Blog #3

   Part 1:

JMC Lighting is a corporation located in Washington, D.C. that specializes in producing desk lamps. These desk lamps are eco-friendly by receiving power from solar energy instead of using electricity. Thus, there is no cord attached to it and no need to ever use a power outlet.  Sheets of solar panels are purely wrapped around the entire lamp’s base and body I order to absorb the sun’s light. A two-hour “charge” in the sunlight will give the lamp 58 hours worth of power. JMC Light attracts 500 people a month to buy its product. The start-up cost for getting the manufacturing factory ready to produce units (desk lamps) is $70,000 and the cost for producing one unit (desk lamp) is $20/unit. JMC Light sells each unit (desk lamp) to a customer for $70 each.

     Part 2:

   a.     Total fixed costs = $70,000
         -Machinery: $55,000
         -Rent: $15,000

   b.     Variable cost = $20/unit

   c.      Price of unit = $70

   d.     C(q) = $70,000 + $20(q)

   e.     R(q) = $70q

   f.      P(q) = $50(q) - $70000 

   g.     BEP_Units = $70,000  / $50 = 1,400 units (desk lamps)  

         BEP_$  = $70000 / 71% = $98,592

   h. Graph of cost function and revenue function with breakeven point

 

        i. The break-even point on the graph represents where JMC Lighting's revenue equals    
          expenses. Thus, the company makes no profit or loss at 1,400 units (desk lamps) with a cost of
          $98,592. As, JMC Lighting has a marginal revenue $70 revenue for every 100 units produced.
          Also, for every 100 units produced, there is a cost of $20 per every 100 units.

   j. Graph of Profit Function

         

 k. At 1400 units, JMC Lighting will reach its break-even point in order to make a profit. This company is now making profit due to its revenue being greater than its cost.

Part 3:

   a. q = 400 products produced/day

   b. Graph of number of units produced daily.

   c. The marginal cost of producing the nth unit would be the slope of my tangent line, which would
       be $7.50 per unit.
       (500, 80,000) (900, 83,000) = 83,000-80,000/900-500 = $7.50/unit

   d. c(400) = $70,000 + $20(400)
       c(400) = $708,000

       a(400) = $78,000/400
       a(400) = $195 per unit (desk lamp)

  e. Graph of Marginal Cost and average cost at q=400 units (desk lamps)

   

      1. The marginal revenue is less than the marginal cost at q =400 units (desk lamps) because the
         marginal cost curve is above the marginal revenue's curve at q=400 units. Thus, JMC Lighting
         is suffering more of a loss than a profit when producing 400 units because their cost exceed
         their revenue.

      2. The number of units sold daily (q=400 units) is before the break-even point. This means that
      the company is suffering a great loss before they even reach their break-even point of producing
      1,400 units. Thus, the company will have to wait a few days until they exceed their break-even
      point to make a profit from the desk lamps.

     3.  If production is increased by one extra unit per day, the company will make a little bit of
          money. At MC = C(q+1)-C(q) of $7.50 per unit  and the MR = R(q+1)-R(q) will be $20 per
          unit. Thus, as the company increases its production, it will be getting closer to its break-even
         point, which will then lead to a profit when it exceeds the break-even point.

    4. At q =400 units (desk lamps), the increase of production would decrease the average cost of the
        company from $195 per unit (desk lamp) to $194.56 per unit (desk lamp). This is a minute
        decrease in average cost, but it will be significant as they produce more units of desk lamps in
        the future.

   5. Decreasing average costs is better for the company because this will cause the marginal cost of
       each unit to decrease. Thus, the company will receive more revenue than cost as they increase
       their production quantity.

Part Four:

     1. Over the next five years, JMC Lighting will do well. Of course JMC Lighting will struggle for the first few weeks due to incurring more cost than revenue, but that is expected with any start-up company. As production levels increase over time, the company's average cost will decrease and their marginal cost will decrease, which will lead to the company incurring less cost. Once JMC Lighting exceeds their break-even point of producing 1,400 units, their revenue will exceed their costs and will then strive.