Final answer:
The supply and demand functions are S(p) = 0.25p and D(p) = -0.25p + 75. The market equilibrium point is a price of $50 and a quantity of 13 calculators.
Step-by-step explanation:
To find the supply and demand functions as well as the market equilibrium point, we can use the information provided. Let's assume the supply function is S(p) = mp + b, where m is the slope and b is the y-intercept.
From the given information, we know that when the price is $100, the supply is 25, and when the price is $50, the supply is 50. This gives us the equations:
25 = 100m + b
50 = 50m + b
Solving these equations, we find that m = 0.25 and b = 0.
Similarly, assuming the demand function is D(p) = mp + b, we can use the given information to find the values of m and b. When the price is $100, the demand is 50, and when the price is $50, the demand is 25. This gives us the equations:
50 = 100m + b
25 = 50m + b
Solving these equations, we get m = -0.25 and b = 75.
The market equilibrium point is where the quantity demanded is equal to the quantity supplied. We can find this by setting the demand function equal to the supply function:
0.25p + 75 = -0.25p + 50
Simplifying this equation, we get:
0.5p = 25
p = 50
So the equilibrium price is $50. Substituting this back into either the supply or demand function, we can find the equilibrium quantity. Using the supply function:
Q = 0.25(50) + 0 = 12.5
Therefore, the market equilibrium point is a price of $50 and a quantity of 12.5 calculators (which can be rounded up to 13 calculators).