Answer to Question #88984 in Economics of Enterprise for Nana Yaw

Question

Most weeks, the demand for long-stem roses can be approximated by QD = 2400 -
50p, where QD is the total quantity demanded (in dozens) at price p (per dozen).
Currently, roses are supplied by 100 identical growers, each having total costs
C=0.25q2
+0.5q+36, where q is the number of roses (again, in dozens) supplied by
the grower. The $36 cost can be avoided on a daily basis.

(a) What is the short-run supply curve for each individual grower? Describe this
curve both algebraically and graphically.

(b) Derive the short-run market supply schedule, which gives quantity supplied as a
function of price.

(c) What is the equilibrium price for a dozen roses in this market? Sketch the market
supply and market demand schedules.

(d) How many dozens of roses will be supplied by each grower?

(e) Assuming there is free entry into and exit from this market. Will there be entry or exits from this market going into the long-run? Explain your answer.

Answer 1

(a) The short-run supply curve for each individual grower is a portion of MC curve above the intersection with AVC curve.

MC = C' = 0.5q + 0.5.

So, MC = p = 0.5qs + 0.5,

qs = 2p - 1.

(b) The short-run market supply is Qs = 100qs = 200p - 100, so its schedule is:

p Qs

0.5 0

5 900

10 1900

15 2900

(c) In equilibrium Qd = Qs, so:

2400 - 50p = 200p - 100,

250p = 2500,

p = $10 for a dozen roses in this market.

(d) qs = 2*10 - 1 = 19 dozens of roses will be supplied by each grower.

(e) To answer this question we need to know if the firms receive profits.

The formula for total profits is TP = (p - ATC)*q.

ATC = C/q = 0.25q + 0.5 + 36/q = 0.25*19 + 0.5 + 36/19 = $7.14.

So, p > ATC and firms will receive profits.

If there is free entry into and exit from this market, then there will be entry to this market into the long-run.