b. If demand for Picasso’s work is inelastic, increasing the number of
pieces sold (by driving down prices) will reducetotal revenue. The
artist’s heirs should try to limit supply by spreading sales of his
artwork over long time periods.- a. Setting QDQSimplies 184 20P 124 4P or 24P 60.
Therefore, P $2.50 and Q 134 pounds per capita.
b. This increase represents only .7 percent of total supply and will have
little price effect. The new quantity supplied is (1.007)(134) 135.
Rearranging the demand curve, we have P 9.20 .05Q. Therefore,
we find that P 9.20 (.05)(135) $2.45. Montana farmers’
revenue should increase by about 8 percent (based on a 10 percent
quantity increase and a 2 percent price drop).
c. If the total harvest is 10 percent above normal, QS(1.10)(134) 147.4
pounds per capita and P 9.20 (0.5)(147.4) $1.83. Farm revenue
drops from (2.50)(134) $335 to (1.83)(147.4) $269.74, a 19.5
percent drop. Demand is inelastic. A modest quantity increase caused a
large price drop and this is detrimental to farmers’ incomes. Because
varying harvest conditions can cause significant price and revenue
changes, today’s farm profits quickly can become tomorrow’s losses. - a. The Green Company’s marginal cost is MC dC/dQ 4 2Q, and
the price is P $40. Setting MC P implies 4 2Q 40, or Q 18
units. More generally, setting MC P generates the supply curve 4
2Q P, or Q (P 4)/2.
b. With the increase in fixed cost, the firm should continue to produce
18 units. Its profit is R C (40)(18) [144 (4)(18)
(18)^2 ] 720 540 $180. Of course, the firm will supply no output
if price falls below the level of minimum average cost. We set MC
AC and find that average cost is a minimum at Qmin12. In turn,
min AC $28. Thus, the firm’s supply is zero if price falls below $28.
c. In part (a) (when fixed costs are 100), min AC $24 at a quantity of
10 units for each firm. Thus, the original long-run equilibrium price
is P $24. With elevated fixed costs, one would expect the long-run
price to rise to $28 (the new minimum level of AC). At this higher
price, total demand is reduced. However, each firm’s output would
rise from 10 units to 12 units. With reduced total demand and greater
output per firm, the number of firms must decline. - a. Average cost is AC 300/Q Q/3. Thus, total cost is C 300
Q^2 /3, which implies MC (2/3)Q. Setting AC MC implies 300/Q
Q/3 (2/3)Q, or 300/Q Q/3. This simplifies to Q^2 900, so
Qmin30. In turn, min AC (2/3)(30) $20.
b. A firm’s supply curve is found by setting P MC (2/3)QF.
Therefore, QF1.5P. With 10 firms, total supply is QS10QF15P.
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