3) Given the deman and supply schedules ofr semiconductors in a perfectly compet

Question

3) Given the deman and supply schedules ofr semiconductors in a perfectly competivite market:

Qd=60-10P+0.5I, Qs=-10+4P-2C

Where I=average income of the demanders of this production

C=unit cost of the inputs used in the production of this commodity.

a) Find the expression for equillibriud price and equillibrium quantity transceted in this market.

b)Find the initial equillibrium and equillibrioum quantity if I=1000 and C=20

c) Determine the impact of an increase in income from 1000 to 1200 on the initial equillibrium values.

d) Assume that an improvement in the teechnoly of producing this commodity results in an increase in supply by a factor of 5, how will this development affect the initial equillibrium values?0

Explanation / Answer

A. Set Qd = Qs Qd = 60 - 10P + 0.5I Qs = -10 + 4P - 2C 60 - 10P + 0.5I = -10 + 4P - 2C 70 + 0.5I = 14P - 2C 14P = 70 + 0.5I + 2C P = (70 + 0.5I + 2C)/14 This is the expression for equilibrium price. Q = 60 - 10P + 0.5I Q = 60 - (10/14)*(70 + 0.5I + 2C) + 0.5I Q = 60 - (10/14)*(70 + 0.5I + 2C) + 0.5I Q = 10 - (10/7)C + I*(0.5 - 5/14) Q = 10 - (10/7)C + I*(0.5 - 5/14) Q = 10 - (10/7)C + I/7 This is the expression for equilibrium quantity. You would get the same thing by substituting price into Qs. B. P = (70 + 0.5I + 2C)/14 P = (70 + 0.5*1000 + 2*20)/14 P = 43.5714286 Q = 10 - (10/7)C + I/7 Q = 10 - (10/7)*20 + 1000/7 Q = 124.285714 C. P = (70 + 0.5I + 2C)/14 P = (70 + 0.5*1200 + 2*20)/14 P = 50.7142857 Q = 10 - (10/7)C + I/7 Q = 10 - (10/7)*20 + 1200/7 Q = 152.857143 D. Qd = 60 - 10P + 0.5I Qs = 5*(-10 + 4P - 2C) Qs = -50 + 20P - 10C Set Qd = Qs 60 - 10P + 0.5I = -50 + 20P - 10C Substitute in equilibrium values. 60 - 10P + 0.5*1000 = -50 + 20P - 10*20 Solve for P 30*P = 10 + 0.5*1000 + 50 + 10*20 P = (10 + 0.5*1000 + 50 + 10*20)/30 P = 25.3333333 Substitute this into demand or supply to find Q. Qd = 60 - 10P + 0.5I Qd = 60 - 10*25.3333333 + 0.5*1000 Qd = 306.666667

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