Question

Week 7 Worksheet 1) Imagine that you work for a firm that sells good x in a perfectly competitively market You know that you are one of 100 firms in this market and that they all have the same short run individual supply function: q10 Px 0.5 PL +K You also know that there is only one type of consumer, that there are 100,000 of them in the market, and that they have individual demand functions: 1 -0.5 P +0.05 1-0.1 Py x What is the Market Demand function? а. b. What is the (short run) Market Supply function? What is the Equilibrium Market Price? c. *(Assume that PL = 10, K 2, Py 2, and I = 200) d. What quantity should your firm produce and sell in the short run? e. At this short run equilibrium, what is the profit/loss the firm is making? *(Assume that L 5 and Pk 25) f. What will happen in this market in the long run? *(show graphically and describe in words)

Answer 1

a. Market demand, X = 100,000x = 100,000*(1 - 0.5Px + 0.05I - 0.1Py) = 100,000 - 50,000Px + 5,000I - 10,000Py
So, X = 100,000 - 50,000Px + 5,000I - 10,000Py

b. Market supply, Q = 100q = 100*(10Px - 0.5PL + K) = 1000Px - 50PL + 100K
So, Q = 1000Px - 50PL + 100K

c. At equilibrium, market demand = market supply
So, 100,000 - 50,000Px + 5,000I - 10,000Py = 1000Px - 50PL + 100K
So, 100,000 - 50,000Px + 5,000*(200) - 10,000*(2) = 1000Px - 50*(10) + 100*(2)
So, 100,000 - 50,000Px + 1,000,000 - 20,000 = 1000Px - 500 + 200
So, 50,000Px + 1,000Px = 100,000 + 1,000,000 - 20,000 + 500 - 200
So, 51,000Px = 1,080,300
So, Px = 1,080,300/51,000
So, Px = 21.18

d. X =  100,000 - 50,000*(21.18) + 5,000*(200) - 10,000*(2) = 100,000 - 1,059,000 + 1,000,000 - 20,000 = 21,000
Firm's supply = 21,000/100 = 210

(Note: Post 4 subparts at a time.)