1. Suppose ACME has a monopoly in the market for cellphones. Inorder to produce X cellphones, it costs Intel C(x)=2x^2. Marginalcost is MC(x)=4x. Quantity Demanded of X is QD(x)=12-.25p.
a. (5 pts) In a generic way, how does one find total revenue?(hint find price)
b. (5 pts) What level of output is profit maximizing?
c. (5 pts) What is the profit maximizing price?
d. (5 pts) What quantity maximizes total surplus?
1. Suppose ACME has a monopoly in the market for cellphones. Inorder to produce X cellphones, it costs Intel C(x)=2x^2. Marginalcost is MC(x)=4x. Quantity Demanded of X is QD(x)=12-.25p.
a. (5 pts) In a generic way, how does one find total revenue?(hint find price)
b. (5 pts) What level of output is profit maximizing?
c. (5 pts) What is the profit maximizing price?
d. (5 pts) What quantity maximizes total surplus?
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Related questions
Cost Formulas
Total Revenue = Price x Output
Total Fixed Costs = Sum of all fixed Costs
Total Variable Costs = Sum of all Variable Costs
Total Costs = TFC +TVC
Ave Fixed Costs(AFC) = TFC/Output
Ave Variable Costs (AVC) = TVC/Output
Ave Total Costs (ATC) = TC/Output
Marginal Cost = ^TC/^Output or ^TVC/^Output
Short Run Rules
Price > ATC, produce make profit
ATC > Price > AVC, produce minimize loss
AVC > Price, donât produce limit loss to fixed costs
Long Run Rules
Price > ATC, produce MR=MC
Price < ATC. Stop and sell fixed assets
1. Complete the Table
2. What actions should the firm take in order to maximize profits or minimize loss in each case, and why?
| Case # | T. Revenue. | T. Cost | T.V.C. | T.F.C. | Profit | Price | A.T.C. | A.V.C. | A.F.C. | M.C. | Output | Action |
| 1 | $ 4.00 | $ 3.00 | $ 2.00 | $ 4.00 | 600 | |||||||
| 2 | $ 8,000.00 | Minimum | 200 | |||||||||
| 3 | $ 8,000.00 | $ 9,000.00 | $ 9.00 | $ 2.00 | $ 8.00 | |||||||
| 4 | $ 16,000.00 | $ 7,000.00 | $ 9.00 | Minimun | 1000 | |||||||
| 5 | $ 7,000.00 | $ 6.00 | $ 8.00 | $ 6.00 | ||||||||
| 6 | $ 55,000.00 | $ 45,000.00 | $ 5,000.00 | $ 90.00 | $ 120.00 | |||||||
| 7 | $ 60,000.00 | $ 10,000.00 | $ 200.00 | $ 200.00 | ||||||||
| 8 | $ (1,000.00) | $ 5.00 | $ 6.00 | $ 5.00 | 800 | |||||||
| 9 | $ 10,000.00 | $ 2,000.00 | $ 8.00 | Minimum | 200 | |||||||
| 10 | $ (200.00) | $ 10.00 | $ 12.00 | $ 8.00 | can't get | 100 |
Concepts: Variable cost Fixed cost Total cost Average total cost Marginal cost
Total revenue Average revenue Marginal revenue Demand Curve
1. Mark Sampson, President of Sampson Switch Company must consider the pricing and production for the Ultra Switch Model B, one of the companyâs top selling models. Switch production includes grinding and assembly of finished components. Marketing efforts consist primarily of print ads in trade publications. Last year the Model B produced a profit of $8,000.
Production facts. Sampson hires part time workers on an âas neededâ basis to do the grinding task. On average, a grinder is paid $8.00 per hour and s/he is expected to produce 200 switch plates per each 8-hour day. Switch assemblers, also part-time workers, are paid $50 per day and they are expected to assemble 5 switches per hour. Each switch consists of two switch plates and assorted other components (the cost of the âother componentsâ is $3.11 per switch).
Fixed Costs. Other costs include the year-long contract for the rental of the assembly line equipment ($1,000 per month).
Marketing facts. According to next yearâs plan, Mark expects to place 10 black and white print ads (each $500) and two special feature, color ads (each $2,500) for the Model B. Salaries for the marketing sales force that are allocated to the Model B will total $18,000 next year.
1a. What is the cost to produce one switch? (i.e., the unit variable cost)?
1b. What and how much are the items composing the total âfixedâ costs for next year?
1c. Graph the relationship between quantity produced (on the X-axis) and Total Cost (on the Y-axis).
1d. How much is the per-unit contribution if the product is priced at $15 a unit?
1e. What was the profit last year? What will be the change in profitability for the Model B if the product is priced at $15 per unit and 2,500 units are sold?
1f. What is the breakeven point if the product is priced at $15? How many must be sold next year in order to produce the same profit level as last year?
1g. Assume that Mark has $50,000 in equity invested in the Model B line. How many units must be sold in order to return 25% on his equity?
2. Answer qs 1a-g assuming that the selling price is reduced to $10 and demand increases by a factor of four.
3. After much investigation, the marketing research department tells Mark that they expect the âdemand curveâ to be. Compare the expected demand with the breakeven point for each price point. Knowing this information, what price should Mark charge in order to maximize profits on the Model B ?
| selling price | units demanded | break even point |
| $15 | 2,500 | ... |
| $10 | 10,000 | ... |
| $9 | 13,000 | .... |
| $8 | 14,000 | ..... |
| $7 | 15,000 | ..... |
4a. Create a graph showing âQuantity Demandedâ on the X-axis and âTotal Revenue $â on the Y-axis for each of the five priceâquantity demanded points listed in q 3 above.
4b. Create a graph that superimposes the Total Revenue for the five points of the âDemand Curveâ on the âBreakevenâ Chart of the Model B (note the $$ Y -axis will represent Total Revenue for the Demand curve and will represent Total Cost for the Breakeven chart). { 01.81 gif k&b785 g pees ]
