6. [10 points] (a) Suppose that the demand equation for a certain commodity is p
ID: 1124427 • Letter: 6
Question
6. [10 points] (a) Suppose that the demand equation for a certain commodity is p = 4-0.0002 q where q units are produced each day and p is the price of each unit. The cost of producing q units is 600+3q. If the daily profit is to be as large as possible, find the number of units produced each day, the price of each and the daily profit MATA32H page 2 (b) Suppose the government now imposes a $0.20 tax on each unit produced. For maximal daily profit, how many units are now produced each day? What is the price of each unit and what is the daily profit?Explanation / Answer
Before tax,
p = 4 - 0.0002q
Total cost (C) = 600 + 3q
Marginal cost (MC) = dC/dq = 3
This is the supply function: p = 3
(b)
The $0.2 tax will lower effective price received by sellers, shifting supply curve leftward. New supply function is
p = 3 + 0.2 = 3.2
Equating with demand,
4 - 0.0002q = 3.2
0.0002q = 0.8
q = 4,000
p = $3.2 (Price paid by buyers)
Price received by sellers = $(3.2 - 0.2) = $3
Total revenue (TR) = p x q = $3.2 x 4,000 = $12,800
C ($) = 600 + (3 x 4,000) = 600 + 12,000 = 12,600
Profit = TR - C = $(12,800 - 12,600) = $200
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