Advanced: Calculation of optimum selling prices using differential calculus

(a) Some businesses which supply two or more markets from a single source charge a higher price for sales to the home market than for export sales. They may justify this pricing policy by saying that they need to recover their research and development costs, plus production overheads. against home demand.

You are required to explain briefly the rationale for such a differential pricing policy and to comment critically on it.

(5 marks)

(b) The Jackass Motor Company of Ruritania has just developed a new motor car called the Midi which it is planning to launch in the near future_ The home market in Ruritania is highly competitive. and prices are low by international standards. In contrast, the neighbouring country of Lusitania tends to have much higher car prices.

These are largely the consequence of Lusitanian Government efforts to assist the relatively inefficient domestic motor industry in Lusitania. Government regulations have been imposed in both countries, for reasons for safety, which make it impossible for anyone other than a motor manufacturer to import or export cars between the two markets. It would be quite possible, therefore, for Jackass to charge different prices in the two markets if it considered it profitable to do so. Market research has indicated that demand functions for the two countries are likely to be:

Ruritania: Price (£) = 4.940 - 0.050 Lusitania: Price (£) = 6.000 - 0.100 where 0 represents monthly sales quantities. Jackass's single plant is close to the border between the two countries, so that its costs are unaffected by any decision to switch car supplies from one market to IM other. Its total cost function for Midi production has been estimated as:

Total cost(£)= 50 million + 2,0000 + 0.01Q²

where 0 again represents monthly quantities.

All Lusitanian sales prices have been converted back into Ruritanian pounds. The two countries have a fixed exchange rate, and Jackass's decisions will not be affected by taxation considerations. Jackass seeks to maximize its profits.

You are required to:

(i) calculate Jackass's monthly profit or loss if it confines its sales solely to its home market of Ruritania, (5 marks)

(ii) calculate the monthly profit or loss should it decide to sell in both Ruritania and Lusitania, (8 marks)

(iii) set out and explain the changes in both price and monthly quantity sold in Ruritania, and in total monthly profits or losses of Jackass, by comparing your answers to (i) and (ii)

above.