Question

At a price of N188 per pound, the supply for cherries in a large city is 16,000 pounds, and the demand is 10,600 pounds. When the price drops to N146 per pound, the supply decreases to 10,000 pounds, and the demand increases to 12,700 pounds. Assume that the price supply and price-demand equations are linear.

a. Find the price-supply equation

b. Find the price-demand equation

c. Find the supply and demand at a price of N209 per pound

d. Find the supply and demand at a price of N132 per pound

e. Use the matrix method to find the equilibrium price and equilibrium demand

Answer 1

The student's question involves calculating the price-supply and price-demand equations based on provided data points, predicting supply and demand at specified prices, and determining equilibrium using the matrix method.

Step-by-step explanation:

The task is to find the linear price-supply and price-demand equations based on changes in price and quantity. For the price-supply equation, at N188 per pound the supply is 16,000 pounds, and at N146 per pound the supply is 10,000 pounds. To form the equation, we use the two points (188, 16000) and (146, 10000). Similarly, for the price-demand equation, at N188 per pound the demand is 10,600 pounds, and at N146 per pound the demand is 12,700 pounds. We use points (188, 10600) and (146, 12700) to form the demand equation.

To calculate the supply and demand at a given price, we simply substitute the price value into the equations obtained. For predicting equilibrium using the matrix method, we need to set the supply equation equal to the demand equation and solve for the price and quantity where supply equals demand.