1. A study of the costs of electricity generation for a sample of 112 British firms in 1946 - 1947 yielded the following long-run average variable cost and marginal cost functions: (3 points)
AVC = 2.48 + .0066Q + .0000058Q2 -.000092QZ -.052Z + .00036Z2
MC= 2.48 + .0132Q + .0000174Q2 - .000184QZ -.052Z + .00036Z2
Where:
AVC = average variable cost measured in pence per kilowatt-hour (kWh). (A pence was a British monetary unit equal, at that time to 2 cents U.S.).
MC =marginal cost measured in pence per kilowatt-hour (kWh).
Q = output measured in millions of kWh per year.
Z=plant size measured in thousands of kilowatts.
a) Determine the long run variable cost function for electricity generation. (Hint VC = AVC*Q)
b) HoldingZ(the plant size) constant at 100,000, determine the AVC and MC functions for electricity. (Hint: substitute 100,000 for Z in both equations.)
c) Holding Z constant at 100,000 kilowatts, determine the output level that minimizes AVC. (Hint: Set AVC = MC and solve for Q or set dAVC/dQ = 0 and solve for Q. Both will generate the same value of Q.)