A utility firm produces electricity to meet the demands of a city. The price it can charge for electricity is fixed by law and it must meet all demand at that price. Let the price of a unit of electricity be p. It turns out that the amount of electricity demanded is always the same over every 24—hour period, but demand differs from day to night. During the day, 4 units are demanded, whereas during the night only 3 units are demanded. Total output for each 24—hour period is thus always equal to 7 units. The utility ?rm produces electricity according to the production function: inVk—f'i: where z' 2 day, night; It is the size of the generating plant; and fi is tons of fuel used. The ?rm must choose how large a plant to build, and it cannot change plant size from day to night. A unit of plant size costs wk per 24—hour period and a ton of fuel costs 10f. o What is this ?rm's pro?t function? Is there anything special about this ?rm's pro?t function? Explain brie?y and intuitively. 0 Find the solution to this ?rm's pro?t maximization problem. Show your work and explain brie?y.

pur-new-sol

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