Consider the following model of the IS curve without an international sector:

Consumption:
𝐶
𝑡
𝑌
¯
𝑡
=
𝑎
¯
𝑐
−
𝑏
¯
𝑐
(
𝑅
𝑡
−
𝑟
¯
)
;

Investment:
𝐼
𝑡
𝑌
¯
𝑡
=
𝑎
¯
𝑖
−
𝑏
¯
𝑖
(
𝑅
𝑡
−
𝑟
¯
)
; and

Government expenditure:
𝐺
𝑡
=
𝑎
¯
𝑔
𝑌
¯
𝑡
.

Note that
𝑏
¯
𝑐
can be a positive or negative real number.

With this formulation, the IS curve is:

Question

Consider the following model of the IS curve without an international sector:

Consumption: 
𝐶
𝑡
𝑌
¯
𝑡
=
𝑎
¯
𝑐
−
𝑏
¯
𝑐
(
𝑅
𝑡
−
𝑟
¯
)
;

Investment: 
𝐼
𝑡
𝑌
¯
𝑡
=
𝑎
¯
𝑖
−
𝑏
¯
𝑖
(
𝑅
𝑡
−
𝑟
¯
)
; and

Government expenditure: 
𝐺
𝑡
=
𝑎
¯
𝑔
𝑌
¯
𝑡
.

Note that 
𝑏
¯
𝑐
 can be a positive or negative real number.

With this formulation, the IS curve is:

BlackTom AI · Accepted Answer

First, let's restate the setup in my own words to ensure clarity: we have a model of the IS curve without an international sector, with consumption C_t given as a function of output and the real interest rate through the form C_t/Y_bar_t = a_c_bar − b_c_bar (R_t − r_bar), investment I_t/Y_bar_t = a_i_bar − b_i_bar (R_t − r_bar), and government expenditure G_t = a_g_bar Y_bar_t. The note that b_bar_c can be either positive or negative means the consumption response to the real rate can go either way. The question asks what the IS curve looks like (i.e., its slope or orientation) given this formulation.

Option 1: 'horizontal.' A horizontal IS curve would imply that Y_bar_t is completely insensitive to the real interest rate R_t, so changes in R_t do not affect equilibrium output. In this model, both C and I depend on (R_t − r_bar), which in turn would influence aggregate demand. However, without the explicit equilibrium condition linking Y_bar_t to C_t, I_t, and G_t (i.e., the national income accounting identity Y_bar_t = C_t + I_t + G_t in the absence of NX), we cannot deduce that the resulting relationship is perfectly flat. Therefore claiming a horizontal IS curve without further information is premature.

Option 2: 'vertical.' A vertical IS curve would mean output is completely unresponsive to changes in the real interest rate, which again would require that aggregate demand be completely independent of R_t or that the model pins Y_bar_t to a fixed level regardless of R_t. Given the C and I expressions depend on (R_t − r_bar), one would expect some response of demand to changes in R_t, unless other terms dominate or the equilibrium condition fixes Y_t. Without the explicit functional form of the equilibrium condition, a vertical slope cannot be established.

Option 3: 'less steeply sloped than the “standard” IS curve.' A less steep (flatter) IS would occur if changes in R_t have a smaller effect on Y_bar_t than in a standard benchmark. In this setup, C and I both respond to R_t, which would tend to move the IS away from being perfectly vertical or horizontal, but the precise steepness depends on how strongly R_t affects desired spending versus how output adjusts through the equilibrium condition. Since we lack that equilibrium linkage, we cannot categorize the slope relative to a standard IS with confidence.

Option 4: 'more steeply sloped than the “standard” IS curve.' Conversely, a steeper IS would require that changes in R_t produce larger changes in Y_bar_t through the aggregate demand components. Again, because the model equations show R_t enters C and I but we do not have the exact IS equilibrium constraint (and because b_bar_c can be positive or negative, altering the sensitivity), we cannot assert a steeper slope over the standard benchmark without additional information.

Option 5: 'Not enough information is given.' This option acknowledges that, although the C_t and I_t equations specify how consumption and investment respond to the real rate, and G_t depends on Y_bar_t, the crucial link is the equilibrium condition that ties Y_bar_t to C_t, I_t, and G_t to determine the IS locus. Without explicitly solving the IS relation or knowing the relative magnitudes and signs of the responses, the slope of the IS cannot be uniquely determined from the information provided. Thus, this option correctly points out the missing piece needed to deduce the IS curve's exact orientation.

In summary, the other four options presuppose a specific slope or orientation for the IS curve that cannot be justified with the given information. The key gap is the explicit equilibrium relationship that translates the components C, I, and G into a function of Y_bar_t and R_t. Since that linkage is not provided, we cannot determine whether the IS curve is horizontal, vertical, flatter, or steeper than a standard benchmark. This is why the most appropriate answer here is not enough information to ascertain the IS curve’s slope.

FA25 ECON 302 002 Final Exam (Chapters 7-9, 11-13, 19-20): Sample Questions

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Similar Questions

To (exactly) offset this demand shock, the Federal Reserve lowers the real interest rate by 0.4 percentage points at time 𝑡 = 2 . Based on this information, you know that the value of 𝑏 ¯ in the IS curve equals ______.

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