Question

Suppose there are 1.000 identical firms producing diamonds. Let the total cost function for each firm be given by C(q, w) = q2 + wq, where q is the firm's output level and w Ls the wage rate of diamond cutters. If w = 10, what will be the firm's (short-run) supply curve? What is the industry's supply curve? How many diamonds will be produced at a price of $20 each? How many more diamonds would be produced at a price of $21? Suppose the wage of diamond cutters depend on the total quantity of diamonds produced. and suppose the form of this relationship is given by w = 0.002Q where Q represents total industry output, which is 1,000 times the output of the typical firm. In this situation, show that the firm's marginal cost (and short-run supply) curve depend on Q. What is the industry supply curve (in the long-run)? How much will be produced at a price of $20? How much more will be produced at a price of $21? What do you conclude about he shape of the short-run supply curve?

Answer 1

For the price of $20 = $3,333.33

For the price of $21 = $3,500

Kindly go through the explanation for the other answers required.

Step-by-step explanation:

(a)

C = q2 +wq = q2 + 10q

Firm's short run supply curve is its marginal cost (MC) schedule.

MC = dC / dq = 2q + 10

So, supply curve is: p = 2q + 10

Or,

q = (p - 10) / 2 = 0.5p - 5

Total industry supply, Q = 1,000 x q = 500p - 5,000

p = (Q + 5,000) / 500 [Industry supply curve]

When p = 20, Q = 500 x 20 - 5,000 = 5,000 [Number of diamonds supplied]

When p = 21, Q = 500 x 21 - 5,000 = 5,500

So, when P = 21, 500 more diamonds will be supplied.

(b)

(i)

If w = 0.002Q then

w = 0.002 x (1000q) [Since Q = 1000q]

w = 2q

C = q2 +wq = q2 + (2q)q = 3q2

So, MC = dC / dq = 6q

MC = 6 x (Q / 1000)

So, MC depends on Q.

(ii)

Long run supply schedule is when price = MC

p = 6q = 6 x (Q / 1000)

p = 3Q / 500 [Long run industry supply schedule]

(iii) When p = 20, Q = p x (500/3) = 20 x 500 / 3 = 3,333.33

(iv) When p = 21, Q = p x (500 / 3) = 21 x 500 / 3 = 3,500

(v) Short run supply curve is the positive part of MC.

p = 6q

Therefore, the SR supply curve is a straight line from origin, sloping upwards.