10. Beta, an accounting firm, competes against Kyklos Associates, another accounting firm in the market for consultancy services to commercial firms. Beta’s demand for its services is a function of its own pricing (pB), the pricing of Kyklos (pK) and the average profitability of its customers (R). This demand function is given mathematically below:

The total cost of Beta as a function of the aggregate number of services (q) it provides is:

TCB(q) = 5,000,000 + 300 ∗ q

a. Suppose that pB = pK = 10,000 and R = 100,000,000. Compute Beta’s demand for its services.

b. Estimate the elasticity of demand with respect to its price for the parameter values of part (a) above.

c. Due to the pandemic, the general profitability in the market has dropped to R = 40,960,000 and Kyklos has responded by slashing its price to pK = 8,000. Find the combination of price and quantity that maximizes Beta’s profit in this case.