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- The consumption and saving functions in the Keynesian model Suppose we observe that a person's disposable income (DI) is 50,000 in 2019 and 63,000 in 2020. Suppose we observe that this person's consumption (C) is 47,000 in 2019 and 58,700 in 2020. Assume that this person's consumption obeys the Keynesian consumption function, so that C = A + MPC*DI. Finally, assume that A and MPC are unchanged between 2019 and 2020. (a) Calculate the values of A and MPC for this consumer, and graph the consumption function. (Hint: subtract the C function in 2019 from the C function of 2020). (b) In general, saving is given by the formula S = DI - C. Calculate this person's saving in 2019 and 2020. Assuming that this person's wealth (net worth) on January 1, 2019 was 80,000, what is their wealth on January 1, 2020? on January 1, 2021? (c) In general, if consumption is given by the function C = A + MPC*DI, then saving will obey the saving function S = -A + (1 - MPC)*DI. Plot the saving function…What happens in the simple Keynesian model if households expect lower income in the future and decide to save more today? Adjust the graph and answer the question. Assume that investment varies directly with aggregate income. Aggregate expenditure (in billions of dollars) 10 9 8 7 5 4 3 2 1 0 0 1 2 3 4 5 6 7 Aggregate income (in billions of dollars) 8 9 AE = AI C+1 10The 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?
- 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.Consider the following model. Expenditure is given by: E = C +1 + G. The consumption function is specified as: C = c0 +cY. We assume a closed macroeconomics system so that: Y=E. If the model parameters are configured such that I= 500, G=2000, c0=1000 and c=0.8, what will the level of consumption expenditure, C, be equal to? a. 4,375 b. 15,000 c. 14,000 Cd. 14,500Consider the two-period Neoclassical growth model seen in class. Suppose that income is measured in dollars. Let the utility function take the logarithmic form U(C)=In C. Suppose that Y, = $50,000, and Y2 = $30,000, and B 1 and R= 5%. %3D B.1 What is the value of lifetime income in terms of dollars today? B.2 Compute the consumption in dollars for period 1 and period 2.
- You can use the AE model to show that an increase in government purchases can increase output but in many cases it is hard to find useful things for the government to quickly spend money on. Many people in Boston say "the T is so slow, why not spend it on building or replacing the subway lines?" but new subways lines can take years to plan. A fast alternative is to cut net taxes by sending people transfer payments. Consider a standard AE model with this consumption function, C=4+0.5Y-bT and unknown and unimportant values for planned investment and planned government purchases. What is the "T multiplier," which is defined as the change in equilibrium income per $1 increase in taxes? -b -2b +b +2b O O O OConsider the two-period Neoclassical growth model seen in class. Let the utility function take the logarithmic form U(C)=In C. A.1 Express the Euler condition under logarithmic utility. A.2 What does the growth rate of consumption depend on under logarithmic utility? Let W denote the total lifetime income in terms of consumption today. A.3. Derive expressions for consumption in period1 and period 2 as a function of W.Explain the Keynesian, saving-consumption relationship, and interpret consumption and saving functions on a single graph.
- Consider the following two-period consumption-saving model: Max C (BC2)}, C1,C2 subject to the following constraints Y1 = C1+S, Y2 = C2 – (1+r)S. 1. Solve for the intertemporal budget constraint 2. Draw the budget constraint (in a graph) with Y1 = 140, Y2 = 70, and r=0.25. Be sure to label the maximum values of C¡ and C2 on the y-axis and x-axis. 3. Suppose that ß = 0.8, solve for the optimal values of consumption, C and C5. %3D 4. Compare your consumption function for period 1 to a consumption function suggested by John Maynard Keynes (the so-called Keynesian consumption function). Are they different? 5. When r does down, how does C1 change? Does it increase or decrease? Show this mathe- matically. 6. Compute the marginal propensity to consume in period 1. Does this fall in the range sug- gested by Keynes?In the Keynesian-cross analysis, if the consumption function is given by C=100+0.6(Y-T),and planned investment is 100,G is 100, and T is 100,then the equilibrium Y is: Select one: a. 400 b. 350 c. 750 d. 600Explain the relationship between consumption and saving in the Keynesian model.