Question

What would be each of the First Order Conditions be for this function?

Intermediary (10 pts) 1) Let a retailer face long run consumer demand D(p) =(100-p) and wholesaler supply S(w)=(-1+4w). Assuming the retailer holds no inventories in the long run, the grocer is constrained to D(p) = S(w), a market clearing condition. a) What is the grocer's long run optimal bid-ask spread? (10 pts)

Answer 1

We are given that

Long run Consumer demand function is

D(p) = (100-p)

Long run Wholesaler supply function is

S(w) = (-1+4w)

We are also given that : D(p)=S(w)

i.e. (100-p)=(-1+4w)

100+1=4w+p

4w+p =101

Therefore the grocer's long run optimal bid ask spread will be

(4w+p)=101; w=(101-p)/4; p=(101-4w)