The industry demand curve in a perfectly competitive market is given by the equation P = 160 - 2Q, and the supply curve is given by the equation P = 40 + Q. The upward-sloping supply curve represents the increasing marginal cost of expanding industry output. The total industry cost of producing Q units of output is C = 800 + 40Q + .5Q2 (Note that taking the derivative of this equation produces the preceding industry MC equation.) In turn, the total benefit associated with consuming Q units of output is given by the equation B = 160Q - Q2 (Total benefit represents the trapezoidal area under the demand curve. It is also the sum of consumer surplus and revenue. Note that taking the derivative of the benefit equation produces the original industry demand curve MB = 160 - 2Q.)
a. Create a spreadsheet similar to the given example. Only the quantity cell (C5) contains a numerical value. All other cells are linked by formulas to the quantity cell.
b. Find the intersection of competitive supply and demand by equating the demand and supply equations or by varying quantity in the spreadsheet until MB equals MC.
c. Alternatively, find the optimal level of industry output by maximizing net benefits (cell F9) or, equivalently, the sum of consumer and producer gains (cell F10). Confirm that the perfectly competitive equilibrium of part (b) is efficient.
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A
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B
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C
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D
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E
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F
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G
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1
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2
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EFFICIENCY OF
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3
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PERFECT COMPETITION
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4
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5
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Quantity
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32
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Price
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96
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6
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7
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Benefit
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4,096
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Con Surplus
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1,024
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8
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P = MB
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96
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9
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B - C
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1,504
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10
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Revenue
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3,072
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CS + Profit
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1,504
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11
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MR
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32
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12
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Profit
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480
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13
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Cost
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2,592
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14
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MC
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72
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15
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