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(Solved) Situations do exist where we might run into three equations / three variables, four equations / four variables and so on. These are referred to as a...


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instructions | help Systems of Equations (Two equations / Two variables) In economics, market analysis in particular, we have two equations (supply and demand) and two variables (price and quantity) to solve for.
Situations do exist where we might run into three equations / three variables, four equations / four variables and so on. These are referred to
as a system of equations. We will concentrate on two equations and two unknown variables. For example, we might be given the following
Example:
The demand for popsicles is given by the following equation, where QD stands for the quantity demanded and P stands for price. The supply of popsicles is given by the following equation, where QS stands for the quantity supplied and P stands for price. First, determine the price of popsicles at equilibrium when quantity demanded 'QD' and quantity supplied 'QS' are equal. To get started,
we set the demand and supply equations equal to each other and solve for P. QD = QS
52 - 2P = -4 + 5P Group the variables.
52 - 2P + 4 = -4 + 5P +4
56 - 2P + 2P = 5P + 2P
56 = 7P Divide by 7.
56 / 7 = 7P / 7
P = 56/7
P=8 Now, using the solution value of price P = 8, find the quantity demanded and quantity supplied of popsicles. QD = 52 - 2P = 52 - (2 × 8) = 52 - 16 = 36 QS = - 4 + 5P = -4 + (5 × 8) = - 4 + 40 = 36 18. value: Required information 1.00 points Given the following equations:
Demand:
Supply:
Solve for the equilibrium price 'P' and quantity (Q: QD = QS):
P* = $
QD = QS = Q* = units Check my work 1/23/2017 19. value: Required information 1.00 points The demand for coffee is given by the following equation, where QD stands for the quantity demanded and P stands for price. The supply of coffee is given by the following equation, where QS stands for the quantity supplied and P stands for price. a. What is the slope of demand? Slope = b. At what price is quantity demanded equal to zero (this is, graphically, the vertical intercept of Demand)?
P=
c. What is the slope of supply?
Slope =
d. At what price is quantity supplied equal to zero (this is, graphically, the vertical intercept of Supply)?
P=
e. In the diagram below use the tool provided to identify the equilibrium price 'P' and quantity 'Q' -- the solution to this system of two
equations. A
50 S1 45
40
35
30
25
20
15
10
5 D1 0
-5
-10
0 10 20 30 40 50 60 Quantity 70 80 90 100 110

 


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