Econ 100 Winter 2015 Problem set 1

Econ 100Winter 2015Problem set 1Due Friday January 16 in Class1. Find the derivative with respect to x for the following functions.a. f ( x ) = ax 3 + bx 2 + x ;b.f ( x ) = ax ln x ;2. What is the price elasticity of the demand curve Q(p) = a – bln(p)?3. Suppose that the demand for water balloons fit the function D(p,ps) = D( p, ps ) = .2 p.5 ps.2where p is the price of water balloons and ps is the price of super soakers (an advanced squirtgun technology).Based upon this demand curve, are super soakers a compliment or a substitute for waterballoons? Demonstrate why.14. Suppose that the current price of oil is $60 per barrel and the quantity sold is 90 millionbarrels per day. Assume that the supply and demand curves for oil are linear. The currentestimates of the price elasticity of supply and demand in the U.S. are = 1 and = – .2respectively. Assume that the supply and demand curves for oil are linear. In other words,supply can be expressed as S(p) = a + bp, and demand as D(p) = e fp.a. Derive a and b, the horizontal (quantity) intercept and slope of the supply curve.b. Derive the components of the demand curve, e and f .24 (continued)Now assume that the U.S. government has decided to purchase and additional 2 millionbarrels of oil per day and put it into the strategic petroleum reserve. In other words, thisadditional oil is pumped into the ground and not circulated in the existing U.S. oil market.c. Draw (using supply and demand curves) the impact of this new governmentpolicy on the U.S. oil market.d. Calculate the new equilibrium price resulting from the governments new policy.