Note: In the exam. round to two decimal places as needed. 1. Equilibrium. Tax and Price Ceiling. (40pts) Consider the following demand function and supply function in a good market: q. = 40 55*; q. 2 2p 9 Find the equilibrium price and equilibrium quantity. Invert the demand function and the supply function. Calculate the consumer surplus and producer surplus. Then. find the total welfare. Suppose that price ceiling has been imposed Lo 3? = 5. Find the consumer surplus. producer surplus. and total welfare with this price ceiling. Find the deadweight loss (DW'L) from this price ceiling. Suppose that the government has decided to remove the price ceiling and impose a per unit tax of $2.00 on every unit of good that consumers buy. Find the price that is received by the supplier and the price a consumer pays. Calculate the tax revenue and deadweight loss from this tax. Based on your asnwers above. which scenario is better for society as a whole? Tax or price ceiling? Explain the reason. 2. Utility. Substitution and Income Effect (30pts) Consider the following utility function: { : mas-20.4 Derive the marginal rate of substitution. Derive the demand functions for good 3: and good 3 as a function of income (Y). the price of 3: (p3) and the price of 2: (pg). Assume Y = 100. p3: = 5 and pz 2 10. Find the equilibrium quantities (bundle A) for this consumer. Let's now assmue good 2 goes on sale for $8 (sz = 8). If nothing else changes. what are the new equilibrium quantities (bundle B)? Calculate the decomposition bundle. (Hell: nd another another bundle, say Bundle C, by using New Prices and Old Utility concept). Calculate the total. income and substitution effect for good 3