Chapter 2 Problems:

 

1. Spadafora Auto, a leading automotive manufacturer, estimates the demand and total cost of its new "Spad 1" sports car as follows:

Q = 10-0.5P

TC= 18+4Q
  1. Determine the firm's optimal price, quantity and profit using profit and marginal profit equations. Also, show graphically.
  2. Repeat Part a using marginal revenue and marginal cost. Also show graphically.
  3. How do the results in Parts a and b compare. Why is calculus helpful?

Answers

  1. P=12, Q=4, P =14
  2. Same as part a.
  3. The approaches are equivalent and lead to the same results. Calculus is a time saver and can provide precise answers very quickly.

 

  1. ABC has the following demand and cost functions:

Q = 18-0.2P

TC=16+10Q
  1. Find the inverse demand function.
  2. Determine TR, MR and MC.
  3. Determine the maximum revenue.
  4. Determine the profit maximizing price, quantity and profit.
  5. ABC lost a patent infringement case on November 1, 1997. The plaintiff was awarded 3.5% of the firm's revenues for the 3 year period beginning January 1, 1997. What effects will this award have on ABC's price and output?

Answers

  1. P=90-5Q
  2. TR=90Q-5Q2, MR=90-10Q, MC=10
  3. TR=405 (with Q=9)
  4. Q=8, P=50, P =294

 

  1. Lenny's hot dog stand buys hot dogs for $0.15 and faces the following demand: Q=50-20P
  1. Determine its optimal price and output and profits (ignore fixed costs).
  2. What happens if the cost of hot dogs doubles to $0.30?
  3. Why does the optimal price increase less than the increase in costs?

Answers

  1. P=$1.33, Q=23.5, P =27.73
  2. P increases to $1.40
  3. Draw a graph and slide a horizontal MC line up. Because the numerical value of the slope of the demand curve is one-half that of the MR curve, change in price will be smaller than the change in MC. Profits will be lower (=24.2).

 

  1. A tobacconist sells 2000 cartons per day of its most popular cigarette brand at $2.20 per carton. A new manager expects to sell 2200 cartons by dropping price to $2.00.
  1. Compare profits at the two prices assuming that each carton cost $0.50 (ignore other costs).
  2. An economist suggests that the demand curve is described by the equation: Q=4200-1000P. Is this correct?
  3. Determine the profit-maximizing price.

 

Answers

a. P =$3400 at P=$2.20 and #3300 at P=$2.

  1. Yes assuming that 2200 will be sold at $2.
  2. Q=1850, P=$2.35.

 

5. A firm's demand and total cost equations are:

Q=96-4P

TC=50+6Q
  1. Find the MR and MC functions.
  2. Find the firm's optimal quantity, price, and profit by:

    3. Using the profit and marginal profit equations

    Setting MR=MC

  3. How will an increase or decrease in fixed costs affect operating decisions?
  4. If the firm can sell any amount of output at a fixed market price of $16, what is the difficulty in applying the either rule to maximize profit?

Answers

  1. MR=24-0.5Q, MC=4
  2. Q=36,P=15,P =274
  3. None
  4. Because MR(16)MC(6), it impossible to equate the two. The firm will wish to expand indefinitely (or up to the capacity level if there is one).

 

  1. Fancy Furniture sells 50 chairs per month at $700 each. Monthly fixed costs for rent and equipment is $5000. Total variable costs: TVC=540Q-30Q2-0.5Q3.
  1. Determine Fancy's monthly profit.
  2. Determine the optimal quantity (and profit) assuming Fancy can sell an unlimited number of chairs.
  3. If costs are represented by TC=500Q+5000, determine Fancy's breakeven quantity.
  4. What is the maximum total revenue.

Answers

  1. TR-TC=P =$15,500
  2. Setting P=MC and solving with the quadratic formula (Q=42.5 or-2.5). Rounding, Q=42. Profits increase to $17,596.
  3. QB=25
  4. There is no maximum TR for a price taker.