You work for a company that makes specialized computer hardware. There is a competing firm that makes many of the same products as you, but sells a GPU that you have so far not been able to manufacture. One of your engineers approaches you, reporting that they have developed a GPU with equivalent performance. If you take the product to market, you will initiate a price war with your competitor. The low cost producer will drive the market price down to just below the MC of the highest cost producer taking the entire market, and earning a unit profit that represents the difference between the two firm's marginal costs.

Your engineers estimate that each GPU has a marginal cost of $3,000 to produce. You do not know your competitor's marginal cost. However, your marketing department has estimated the demand elasticity for the GPU ( = 1.2), and you that know your competitors GPUs sell for $30,000. And then, you remember the inverse elasticity pricing rule you learned in OTM 732:

mcpmc=(+11) and,

p=(1+1/mc)

A. Assuming that your competitor is setting optimal prices as a monopolist, use the inverse elasticity pricing rule to estimate their marginal cost. Can you offer a lower price than your competitor in a price war?

B. Assume that you can charge a price equal to your competitor's marginal cost (you are now engaging in price competition so the IEPR no longer applies), how much variable profit would you make on each unit?

C. Recall that the elasticity of demand depends on current prices and quantities. If your price war results in a lower price, the quantity sold may also increase dramatically. You want to generate a back of the envelope estimate of the conditions under which you can cover your fixed costs. If face a fixed cost of $10m to scale up production of the GPU. What is the minimum number of units would you need to sell for entry to be profitable?