Consider the inter-temporal model of consumption studied in class, with two possible periods. Which statement is true?Group of answer choicesA consumer will never consume its endowment point (where c1 = m1 and c2 = m2)An interest rate rise increases the maximum possible first period consumption level.An interest rate rise always makes the individual better off.A rise in the interest rate rotates the inter-temporal budget constraint around the point at which it cuts the c2 axis.None of the above
Question
Consider the inter-temporal model of consumption studied in class, with two possible periods. Which statement is true?Group of answer choicesA consumer will never consume its endowment point (where c1 = m1 and c2 = m2)An interest rate rise increases the maximum possible first period consumption level.An interest rate rise always makes the individual better off.A rise in the interest rate rotates the inter-temporal budget constraint around the point at which it cuts the c2 axis.None of the above
Solution 1
The correct statement is: "A rise in the interest rate rotates the inter-temporal budget constraint around the point at which it cuts the c2 axis."
Here's why:
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In the inter-temporal model of consumption, a consumer makes decisions about how much to consume in the present (period 1) and how much to save for future consumption (period 2). The consumer's choices are constrained by their income in each period and the interest rate, which determines how much future consumption they can get from saving a unit of present consumption.
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The inter-temporal budget constraint shows all combinations of present and future consumption that the consumer can afford given their income, the interest rate, and the assumption that they spend all their income in the two periods.
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A rise in the interest rate means that the consumer can get more future consumption from
Solution 2
The correct statement is: "A rise in the interest rate rotates the inter-temporal budget constraint around the point at which it cuts the c2 axis."
Here's why:
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In the inter-temporal model of consumption, a consumer makes decisions about how much to consume in the present (period 1) and how much to save for future consumption (period 2). The consumer's choices are constrained by their income in each period and the interest rate, which determines how much future consumption they can get from saving a unit of present consumption.
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The inter-temporal budget constraint shows all combinations of present and future consumption that the consumer can afford given their income, the interest rate, and the assumption that they spend all their income in the two periods.
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A rise in the interest rate means that the consumer can get more future consumption from saving a unit of present consumption. This makes future consumption cheaper relative to present consumption.
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As a result, the inter-temporal budget constraint rotates around the point at which it cuts the c2 axis (the vertical axis representing future consumption). The higher the interest rate, the steeper the budget constraint.
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This doesn't mean that the consumer will necessarily be better off, as it depends on their preferences for present versus future consumption. And it doesn't necessarily increase the maximum possible first period consumption level, as this depends on the consumer's income. Finally, there's no reason why a consumer would never consume at their endowment point (where c1 = m1 and c2 = m2); this would just mean that they choose to consume their entire income in each period without saving or borrowing.
Similar Questions
Consider the inter-temporal model of consumption studied in class, with two possible periods. Assume that initially that an individual is a saver. If the interest rate rises, which statement is false?Group of answer choicesThe individual will never become a borrower.The individual will necessarily increase their savings.The individual must remain a saverThe individual could increase or decrease their savings, but she must remain a saver.
If Brian chooses to consume c0 = 8=7 in period 0, explainwhat his intertemporal budget set B1 ((c0; c1; c2)) will be in period 1.Show that the continuation of his original consumption plan (c1; c2) =(8=7; 8=7) is indeed the optimal consumption plan for him to choosein period 1 from this budget set. Explain what property of his choicebehavior does this reáect.Now suppose that Brian is a naive (quasi-)hyperbolic discounted utility max-imizer characterized by an ìinstantaneousîutility function u (c) = 2c c2=2,a long-term discount factor = 1=2, and a short-term discount factor (orpresent bias) = 0:5
Fixed-time period models are used when demand is variableGroup of answer choicesTrueFalse
Consider an economy at the steady state according to the Solow Growth Model with a per capita production function where n=0.04, d=0.08, and s=0.3. Suppose a change in the age profile of the population leads to a reduction of the savings rate to s=0.28. As a result,Group of answer choicesconsumption initially falls but then increases to a new steady state level of consumption that is above the the original.consumption initially falls and continues to decline until reaching the new steady state.consumption initially rises but then decreases to a new steady state level of consumption that is below the the original.consumption initially rises and continues to increase until reaching the new steady state that is above the original.
(b) (10 points) Utilizing the fact that his marginal utility of consumptionmu (c) = 2 c, show that in period 0 his optimal consumption plan(measured in millions of dollars) is(c0; c1; c2) = 87 ; 87 ; 87.(c) (5 points) Explain qualitatively how this optimal plan would changeif the interest rate was greater than 1. Explain qualitatively how thisoptimal plan would change if the interest rate was less than 1.(d) (10 points) If Brian chooses to consume c0 = 8=7 in period 0, explainwhat his intertemporal budget set B1 ((c0; c1; c2)) will be in period 1.Show that the continuation of his original consumption plan (c1; c2) =(8=7; 8=7) is indeed the optimal consumption plan for him to choosein period 1 from this budget set. Explain what property of his choicebehavior does this reáect.
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