.Kalamazoo Competition-Free Concrete (KCC) is a local monopolist of ready-mix co
ID: 1193651 • Letter: #
Question
.Kalamazoo Competition-Free Concrete (KCC) is a local monopolist of ready-mix concrete. Its annual demand function is Qd= 24000-400P where P is the price, in dollars, of a cubic yard of concrete and Q is the number of cubic yards sold per year. Suppose that Kalamazoo's marginal cost is MC=20+0.0075Q
The monopolist maximizes profit with an output of 3200 units and a price of $52.00.
a. Suppose the government puts a $2 per cubic yard tax on the monopolist’s product, paid by the monopolist. What happens to the price consumers pay? What share of the tax is this?
Explanation / Answer
Q = 24,000 - 400P
Pd = (24,000 - Q) / 400 = 60 - 0.0025Q
But, Ps = 60 - 0.0025Q - 2 = 58 - 0.0025Q
Total revenue to supplier, TR = Ps x Q = 58Q - 0.0025Q2
Marginal revenue, MR = dTR / dQ = 58 - 0.005Q
Equating with MC:
20 + 0.0075Q = 58 - 0.005Q
0.0125Q = 38
Q = 3,040
Pd = 60 - 0.0025Q = 60 - (0.0025 x 3,040) = 52.40
Ps = 58 - 0.0025Q = 58 - (0.0025 x 3,040) = 50.40
So, consumer pays tax of 0.40 out of total tax of $2, that is, 20% share of tax.
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