Equilibrium price is the price set by the market as it clears itself from any surplus or shortage. It is computed by equating the demand equation to the supply equation as equilibrium suggests balance between the two forces of the market (McConnell & Brue, 1993, 58). From the given, = 1144 - 400+200+ 1.5 Y is the demand function and = 1744 + 100 is the supply function. By equating the demand and supply function and substituting given variables like the or the price of sandwich and Y or the income in the formulas, the value for which is the price of pies is computed to be $3.
This is also the equilibrium price of pies. Supply varies with the price changes as producers will always depend on the price set by the market for their profit (McConnell & Brue, 1993, 55). By substituting the equilibrium price to the given supply function, the quantity of pies produced and purchased can be computed. At the price of $3, the island produced and purchased 2 044 pies. Producer profit or producer surplus exists when there is a change in the price or when producers are able to sell their pies at prices higher than what the consumers are willing to pay.
In this case, there will be producer surplus only if producers will be able to sell their pies at prices higher than $3 which is the price which consumers are willing to pay in exchange for pie. Imposition of taxes on goods affects the equilibrium price on both consumers and producers (McConnell & Brue, 2005, 47). A $1/pie tax imposed to the consumers reduces their willingness to pay extra amount for the tax and reduces quantity demanded.
Producers are also affected by the imposition of this tax because every time they sell 1 pie they incur $1 less from their sales. Thus a new set of equilibrium price will be acquired. For the consumers, it is computed as substituting P-1 to the price of pie in the demand equation and equating it to the supply equation. This will give $3.67 as the equilibrium price after the $1/pie tax. By doing the same, but this time to the supply equation will give $5.33 as the new equilibrium price for the producers.
And with this price, 1 211 pies are produced and sold. The tax imposed also generated $833 revenue as it is the difference of the quantity of pies produced and sold before and after the tax multiplied by the $1 tax. Monopolists are not price takers but instead are price setters or makers. They maximize their profits by producing output at MR=MC and set their prices by following the P=MC rule (McConnell & Brue, 2005, 363).
In the given situation, with the marginal cost of production set at m = 1.744 + 0.0025 , and quantity produced is set at = 1744 + 100 , the princess will sell pie at $6.85 each and will produce 2 429 pies to maximize her profit. Direct substitution is used for the computations of the answers. With the changes that took place at the palace, the economy will also experience some changes. These include changes in the quantity of pie available in the market and its price.
The entry of new producers in the market means additional supply of pies. By combining the two supply functions given, = 1744 + 100 and = 1000 + 100, new price of $0.83 for pie is set. And with this new price, the quantity of pie that can be produced locally is 2 910 pies. This computed by substituting the new price $0.83 to the sum of the two supply functions. Bibliography McConnell, C.
R., & Brue, S. L. (2002). Microeconomics: Principles, Problems and Policies. New York: McGraw-Hill, Inc. McConnell, C. R., & Brue, S. L. (2005). Macroeconomics: Principles, Problems, and Policies. New York: McGraw-Hill Companies, Inc.