The LM curve is steeper the ______ the interest sensitivity of money demand and the ______ the effect of income on money demand. (This is a difficult question. If you do not have the answer, pls try your best guess, considering also going by elimination. Hint: Draw two LM curves with different slopes, one flatter and one steeper, and then compare the interest rate change for a given IS shift at the initial income level and the income change for the same IS shift at the initial interest rate level).

Question

The LM curve is steeper the ______ the interest sensitivity of money demand and the ______ the effect of income on money demand.   (This is a difficult question. If you do not have the answer, pls try your best guess, considering also going by elimination.  Hint:  Draw two LM curves with different slopes, one flatter and one steeper, and then compare the interest rate change for a given IS shift at the initial income level and the income change for the same IS shift at the initial interest rate level).

BlackTom AI · Accepted Answer

We start by restating the question and the options in our own words to focus on what is being asked: How does the LM curve respond to the through-the-middle effects of money demand sensitivity to interest rates and to income when the IS curve shifts? The prompt asks us to compare two features: (i) the interest sensitivity of money demand, and (ii) the responsiveness of money demand to income, and how these affect the slope of the LM curve and the magnitude of income changes for a given IS shift.

Option a: 'greater; greater' suggests that if money demand is more sensitive to the interest rate, and money demand responds more to income, the LM would be steeper and the income effect of an IS shift would be larger. However, higher interest sensitivity of money demand tends to make the LM steeper, not necessarily larger income responses. The combination 'greater; greater' would imply both a steeper LM and a larger income effect, but the standard intuition under liquidity preference is that higher interest sensitivity of money demand makes the LM steeper (larger changes in r for a given money market imbalance) while higher income sensitivity of money demand tends to reduce the slope of the LM for a given r, or at least change the way income translates into money demand; this option mixes two effects that do not align cleanly with the standard comparative statics for the LM.

Option b: 'greater; smaller' posits a steeper LM due to higher interest sensitivity of money demand, and a smaller income effect on money demand. If money demand is more responsive to income (larger income effect), the demand for money would rise more with income, which tends to reduce the LM slope (as changes in income translate into wallet changes that offset interest rate movements) or flatten the curve. This combination is inconsistent with the hint that compares a flatter vs steeper LM: making money demand more responsive to income usually reduces the slope of LM, not increases it, when considering a given IS shift.

Option c: 'smaller; smaller' claims a flatter LM from lower interest sensitivity and also a smaller income effect on money demand. A smaller interest sensitivity of money demand would indeed make the LM flatter, since money market equilibrates with less change in r for a given money supply/demand shift. If money demand is also less responsive to income, the income-driven component of money demand is dampened, which also tends to flatten the LM further. However, the hint asks us to compare two LMs with different slopes and seems to imply that the slope differences arise primarily from interest sensitivity; this option would produce a flatter LM on both dimensions, which is technically possible but does not capture the typical comparative scenario highlighted in the hint that links the slope more directly to interest sensitivity.

Option d: 'smaller; greater' indicates that a smaller interest sensitivity of money demand yields a flatter LM, while a greater responsiveness of money demand to income yields a larger impact of income on money demand, influencing the LM slope in the opposite direction to the interest sensitivity effect. Specifically, a smaller interest sensitivity of money demand means money demand reacts less to interest-rate changes, which flattens the LM. Conversely, a greater income sensitivity of money demand means that increases in income raise money demand more strongly, which amplifies the effect of IS shifts on the money market, leading to more pronounced income-driven changes and a steeper response in the LM relative to income changes. This combination aligns with the standard intuition: reducing interest-rate responsiveness lowers the slope of the LM, while increasing income responsiveness enhances the impact of income movements on money demand, producing a larger adjustment for a given IS shift at the initial income level and making the LM more sensitive to income variations.

In sum, each option attempts to describe the combined effects of two money-demand characteristics on the LM curve. The dominant intuition from the liquidity-preference framework is that lowering the interest-rate sensitivity of money demand tends to flatten the LM, whereas increasing the income sensitivity of money demand tends to heighten the LM’s response to income changes. When evaluated together, option d captures the opposite directions of the two effects in a way that matches this reasoning: a flatter LM from smaller interest sensitivity and a more pronounced income-driven response to IS shifts. The other options either overshoot or misalign these complementary effects, leading to inconsistent or less plausible implications for the LM’s slope and the magnitude of responses to IS shifts.

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A project has a required return of 12.6 percent, an initial cash outflow of $42,100, and cash inflows of $16,500 in Year 1, $11,700 in Year 2, and $10,400 in Year 4. What is the net present value?

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