5. Your company has monopoly over product H. It sells it in the UK and in the US. The total cost function for your firm is TC = 10q, and your marginal cost curve is MC = 10.

Your marketing department has identified the UK and the US demand curves for H to be

q_US = 50,000 2,000P_US

q_UK = 10,000 - 500P_UK,

where q_US and q_UK represent the quantities demanded by US and UK consumers respectively, and

P_US and P_UK the (US dollar) prices charged for the product in the US and in the UK, respectively. Note these are demand functions, not inverse demand functions!

a. If you could charge different prices in the US and the UK what prices would you choose and

how many units would you sell in the US and how many in the UK?

b. What is the own price elasticity of demand in the US market at the quantity and price you have determined in part a? Prove that the inverse elasticity pricing rule holds at your chosen P_US and a.