Question

2. (35 ots)magine 20 years into the future when a perfectly competutive market for teleportation pads (denoted by a) has developed. There are many identical smali firms selling teleportation pads, each has the same cost function C()F+4q +3q2, where F represents the cost of capital used in teleportation pad productiorn a. Consider the short-run where capital is fixed such that F 1200. Determine the quantity a representative firm would produce if the market price is $130. What profits would it earn? in no more than two sentences explain why the firm would or wouldn't to shut down in the short run Now consider what would happen if the market price fell to $64. lf the firm chooses to produce, how much would it produce and what profits would it earn? in no more than two sentences explain why the firm would or wouldn't to shut down in the short-run. b. c. Do your answers to part (a and (b depend on the level of Justdy our eise rre than two sentences d. Suppose the demand for teleportation pads is given by Qa(P) 2400 2P and that initially there are 27 firms in the market. Give an expression for the short run market supply curve and solve for the equilibrium price and quantity.

Answer 1

a.

0(g) = 1 200 + 4g + 392, P = 1 30

$\small \pi=pq-(1200+4q+3q^2)\rightarrow \pi'=0=p-4-6q\rightarrow q=\frac{p-4}{6}$

Plugging the value of P, we get:

126 9621

Profit = π = 2730-1200-4(21)-3(21 )2-2730-1200-84-1 323 = 1 23

Revenue = pg 1 30 ® 21 = 2730

Hevenue>

Firm will not shut down

b.
π=64g-1200-49-392 → π' = 64-4-64→g=10

At q = 10,

Profit = π = 640-1200-4(10)-3(100)

which is a negative number. Hence, the firm will not produce anything when price falls to 64.

Revenue = 640, Revenue FC

Hence, the firm would shut down in the short run

c. No, the answers do not depend on FC because the firm cannot control the Ficed Cost, it can only take decisions based on the market price.

d.

Qdlp) 2400 2P,n 27

$\small C(q)=F+4q+3q^2$

$\small \pi_i=pq-F-4q-3q^2 \rightarrow \pi_i'=0=p-4-6q \rightarrow q=\frac{p-4}{6}$

Since there are 27 firms in the market,

$\small q=27(\frac{p-4}{6})=\frac{9p-36}{2}$

Plugging the value of q in the demand function, we get:

9p-36 = 2400-2p → 5p-4836 → p-967.2

At this p, q is:

$\small q=2400-2*967.2=465.6$

Each firm produces 17.24 units