Question

Suppose the market demand and supply functions are Qd= 32,000-20P and Qs=30P+750. You have just graduated and moved to this city; as a new MBA and an entrepreneur, you are considering entering the market for this product.
a. Determine the equilibrium price and quantity in this market.

b. TC=5000+1000Q-12Q^2+0.08Q^3. Determine whether or not you should enter this market.

c. Due to unforeseen delays, you don’t enter the market. However, a year later the market supply has changed to Qs=30P+1500. Are you surprised at this shift in supply?

d. Given the new supply conditions, determine whether or not you should enter the market.

Answer 1

a.

Qd = Qs

32,000 – 20P = 30P + 750

32,000 – 750 = 30P + 20P

31,250 = 50P

31,250 / 50 = P

P = 625

Now, this is to be placed in either Qd or Qs,

Qd = 32,000 – 20P

Q = 32,000 – 20 × 625

    = 32,000 – 12,500

    = 19,500

Answer: equilibrium price is 625 and quantity is 19,500 units.

b.

If AVC is smaller than price (625), the firm should enter the market.

Given,

TC = 5000 + 1000Q – 12Q^2 + 0.08Q^3

Hence,

TVC = 1000Q – 12Q^2 + 0.08Q^3

AVC = TVC / Q

            = (1000Q – 12Q^2 + 0.08Q^3) / Q

            = 1,000 – 12Q + 0.08Q^2

Now, (Q = 19,500) should be placed.

AVC = 1,000 – 12Q + 0.08Q^2

            = 1,000 – 12 × 19,500 + 0.08 × 19,500^2

            = 1,000 – 234,000 + 0.08 × 380,250,000

            = 1,000 – 234,000 + 30,420,000

            = 30,187,000

Since AVC is too high, the firm will incur a huge loss; therefore, should not be entered.

c.

Yes; it is surprising; although AVC is too high, firms are still entering, making the supply high.

d.

New equilibrium should be calculated first.

Qd = Qs

32,000 – 20P = 30P + 1500

32,000 – 1500 = 30P + 20P

30,500 = 50P

30,500 / 50 = P

P = 610

Now, this is to be placed in either Qd or Qs,

Qd = 32,000 – 20P

Q = 32,000 – 20 × 610

    = 32,000 – 12,200

    = 19,800

Equilibrium price is 610 and quantity is 19,800 units.

Now, (Q = 19,800) should be placed in AVC.

AVC = 1,000 – 12Q + 0.08Q^2

            = 1,000 – 12 × 19,800 + 0.08 × 19,800^2

            = 1,000 – 237,600 + 0.08 × 392,040,000

            = 1,000 – 237,600 + 31,363,200

            = 31,126,600

AVC is still very high; therefore, there should not be entry.