period model, an individual earns and consumes C1 in period 1 and only consumes C2 in period 2. Suppose the saving interest rate is 3.3% and the income in period 1 is $4,500. Assuming consumption smoothing, the consumption (C1 or C2) for period 1 and period 2 should be $ A . Compute A.In a two-period model, an individual earns and consumes C1 in period 1 and only consumes C2 in period 2. Suppose the saving interest rate is 3.3% and the income in period 1 is $4,500. Assuming consumption smoothing, the consumption (C1 or C2) for period 1 and period 2 should be $ A . Compute A.In the Neoclassical model of determination of income in the long run we assumed that aggregate consumption was an increasing function of disposable income, , and nothing else. Suppose that instead we assume that consumption is an increasing function of disposable income, , and a decreasing function of the real interest rate, . Provide an economic rationale for making consumption a function of the real interest rate. How does this assumption change the national saving function relative to the benchmark model Using the model developed in (1), use a diagram for the market for loanable funds to describe what happens to national saving, national investment, and the real interest rate when government expenditure increases. Make sure to also explain in your own words the economic intuition of your results.
- Solve for Y2 in the two-period consumption model with the following given information: Y1 = 1,100 r = 3% C1 = 1,250 C2 = 1,400The life cycle model of consumption argues that people consume and save in different proportions as they age. Seniors tend to consume more than save as their lives adjust to the realities of old age. Assuming the hypothesis is true, how would the aging of the very large baby boomer generation affect consumption and income?Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…
- In the Neoclassical model of determination of income in the long run we assumed that aggregate consumption was an increasing function of disposable income, , and nothing else. Suppose that instead we assume that consumption is an increasing function of disposable income, , and a decreasing function of the real interest rate, . Provide an economic rationale for making consumption a function of the real interest rate. How does this assumption change the national saving function relative to the benchmark model?What is the Euler equation for consumption, and what is its economicinterpretation?In the discussion of the life-cycle hypothesis, income is assumed to be constant during the period before retirement. For most people, however, income grows over their lifetimes. How does this growth in income influence the lifetime pattern of consumption and wealth accumulation shown in Figure 17-12 under the following conditions? Consumers can borrow, so their wealth can be negative. Consumers face borrowing constraints that prevent their wealth from falling below zero. Do you consider case (a) or case (b) to be more realistic? Why?
- Jack and Jill both obey the two-period Fisher model of consumption. Jack earns $100 in the first period and $100 in the second period. Jill earns nothing in the first period and $210 in the second period. Both can borrow or lend at the interest rate r. a. You observe both Jack and Jill consuming $100 in the first period and $100 in the second period. What is the interest rate r? b. Suppose the interest rate increases. What will happen to Jack’s consumption in the first period? Is Jack better off or worse off than before the interest rate rose?What is the Euler equation for consumption and what is What is the Euler equation for consumption, and what is its economic interpretation? What is the Euler equation for consumption and what isExplain the Keynesian, saving-consumption relationship, and interpret consumption and saving functions on a single graph.
