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Supply and Demand in Math Terms

Supply and Demand in Math Terms. Say you have a competitive market where the demand from consumers is Qd = 6000/9 – (50/9)P. Point A in the graph is the vertical intercept of the demand curve. We had Qd = 6000/9 – (50/9)P. A is the value of P when Qd=0. So to get this P we put Qd = 0,

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Supply and Demand in Math Terms

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  1. Supply and Demand in Math Terms

  2. Say you have a competitive market where the demand from consumers is Qd = 6000/9 – (50/9)P. Point A in the graph is the vertical intercept of the demand curve. We had Qd = 6000/9 – (50/9)P. A is the value of P when Qd=0. So to get this P we put Qd = 0, 0 = 6000/9 – (50/9)P, or solving for P we get P = 6000 /50 =120. P D1 A Q Market

  3. Say you have a competitive market where the supply from sellers is Qs = 25P – 250. Point B in the graph is the vertical intercept of the supply curve. B is the value of P when Qs=0. So to get this P we put Qs = 0, 0 = 25P – 250, and solve for P. P = 250 /25 =10. P S1 B Q Market

  4. So, we had demand Qd = 6000/9 – (50/9)P, and supply Qs = 25P – 250. The market price and quantity traded are determined where Qs = Qd, or where the curves cross. So we have 25P – 250 = 6000/9 – (50/9)P, or (and note 25 = 225/9) (225/9)P + (50/9)P = 6000/9 + 2250/9, or (275/9)P = 8250/9, or P = 8250/275 = 30. Plug P = 30 into either Qd or Qs to get the quantity traded in the market. In Qs we have 25(30) – 250 = 500.

  5. Here is the market situation we have in this example. My graph is not totally to scale. P D1 S1 120 P1 =30 10 Q Q1=500 Market

  6. Solving for the equilibrium market price and quantity traded is just one example of a more general situation of solving for 2 unknowns with 2 equations. I want to show you how Excel can do the work for you. But first lets re-arrange our supply and demand to the following Demand (50/9)P + Qd = 6000/9, and Supply -25P + Qs = -250. Notice how I put the price terms first in each equation, then I put the quantity term and then on the right side of the equal sign I put the part of the equations with no variable attached to it. (I also always followed the laws of algebra when I did this.) Let’s call this right hand side of the equations the constants. The numbers attached to the P and Q in each line will be called coefficients (and note the Q’s here have a coefficient = 1).

  7. We had Demand (50/9)P + Qd = 6000/9, and Supply -25P + Qs = -250. In Excel we will put the coefficients into adjoining cells like 50/9 1 -25 1 and we will say we have a coefficient matrix (a table). The constants will also be in a column like 6000/9 -250 Note in Excel if you want to put a negative number in a cell, like -250, you type =-250 in the cell. Plus when you have a fraction like 6000/9 you would type =6000/9. I have an Excel file that shows you the rest of the story here.

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