XYZ manufactures a product called the X. During recent months the X has been sold at a
unit price of around £6.25, with small adjustments to this price being made in order to try
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and find a profit-maximizing selling price.
Consultants engaged by XYZ have reported that at a unit price of £10 there is no
demand for Xs but that demand increases by 40 Xs for each 1p that the unit price is reduced
below £10. The consultants have further reported that ‘when demand is at around half its
theoretical maximum the elasticity of demand is 1’.
Upon receiving this report XYZ’s commercial manager makes the following statement:
Recent experience gained in adjusting the unit selling price of the X suggests that the product has quite an elastic demand structure. Small changes in the unit selling price produce far larger proportionate increases in demand. I do not believe that the elasticity of demand for the X is only 1.
(a) Reconcile the consultants’ report with the commercial manager’s observations concerning
the elasticity of demand for the X.
(b) The consultants have determined that the profit-maximising price is £5.75. Calculate
(i) The profit-maximising sales volume for the X;
(ii) The elasticity of demand for the X at a price of £5.75.
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