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Sotiris Georganas September 2015  I. Introduction: 1. Suppose the supply curve for wool is given by Qs = P, where Qs is the quantity offered for sale when the price is P. Also suppose the demand curve for wool is given by Qd = 10 ? P + I , where Qd is the quantity of wool demanded when the price is P and the level of income is I. Assume I is an exogenous variable.. Suppose income rises from I1 = 20 to I2 = 24. a) Using comparative statics analysis, find the impact of the change in income on the equilibrium price of wool. b) Using comparative statics analysis, find the impact of the change in income on the equilibrium quantity of wool. Eq1: P = Q = (10+I)/2 , Shift up the demand curve II. Problems about Demand and Supply 1. Suppose price is initially $5, and the corresponding quantity demanded is 1000 units. Suppose, too, that if the price rises to $5.75, the quantity demanded will fall to 800 units. What is the price elasticity of demand over this region of the demand curve? Is demand elastic or inelastic? 2. Suppose a constant elasticity demand curve is given by the formula Q = 200P?1/2 What is the price elasticity of demand? 3. Suppose a linear demand curve is given by the formula Q = 400 ? 10P. What is the price elasticity of demand at P = 30? At P = 10? III Problem set Consumer Choice Theory 1. Let’s look at a utility function that satisfies the assumptions that more is better and that marginal utilities are diminishing. Suppose a consumer’s preferences between food and clothing can be represented by the utility function U = √xy, where x measures the number of units of food and y the number of units of Clothing. (a) Show that a consumer with this utility function believes that more is better for each good. (b) Show that the marginal utility of food is diminishing and that the marginal utility of clothing is diminishing. (a) By examining the utility function, we can see that U increases whenever x or y increases. Th