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A bakery in a small town has a supply curve for custom cakes given by the equation [tex]P = 2 + 5Q[/tex]. The bakery faces a weekly demand curve for cakes given by [tex]P = 45 - 3Q[/tex], where price is measured in dollars and quantity is measured per cake.

a) Plot the supply and demand curves on a scale diagram.

b) What is the equilibrium market price the bakery will charge, and how many cakes will consumers buy?

c) How much is the consumer surplus?

d) What is the bakery’s revenue?

e) Suppose the local government is concerned about the health impacts of sugar and decides to add a tax of $5 per cake to discourage consumption. How many cakes will consumers now buy, and how much will they have to pay?

Answer :

We need to plot the supply and demand curves, find the equilibrium price and quantity, calculate the consumer surplus, determine the bakery's revenue, and then consider the effects of the added tax on the quantity and price.

A) To plot the supply and demand curves on a scale diagram, we need to plot the price (P) on the y-axis and the quantity (Q) on the x-axis.
- For the supply curve, the equation is P = 2 + 5Q. We can choose some values for Q and calculate the corresponding P values to plot the points.
- For the demand curve, the equation is P = 45 - 3Q. Similarly, we can choose values for Q and calculate P to plot the points.

B) The equilibrium market price is the price at which the quantity supplied equals the quantity demanded. To find it, we set the supply and demand equations equal to each other and solve for Q. Once we find Q, we can substitute it back into either the supply or demand equation to find the equilibrium price.

C) Consumer surplus is the difference between what consumers are willing to pay and what they actually pay. To calculate it, we need to find the area between the demand curve and the equilibrium price, multiplied by the quantity of cakes consumers buy.

D) The bakery's revenue is the price per cake multiplied by the quantity of cakes sold.

E) To find the new quantity of cakes consumers will buy and how much they will have to pay with the added tax, we need to subtract the tax amount from the equilibrium price and solve for the new quantity using the demand curve equation.

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