1. As the newest member of a team of economic advisors for the great state of Pennsylvania, you are assigned to analyze the gasoline market. Suppose demand for gas is a function of the price of gas, P, and the price of electricity at charging stations for electric vehicles, Po. Assume that electric charging is a substitute for gasoline. Supply of gasoline is a function only of the price of gas, P. The first question posed by the governor's office is how the market equilibrium price and quantity of gasoline, P* and Q*, will be impacted if there is a decrease in the price of electricity P. at charging stations for electric vehicles. Use a diagram for the market for gasoline, assuming downward sloping demand and upward sloping supply, to provide an answer, and explain why the answer makes sense using the concept of substitute goods. а. b. The governor's office is worried that your answer about the impact on price might be wrong because you do not know the exact shapes of the true demand and supply functions in the market for gasoline. Use calculus, and the most general forms of the demand and suppy functions (Qd=D(P, P.) & Qs=S(P)), to demonstrate that you do not need to know the exact functions. Show that your predictions for equilibrium price will be correct as long as demand for gasoline slopes down, and supply slopes up, assuming electric charge is a substitute good for gasoline. Use calculus to show that your prediction for equilibrium quantity holds under the same assumptions needed in the previous part. С. d. As a follow-up, the governor's office asks how the slope of the market supply curve will matter for how large the response of gasoline price is to the decreased price of electricity at charging stations. Give an answer to this question using the formula you derived in part (b). Also draw a diagram that illustrates graphically how the slope of supply affects the response of equilibrium price (and quantity) to a decrease in electricity price. e. Suppose your best estimate for the demand curve for gasoline is given by Qa = a + bP +cPo, where a, b, and c represent numerical constants (i.e., parameters), with b<0 and a and c positive. The governor's office asks you for a prediction about the percentage increase in Qa if price of gasoline increases by 1% (or a small amount). Derive a formula for the price elasticity of demand. Assuming you have numerical estimates for the parameters of the demand function, what additional information does the governor's office need to specify, in order for you to be able to provide a numerical answer the question? Use your formula for price elasticity to explain what happens to the price elasticity of demand for gasoline as you move down the (linear) demand curve. f. Gas prices fell early in the pandemic, when the state imposed travel restrictions, such as rules preventing people from traveling across state borders. The governor's office asks you to explain why this happened to the price. Assume that with travel restrictions, the market demand curve for gasoline is given by Qd = a + bP + cP, + dR, where a higher value of R means greater restriction on travel (in g. normal times without restrictions R is zero). What do you expect to be the sign of the parameter d? Use a demand and supply diagram to show the impact on the equilibrium in the market for gasoline, when R goes from zero to some positive amount.