In an economy, C = 50 + 0.75Y and planned investment is 50. Producers plan to produce an output of 500, and households consume as planned. Which of the following is correct at this output?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Ex ante aggregate demand is 475; ex post investment is 75, so ex post output still equals ex post consumption plus ex post investment.
Given:
C = 50 + 0.75Y
Planned I = 50
Planned output = 500
Planned output (500) is more than planned demand, so the unsold part piles up as unintended inventories. These are counted in ex post investment, so the accounting identity still holds.
\( AD = 50 + 0.75 \times 500 + 50 = 475 \)
\( \text{Unsold output} = 500 - 475 = 25 \)
\( \text{Ex post } I = 50 + 25 = 75 \)
\( \text{Ex post } C + I = 425 + 75 = 500 \)
Option (1) Ex ante aggregate demand is 500, so the economy is in equilibrium at this output. — Incorrect. Ex ante AD is 475, below 500, so this output is not an equilibrium.
Option (2) Ex ante aggregate demand is 475; ex post investment is 25, so ex post output still equals ex post consumption plus ex post investment. — Incorrect. Ex post investment is planned 50 plus the unsold 25, not 25 alone.
Option (3) Ex ante aggregate demand is 475; ex post investment is 50, so ex post output exceeds ex post consumption plus ex post investment by 25. — Incorrect. Ex post output and ex post C + I are always equal; the 25 shows up inside ex post I.
Option (4) Ex ante aggregate demand is 475; ex post investment is 75, so ex post output still equals ex post consumption plus ex post investment. — Correct. AD is 475, ex post I is 75, and 425 + 75 = 500.
NCERT (2026-27): “4.2 Determination of Income in Two-sector Model … If ex ante demand for final goods falls short of the output of final goods that the producers have planned to produce in a given year, equation (4.3) will not hold. Stocks will be piling up in the warehouses which we may consider as unintended accumulation of inventories. It should be noted that inventories or stocks refers to that part of output produced which is not sold and therefore remains with the firm. Change in inventory is called inventory investment. It can be negative as well as positive: if there is a rise in inventory, it is positive inventory investment, while a depletion of inventory is negative inventory investment. The inventory investment can take place due to two reasons: (i) the firm decides to keep some stocks for various reasons (this is called planned inventory investment) (ii) the sales differ from the planned level of sales, in which case the firm has to add to/run down existing inventories (this is called unplanned inventory investment). Thus even though planned Y is greater than planned C + I, actual Y will be equal to actual C + I, with the extra output showing up as unintended accumulation of inventories in the ex post I on the right hand side of the accounting identity.” |