Answer to Question #56428 in Microeconomics for afy

Question #56428
Ben Laden Rugs, Inc., sells hand-made cotton rugs to tourists at a price of $50. Of this amount, $40 is profit contribution. Ben Laden is considering an attempt to differentiate his product from several other competitors by using high quality natural herb dyes. Doing so would increase Ben Laden’s unit cost by $15 per rug. Current annual profits are $35,000 on 1,000 rug sales.
A. Assuming average variable costs are constant at all output levels, what is Ben
Laden’s total cost function before the proposed change?
B. What will the total cost function be if high quality natural herb dyes are used?
C. Assume rug prices remain stable at $50. What percentage increase in sales would
be necessary to maintain current profit levels?
Expert's answer
P = $50, TP1 per unit = $40 is profit contribution, ATC2 = $15 per rug, TP1 = $35,000, Q1 = 1,000.
A. If AVC is constant, then Ben Laden’s total cost function before the proposed change was TC1 = (P - TP1 per unit)*Q + FC = (50 - 40)*Q + 40*1,000 - 35,000 = 10Q + 5000.
B. If high quality natural herb dyes are used, then TC2 = ATC2*Q + FC = 15Q + 5,000.
C. If rug prices remain stable at P = $50, the percentage increase in sales to maintain current profit levels would be:
TR2 - TC2 = TP1
50*Q2 - 15Q2 - 5,000 = 35,000
35Q2 = 40,000
Q2 = 40,000/35 = 1142.86 = 1143 units.

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