Terms in this set (21)

Suppose initially that consumers must pay the tax to the government. Since the total price (including the tax)
that consumers would be willing to pay remains unchanged, we know that
the demand function is
P* + t = 120 − 0.02Q, or
P* = 120 − 0.02Q − t,
where P* is the price received by the suppliers and t is the tax per unit. Because the tax increases the price
consumers pay for each unit, total revenue for the monopolist decreases by tQ. You can see this most easily
by expressing R = P*Q, which means tQ is subtracted from revenue. Marginal revenue, the revenue on each
additional unit, decreases by t:
MR = 120 − 0.04Q − t
where t = 14 cents. To determine the profit-maximizing level of output with the tax, equate marginal revenue
with marginal cost:
120 − 0.04Q − 14 = 60, or
Q = 1150 units.
Substituting Q into the demand function to determine price:
P* = 120 − (0.02)(1150) − 14 = 83 cents.
Profit is total revenue minus total cost:

= (83)(1150) − [(60)(1150) + 25,000] = 1450 cents, or
$14.50 per week.
Note: The price facing the consumer after the imposition of the tax is 83 + 14 = 97 cents. Compared to the
90-cent price before the tax is imposed, consumers and the monopolist each
pay 7 cents of the tax.
If the monopolist had to pay the tax instead of the consumer, we would arrive at the same result. The
monopolist's cost function would then be
TC = 60Q + 25,000 + tQ = (60 + t)Q + 25,000.
The slope of the cost function is (60 + t), so MC = 60 + t. We set this MC equal to the marginal revenue
function from part a:120 − 0.04Q = 60 + 14, or
Q = 1150.
Thus, it does not matter who sends the tax payment to the government. The burden of the tax is shared by
consumers and the monopolist in exactly the same way.
If the firms collude, they face the market demand curve, so their marginal revenue curve is:
MR = 50 − 10Q.
Set marginal revenue equal to marginal cost (the marginal cost of Firm 1, since it is lower than that of Firm 2)
to determine the profit-maximizing quantity, Q:
50 − 10Q = 10, or Q = 4.
Substituting Q = 4 into the demand function to determine price:
P = 50 − 5(4) = $30.
The question now is how the firms will divide the total output of 4 among themselves. The joint profitmaximizing
solution is for Firm 1 to produce all of the output because its marginal cost is less than Firm 2's
marginal cost. We can ignore fixed costs because both firms are already in the market and will be saddled
with their fixed costs no matter how many units each produces. If Firm 1 produces all 4 units, its profit will
be π1 = (30)(4) − (20 + (10)(4)) = $60.
The profit for Firm 2 will be:
π2 = (30)(0) − (10 + (12)(0)) = −$10.
Total industry profit will be:
πT = π1 + π2 = 60 − 10 = $50.
Firm 2, of course, will not like this. One solution is for Firm 1 to pay Firm 2 $35 so that both earn a profit of
$25, although they may well disagree about the amount to be paid. If they split the output evenly between
them, so that each firm produces 2 units, then total profit would be $46 ($20 for Firm 1 and $26 for Firm 2).
This does not maximize total profit, but Firm 2 would prefer it to the $25 it gets from an even split of the
maximum $50 profit. So there is no clear-cut answer to this question.
If Firm 1 were the only entrant, its profits would be $60 and Firm 2's would be 0.
If Firm 2 were the only entrant, then it would equate marginal revenue with its marginal cost to determine its
profit-maximizing quantity:
50 − 10Q2 = 12, or Q2 = 3.8.
Substituting Q2 into the demand equation to determine price:
P = 50 − 5(3.8) = $31.
The profits for Firm 2 would be:
π2 = (31)(3.8) − (10 + (12)(3.8)) = $62.20,
and Firm 1 would earn 0. Thus, Firm 2 would make a larger profit than Firm 1 if it were the only firm in the
market, because Firm 2 has lower fixed costs.
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