The XYZ Co sells shirts. Shirts with the company label on the tag are perceived to be of higher quality than shirts with the store's label. Yet, shirts are of identical quality regardless of label
The demand for perceived high-quality shirts is ph = 50 - qh. The demand for perceived low-quality shirts is pl = 10 + ph – ql. The firm can produce shirts at TC = qh + ql. How many shirts does the firm label as low quality and how many as high quality? What prices are charged?
The marginal cost of a shirt equals 1 regardless of label.
Setting MRh = MRl = 1 yields 50 - 2qh = 1 or qh = 24.5. Substituting into the demand function yields
ph = 25.50 for the brand-label shirts. For the store label, 10 + 25.50 - 2ql = 1 or ql = 17.25. The store-label shirts sell for 18.25.
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