10. Consumption and the real interest rate: According to the life-cycle/permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing consumption. To incorporate this channel into the model, suppose the consumption equation is given by
10. Consumption and the real interest rate: According to the life-cycle/permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing consumption. To incorporate this channel into the model, suppose the consumption equation is given by
Chapter1: Making Economics Decisions
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![**Consumption and the Real Interest Rate**
According to the life-cycle/permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing consumption. To incorporate this channel into the model, suppose the consumption equation is given by:
\[ C_t = \bar{a}_c \bar{Y}_t - \bar{b}_c (R_t - \bar{r}) \bar{Y}_t. \]
Assume the remainder of the model is unchanged from the original setup, as in Table 11.1.
**(a) Derive the IS curve for this new specification.**
**(b) How and why does it differ from the original IS curve?**
*(Hint: Think about the slope of the IS curve.)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe806c6de-9c77-40e2-a02e-3d58c6f3d9d9%2F06d97dc5-ad23-48d1-9f39-daf35b82d636%2Fhxn342e_processed.png&w=3840&q=75)
Transcribed Image Text:**Consumption and the Real Interest Rate**
According to the life-cycle/permanent-income hypothesis, consumption depends on the present discounted value of income. An increase in the real interest rate will make future income worth less, thereby reducing the present discounted value and reducing consumption. To incorporate this channel into the model, suppose the consumption equation is given by:
\[ C_t = \bar{a}_c \bar{Y}_t - \bar{b}_c (R_t - \bar{r}) \bar{Y}_t. \]
Assume the remainder of the model is unchanged from the original setup, as in Table 11.1.
**(a) Derive the IS curve for this new specification.**
**(b) How and why does it differ from the original IS curve?**
*(Hint: Think about the slope of the IS curve.)*
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