1. Suppose in the market for bicycles, the supply curve is = 30 + 2 and the demand curve is = 90 2, where is the price of bicycles and is the quantity of bicycles supplied or demanded per year. Note: Part (c) requires you to plot your results from part (a) and part (b).

(a) Show how to solve for equilibrium quantity and price of bicycles, total revenue to producers , consumer surplus , producer surplus , and total surplus .

(b) Suppose the government considers the equilibrium price from part (a) being too high such that low-income households cannot afford bicycles and it legislates to change the price of bicycles by $20 with a binding price ceiling . Show how to solve for the binding price ceiling ,. At , solve the quantity of bicycles supplied and demanded , the quantity of excess supply (surplus) or demand (shortage), total revenue to producers , consumer surplus , producer surplus , total surplus , and the deadweight loss .

(c) Plot your results from part (a) and part (b) in a properly labeled diagram.

(d) Following the notations: 12 represents the cross elasticity of the quantity demanded for good 1 when the price of good 2 changes, "" for bicycles, "" for skateboards, and "" for unicycles. The cross-price elasticity of the quantity demanded for unicycles when the price of bicycles changes is = 2, and the cross-price elasticity of the quantity demanded for skateboards when the price of bicycles changes is = 1.5. According to the price change between part (a) and part (b), calculate the percentage change in quantity demanded for unicycles and skateboards. Use your results to explain how unicycles and skateboards are related to bicycles. Hint: Use the midpoint formula.

(e) Suppose bicycle producers used to consume 40 bottles of red wine when their income was at in part (a) and their red wine consumption drops to 8 bottles as their income changes to in part (b). Calculate the income elasticity of red wine for bicycle producers. Hint: Use the midpoint formula. Is red wine an inferior, a normal, or a luxury item to bicycle producers?