Assume a perfectly competitive market for nails, demand in the market is given by Qd = 70, whereas supply in the market is given by : Qs = 10 + 2p. If supply changes in the market to Qs = 20 + 2p, then the predicted change in the price elasticity of demand is:

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We start by restating the scenario and the answer choices to ensure clarity of what's being analyzed.
Question and options: In a perfectly competitive nails market, initial demand is Qd = 70 and initial supply is Qs = 10 + 2p. After a supply shift to Qs = 20 + 2p, which of the following describes the predicted change in the price elasticity of demand? Options are: No change; Price elasticity of demand increases; The predicted change cannot be determined; Price elasticity of demand decreases.
First, analyze the demand function. Here Qd is given as a constant 70, which means the quantity demanded does not respond at all to changes in price. This describes a perfectly inelastic demand, where the price elasticity of demand is zero (because elasticity is (dQ/dP) * (P/Q, and dQ/dP = 0 for a vertical or perfectly inelastic demand curve).
Next, consider how the change in supply affects the market. The supply curve shifts from Qs = 10 + 2p to Qs = 20 + 2p, which lowers the equilibrium price from p = 30 to p = 25, while the equilibrium quantity remains at Q = 70 (since 70 = 20 + 2p implies p = 25, and demand was fixed at 70).
Now evaluate each option in light of the demand condition:
- No change: This would be true if the price elasticity of demand remained the same after the supply shift. Given that the demand function is perfectly inelastic (Qd = 70 regardless of price), the elasticity remains zero before and after the shift. The elasticity value does not depend on the observed price change or the shift in supply in this setup, so it does not change.
- Price elasticity of demand increases: This would require the demand to become more responsive to price after the shift. Since Qd does not respond to price at all in this model, there is no mechanism for elasticity to rise; this option appears inconsistent with the given demand specification.
- The predicted change cannot be determined: Based on the information provided, we can determine elasticity precisely because Qd is constant, yielding elasticity zero regardless of price. Therefore the change is determinable.
- Price elasticity of demand decreases: This would imply the elasticity moves from some negative value toward zero or more negative, but with Qd constant, elasticity is already zero and cannot become more negative or decrease further.
In summary, given a perfectly inelastic demand with Qd = 70, the price elasticity of demand stays at zero no matter how supply shifts affect price and quantity in this setup. The reasoning shows why the other statements do not align with the specified demand form, and why the change cannot be characterized as an increase or decrease under this model.

Assume a perfectly competitive market for nails, demand in the market is given by Qd = 70, whereas supply in the market is given by : Qs = 10 + 2p. If supply changes in the market to Qs = 20 + 2p, then the predicted change in the price elasticity of demand is: Single choice

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