Question

13. The San Francisco Power Company faces a total cost function of TC = (1/2)Q2 + 100,000 where prices are in cents/kilowatt-hour and quantities are in millions of kilowatt-hours. The demand function of San Francisco residents for off-peak hours is: D: P = 4-Q or D.: Q=4-P. The demand function of San Francisco residents for peak hours is: D: P = 8-Q or D : Q = 8 - P Calculate (a) the short-run marginal cost function (SMC); (b) the equilibrium price (P) and quantity demanded (Q) during off-peak hours; (c) the equilibrium price (P) and quantity demanded (2) during peak hours; and (d) the total demand for electricity (Q,+Q). 14. Assume that the San Francisco Power Authority of Problem 13 has set a rate of 3 cents per kilowatt- hour for both peak and off-peak hours. Calculate (a) the new equilibrium quantity demanded during off-peak hours (Q *); (b) the new equilibrium quantity demanded during peak hours (Q.*); and (c) the new total demand for electricity (0* +Q,*).

Please help me answer Problem #14. Thank you so much

Answer 1

14 solution, P = 3 cent/kw   ( fixed)

put the value of P=3 in the respective demand functions ;

• off—peak hour Qo =4—P = 4—3 = 1 million kw.(equilibrium quantity demand of off peak hour)
• Peak-hour Qp =8—P = 8—3= 5 million kw ( equilibrium quantity demanded of peak hour. )
• New total demand Q=(Qo+ Qp) =(1+5) =6 million kw.