Question

In a particular city there are a number of fruit vendors selling bags of mixed fruit. Suppose that each vendor has a marginal cost of R1.50 per bag of fruit sold an no fixed cost. Suppose the maximum number of bags of fruit that any one vendor can sell is 100 per day. a) If the price of fruit is R2, how many bags does each vendor want to sell? b) If the industry is perfectly competitive, will the price remain at R2 for a bag if fruit. If not, what will the price be? c) If each vendor sells exactly 100 bags of fruit a day and the demand for the fruit from venords in the city is Q= 4400-1200P, how many vendors are there?

Answer 1

a)

$n=\frac{1.5x_n-100}{x_n},$

b)

$R_2=\underset{ n \to \infin}{\lim}p(n)=\underset{ n \to \infin}{\lim}\frac{1.5x_n-100}{x_n}=1.5,$

c)

$Q=\frac{4400-1200\cdot 1.5}{100}=26.$