Question

The quantity demanded x (in units of a hundred) of the Mikado miniature cameras per week is related to the unit price p (in dollars) by p = −0.2x2 + 220 and the quantity x (in units of a hundred) that the supplier is willing to make available in the market is related to the unit price p (in dollars) by p = 0.1x2 + 8x + 110. If the market price is set at the equilibrium price, find the consumers' surplus and the producers' surplus. (Round your answers to the nearest dollar.)'

Answer 1

To determine the consumer surplus and producer surplus at the market's equilibrium price for Mikado miniature cameras, one must first find the equilibrium by setting the demand equation equal to the supply equation. Then, using the concepts of consumer and producer surplus in economic graphs, calculate the areas below the demand curve and above the supply curve to find the respective surpluses.

Step-by-step explanation:

The student has asked to find the consumer surplus and the producer surplus at the equilibrium price for Mikado miniature cameras. The equilibrium price is the point where the quantity demanded equals the quantity supplied, which can be found by equating the two given equations:

For demand: p = −0.2x² + 220

For supply: p = 0.1x² + 8x + 110

Once the equilibrium price and quantity are found, the consumer surplus is the area below the demand curve and above the market price while the producer surplus is the area above the supply curve and below the market price. These areas form triangular regions on the graph of demand and supply.