Answer to Question #230790 in Statistics and Probability for huzaifa azmat

Question

A consumer survey was conducted to determine the demand function for the same product as in the previous example discussed for supply function. The researchers asked consumers if they would purchase the product at various prices and from their responses constructed estimates of market demand at various market prices. After sample data points were plotted, it was concluded that the demand relationship was estimated best by a quadratic function. The researchers concluded that the quadratic representation was valid for prices between $5 and $45. Three data points chosen for fitting the curve were (5, 2025), (10, 1600) and (20, 900).

Answer 1

The quadratic function is given by the formula y = a*x² + b*x + c

The system we have:

2025 = a*5² + b*5 + c

1600 = a*10² + b*10 + c

900 = a*20² + b*20 + c

a = 1

b = -100

c = 2500

Substituting these data points into the general equation for the quadratic function and solving the resulting system, we simultaneously obtain the demand function q_d = p²-100*p + 2500. Here q_d is the demand expressed in thousands of units, and p is equal to the sale price in dollars.