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Decision Making based upon Costs and Revenues

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Please refer attached file for better clarity of tables.

Problems :

1. Kate's Katering provides catered meals, and the catered meals industry is perfectly competitive. Kate's machinery costs $100 per day and is the only fixed input. Her variable cost is comprised of the wages paid to the cooks and the food ingredients.

The variable cost associated with each level of output is given in the accompanying table.
Quantity of meals VC
0 $0
10 200
20 300
30 480
40 700
50 1000

a. Calculate the total cost, the average variable cost, the average total cost, and the marginal cost for each quantity of output.
Quantity of meals FC VC TC MC AVC ATC
0 $100 $0
10 100 200
20 100 300
30 100 480
40 100 700
50 100 1,000

b. What is the break-even price?
What is the shut-down price?

c. Suppose that the price at which Kate can sell catered meals is $21 per meal. In the short run, will Kate earn a profit?
In the short run, should she produce or shut down?

d. Suppose that the price at which Kate can sell catered meals is $17 per meal. In the short run, will Kate earn a profit?
In the short run, should she produce or shut down?

e. Suppose that the price at which Kate can sell catered meals is $13 per meal. In the short run, will Kate earn a profit?
In the short run, should she produce or shut down?

2. Evaluate each of the following statements. If a statement is true, explain why; if it is false, identify the mistake and try to correct it.

a. A profit-maximizing firm should select the output level at which the difference between the market price and marginal cost is greatest.

b. An increase in fixed cost lowers the profit-maximizing quantity of output produced in the short run.

3. Suppose that De Beers is a single-price monopolist in the market for diamonds. De Beers has five potential customers: Raquel, Jackie, Joan, Mia, and Sophia. Each of these customers will buy at most one diamond-and only if the price is just equal to, or lower than, her willingness to pay. Raquel's willingness to pay is $400; Jackie's, $300; Joan's, $200; Mia's, $100; and Sophia's, $0. De Beers's marginal cost per diamond is $100. This leads to the demand schedule for diamonds shown in the accompanying table.

Price of diamond Qty of diamonds demanded
$500 0
400 1
300 2
200 3
100 4
0 5

a. Calculate De Beers's total revenue and its marginal revenue
Price of diamond Qty of diamonds demanded Total Revenue Marginal Revenue
$500 0 -
400 1
300 2
200 3
100 4
0 5

From your calculation, draw the demand curve and the marginal revenue curve.

b. Explain why De Beers faces a downward-sloping demand curve
c. Explain why the marginal revenue from an additional diamond sale is less than the price of the diamond
d. Suppose De Beers currently charges $200 for its diamonds.

If it lowered the price to $100, how large is the price effect?
How large is the quantity effect?

e. Draw the marginal cost curve into your diagram and determine which quantity maximizes De Beers's profit and which price De Beers will charge

4.A monopolist knows that if it expands the quantity of output it produces from 8 to 9 units, that will lower the price of its output from $2 to $1.

Calculate the quantity effect and the price effect.

Use these results to calculate the monopolist's marginal revenue of producing the 9th unit.

The marginal cost of producing the 9th unit is positive. Is it a good idea for the monopolist to produce the 9th unit?

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Solution Summary

There are four problems. Solution to these problems explain the methodology to calculate various costs and to take production decisions based upon these calculations.

Solution Preview

Please refer attached file for better clarity of tables and missing graphs.
Solution:

1 a.
Quantity of meals=Q FC VC TC=FC+VC MC* AVC=VC/Q ATC=TC/Q
0 $100 $0 $100
10 100 200 $300 $20 $20 $30
20 100 300 $400 $10 $15 $20
30 100 480 $580 $18 $16 $19
40 100 700 $800 $22 $18 $20
50 100 1,000 $1,100 $30 $20 $22
* Marginal Cost=Change in total cost/Change in output

b. What is the break-even price?
Break even price is defined as the price at which total revenue is just equal to total cost. At this level profit is zero.
What is the shut-down price?
Shut down point comes at a point where market price is just sufficient to cover average variable cost and no more. At this point firm's losses per period are just equal to fixed costs.

c. Suppose that the price at which Kate can sell catered meals is $21 per meal. In the short run, will Kate earn a profit?
For profit maximization, Kate will choose output level at which MR should be greater than or equal to MC.

At Output level of 30, MC($18)<MR (P=$21)
At output level of 40, MC($22)>MR(P=$21)
Kate will produce 30 meals to maximize profits.
Profit=(P-ATC)*Q=(21-19)*30=$60
In the short run, should she produce or shut down?
Kate is making profit at this level of output. It should continue to ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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