Question

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: q=2 Px – 0.5 PŁ + 0.5 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: x= 10 – 0.1 Px + 0.5 I + 0.02 Py a. What is the Market Demand function? b. What is the (short run) Market Supply function? c. What is the Equilibrium Market Price? *(Assume that PL = 20, K = 2, Py = 4, and I = 200) d. What is the market equilibrium quantity?

Answer 1

Answer 1

(a)

Market demand function is the sum of individual demand function.

Here individual demand function is given by :

x = 10 - 0.1P_x + 0.5I + 0.02P_y

=> Market Demand (Q_d) = 100,000x = 100,000(10 - 0.1P_x + 0.5I + 0.02P_y)

=> Q_d = 100,000(10 - 0.1P_x + 0.5I + 0.02P_y) ---------------------------Market demand function

(b)

Market supply function is the sum of individual supply function.

Here individual supply function is given by :

q = 2P_x - 0.5P_L + 0.5K

=> Market Demand (Q_d) = 100q = 100(2P_x - 0.5P_L + 0.5K)

=> Q_s = 100(2P_x - 0.5P_L + 0.5K) ---------------------------Market supply function

(c)

Market is in equilibrium when :

Q_s = Q_d

=> 100(2P_x - 0.5P_L + 0.5K) = 100,000(10 - 0.1P_x + 0.5I + 0.02P_y)

=> 2P_x - 0.5P_L + 0.5K = 1000(10 - 0.1P_x + 0.5I + 0.02P_y)

It is given that P_L = 20, K = 2, P_y = 4 and I = 200

=> 2P_x - 0.5*20 + 0.5*2 = 1000(10 - 0.1P_x + 0.5*200 + 0.02*4)

=> 2P_x - 9 = 110080 - 100P_x

=> 102P_x = 110089

=> P_x = 1079.304 ----------------------------Equilibrium market price

(d)

Thus equilibrium quantity = Q = Q_s = Q_d = 100,000(10 - 0.1*1079.304 + 0.5*200 + 0.02*4) = 214960

Hence Equilibrium quantity = 214960(approx)