Consider Uncle Rico who runs a small barbershop. Being a sharp guy, Uncle Rico p

Question

Consider Uncle Rico who runs a small barbershop. Being a sharp guy, Uncle Rico patented a unique type of haircutting shears (scissors). Being the only one who can sell these special shears, Uncle Rico is a monopolist in this niche shears market. Suppose, because it is an odd product, the market demand for these shears is nonlinear and given by, p(q) = 2q^-3 + 8. And since he runs a small operation, his cost function is quite simple, c(y) = 7.5y + 1. Write out the monopolist profit maximization problem Uncle Rico faces when choosing how many shears to sell. Solve for the optimal value of y that will maximize his profit from selling shears. At what price should he sell his shears? (Technically at what price will the market let him sell y" number of shears?) At the optimal level of output and the corresponding price, how much profit is Uncle Rico making?

Explanation / Answer

Profit = Total Revenue - Total Cost = P.Q - TC

= (2q^-3 + 8)*q - (7.5q + 1)

= 2q^-2 + 8q - 7.5q -1

profit = 2q^-2 + 0.5q - 1

this is the profit maximization equation

dProfit/dq = -4q^-3 + 0.5

Putting dProfit/dq = 0

q^3 = 4/0.5 = 8

q = 2

c. P = 2q^-3 + 8 = 2*2^-3 + 8 = 1/4 + 8 = 33/4

d. Profit = 2q^-2 + 0.5q - 1 = 2*2^-2 + 0.5*2 - 1 = 1/2 + 1 - 1 = 1/2

If you don't understand anything then comment , I'ill revert back on the same. :)

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