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. Explain how economists use marginal analyses to reach optimal decision making.

1. Economists assume that the goal of a firm is to maximize profits.
a. Explain fully how the firm achieves this goal.
If its marginal costs equal marginal revenue.
b. Why do economists use Economic instead of Accounting profits?
Because the first one also counts the opportunity costs of other possibilities of using money and time.
c. Identify and explain FOUR other important goals, in addition to profit
maximization, that firms may pursue?
Cost minimization, economy on scale and the satisfying the demand for product
2. a. Explain how economists use marginal analyses to reach optimal decision
making. Explain how marginal analyses can be used for cost minimization,
revenue maximization and output maximization?
Marginal analysis shows clearly why decision makers should ignore average costs, fixed cost, and sunk costs when making decision about the optimal level of activities. Since it is marginal cost that must equal marginal benefit to reach the optimal level of activity, any other cost is irrelevant for making decisions about how much of an activity to undertake.
b- Using marginal analyses, explain why the output which maximizes the total
revenue of a firm must exceed the output which maximizes the total profits of
a firm. Provide a single graph of a typical total revenue and a typical total
profit function to illustrate your answer. Be sure to label your axes correctly.
A perfectly competitive firm is assumed to produce the quantity of output that maximizes economic profit-the difference between total revenue and total cost. This production decision can be analyzed directly with economic profit, by identifying the greatest difference between total revenue and total cost, or by the equality between marginal revenue and marginal cost.
Total Revenue and Total Cost: profit maximization can be identified by comparison of total revenue and total cost. The quantity of out put that achieves the greatest difference of total revenue over total cost is profit maximization. In the middle panel, the vertical gap between the total revenue and total cost curves is the greatest at 7 pounds of zucchinis. For smaller or larger output levels, the gap is either less or the total curve lies above the total revenue curve.
Cost and Revenue
TC
50-
– Maximum TR
40 – profit

30-

20 –
– –
10 –

0 1 2 3 4 5 6 7 8 9 10 –
Quantity

As we can see, in the point, where the difference (TR-TC) is maximized, total revenue isn’t maximized, so the output which maximized the total revenue of a firm must exceed the output which maximizes the total profit of a firm.
3. a. Explain fully the concept of net present value. Why must firms use net
present value to determine if an investment is profitable?
Net present value (NPV) is determined by calculating the costs (negative cash flows) and benefits (positive cash flows) for each period of an investment.
Because of its simplicity, NPV is a useful tool to determine whether a project or investment will result in a net profit or a loss. A positive NPV results in profit, while a negative NPV results in a loss. The NPV measures the excess or shortfall of cash flows, in present value terms, above the cost of funds.
b. Assume that managers take two years off without pay to complete an MBA.
Use the concepts of opportunity cost and net present value to explain how
you would measure if an MBA is profitable?
If managers take two years off without pay to complete an MBA, then an MBA will be profitable, if the opportunity costs will be comparatively low and net present value of such kind of investment will be positive.
4. Given that the total cost function is:
TC = 100Q – Q^2 + 1/3 Q^3

where Q = rate of output and TC = total cost

a. Determine the marginal and average cost functions.
MC = TC = 100 – 2Q + Q^2
ATC = TC/Q = 100 – Q + 1/3Q^2
b. Calculate the output level that minimizes average cost. (8 marks)
ATC” = 0 (ATC” = 1/3>0), so
-1 + 2/3Q = 0
2/3Q = 1
Q = 1.5 units

c. Calculate the output level that minimizes marginal cost. (8 marks)
MC” = 0 (MC” = 1>0), so
-2 +2Q = 0
2Q = 2
Q= 1 units
5. The demand for widgets (X) is given by:
Px = 160 – 4x
The production of widgets has the following average variable costs:
AVC = 2x – 20
Fixed costs are 162.
Calculate the output level of widgets that: (5 marks each)

a. Maximizes total revenue.
Total revenue is maximized in the point, where TR’ = 0 or MR = 0 (TR” < 0 ):
TR = P*Q = (160 – 4x)*x = 160x – 4x^2
TR’ = MR = 0, so
160 – 8x = 0
8x = 160
x = 20 (units)
b. Minimizes the average total cost (ATC) of widgets.
The average total cost of widgets is minimized in the point, where ATC’ = 0 (ATC” < 0):
ATC = TC/Q = AVC + AFC = AVC + FC/Q = 2x – 20 + 162/x
ATC’ = 0, so
2 – 162/x^2 = 0
162/x^2 = 2
x^2 = 81
x = 9 units (value -9 is disregarded because it is not positive).

c. Minimizes the total cost (TC) of widgets.
The total cost of widgets is minimized, when TC’ = MC = 0 (TC” >0):
TC = AVC*Q + FC = 2x^2 – 20x + 162
TC’ = MC = 0, so
4x – 20 = 0
4x = 20
x = 5 (units)
d. Maximizes profits.
Profits are maximized, when MR = MC, so
160 – 8x = 4x – 20
12x = 180,
x = 15 (units).


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