Final answer:
To determine the level of production and unit price at market equilibrium, set the supply function equal to the demand function and solve for the quantity.
Step-by-step explanation:
The correct answer is to find the market equilibrium by setting the supply function S(x) equal to the demand function D(x), which means solving the equation 2x + 7.43 = -0.21x^2 - 0.84x + 50. To solve for x, we can rearrange the terms to have a quadratic equation: 0.21x^2 + (2 + 0.84)x + (7.43 - 50) = 0. Solving this quadratic will give us the equilibrium quantity (x), and then we can plug this value back into either S(x) or D(x) to find the equilibrium price (p).
Alternatively, we can use the method of graphing if algebra is challenging. We would graph both supply and demand functions on the same axes, where the vertical axis represents price (P) and the horizontal axis represents quantity (Q). The point where both curves intersect is the equilibrium point, showing the equilibrium price and quantity.
Then, substitute the equilibrium quantity back into either function to get the equilibrium price.