Monopoly: Marginal Cost and Long Run Equilibrium
Chapter 11: Problems 2(a, b), 4(a, c), and 6
2. Ajax cleaning Products is a medium sized operating in an industry dominated by one large firm Tile King; Ajax produces a multi-headed tunnel wall scrubber that is similar to a model produced by Title King to avoid the possibility of price war. The price charged by Title King is $ 20,000.
Ajax has the following short-run cost curve:
TC = 800,000 - 5,000Q + 100Q^2
a) Compute the marginal cost curve for Ajax
answer:
Marginal Cost (MC) = dTC/dQ
Since the derivative of a constant = 0,
MC = -5,000 + 200Q
b) Given Ajax pricing strategy, what is the marginal revenue function for Ajax?
Since Ajax is pricing as if it were a perfectly competitive firm, then, it's price would equal its marginal revenue, thus:
P = MR = $20,000
c) Compute the profit maximizing level of output for Ajax:
A profit maximizing level of output would be achieved at the point where MR = MC
We thus have to set both functions equal each other and then solve for Q.
20,000 = -5000 + 200Q
Solving for Q:
20000 + 5000 = 200Q
25,000 = 200Q
25,000/200 = Q
125 = Q
125 is the profit maximizing quantity that Ajax would have to produce in order to realize the maximum profit possible.
d) Compute Ajax's total dollar profits:
profit = TR - TC
Profit = (20,000*Q) - (800,000 - 5000Q + 100Q^2)
Profit = (20,000*125) - (800,000 - 5000*125 + 100*125^2)
Profit = 2,500,000 - (800,000 - 625,000 + 1,562,500)
Profit = 2,500,000 - 1,737,500
Profit = $762,500
4. Unique creations hold a monopoly position in the production and sale of magnometers the cost function facing Unique is estimated to be
Marginal cost of unique is $ 20.00 as a marginal cost is the cost that is incurred due to the increase of the cost divided by increase in the quantity.
Answer:
Suppose that unique produces 10 units
Total cost: 100,200
20 Units produced: 100, 400
Increase in cost =8 100,400-100,200 =200
2. Ajax cleaning Products is a medium sized operating in an industry dominated by one large firm Tile King; Ajax produces a multi-headed tunnel wall scrubber that is similar to a model produced by Title King to avoid the possibility of price war. The price charged by Title King is $ 20,000.
Ajax has the following short-run cost curve:
TC = 800,000 - 5,000Q + 100Q^2
a) Compute the marginal cost curve for Ajax
answer:
Marginal Cost (MC) = dTC/dQ
Since the derivative of a constant = 0,
MC = -5,000 + 200Q
b) Given Ajax pricing strategy, what is the marginal revenue function for Ajax?
Since Ajax is pricing as if it were a perfectly competitive firm, then, it's price would equal its marginal revenue, thus:
P = MR = $20,000
c) Compute the profit maximizing level of output for Ajax:
A profit maximizing level of output would be achieved at the point where MR = MC
We thus have to set both functions equal each other and then solve for Q.
20,000 = -5000 + 200Q
Solving for Q:
20000 + 5000 = 200Q
25,000 = 200Q
25,000/200 = Q
125 = Q
125 is the profit maximizing quantity that Ajax would have to produce in order to realize the maximum profit possible.
d) Compute Ajax's total dollar profits:
profit = TR - TC
Profit = (20,000*Q) - (800,000 - 5000Q + 100Q^2)
Profit = (20,000*125) - (800,000 - 5000*125 + 100*125^2)
Profit = 2,500,000 - (800,000 - 625,000 + 1,562,500)
Profit = 2,500,000 - 1,737,500
Profit = $762,500
4. Unique creations hold a monopoly position in the production and sale of magnometers the cost function facing Unique is estimated to be
Marginal cost of unique is $ 20.00 as a marginal cost is the cost that is incurred due to the increase of the cost divided by increase in the quantity.
Answer:
Suppose that unique produces 10 units
Total cost: 100,200
20 Units produced: 100, 400
Increase in cost =8 100,400-100,200 =200