Advanced: Calculation of optimum selling prices using differential calculus Cassidy Computers pic sells one of its products, a plug-in card for personal computer systems, in both the UK and Ruritania. The relationship between price and demand is different in the two markets, and can be represented as follows:

Home market: Price (in £) = 68 — 8(91 Export market: Price (in $)= 110 — 10(92 where Ql is the quantity demanded (in 000) in the home market and Q2 is the quantity demanded (in 000) in the export market. The current exchange rate is 2 Ruritanian dollars to the pound.

The variable cost of producing the cards is subject to economies of scale, and can be rep¬ resented as:

Unit variable cost (in £) = 19 - (9 (where Q =

<21 + Ql).

Requirements

(a) Calculate the optimum selling price and total contribution made by the product if it can be sold

(i) only in the home market

(ii) only in the export market

(iii) in both markets. (10 marks)

(b) Calculate the optimum selling prices and total contribution made by the product if it can be sold in both markets, but subject to a constraint imposed by the Ruritanian govern¬ ment that the company can sell no more cards in Ruritania than it sells in its home market. How sensitive are the prices to be charged in each market and the total contribution, to changes in the exchange rate over the range $1 =£0.25 to $1 =£1.00? (8 marks)

(c) How does the volatility of foreign exchange rates affect the ways in which export sales are priced in practice?

LO1