Question 1. Read section 3.1 of the theoretical model in Anderson (2012) and answer the following questions:

(1) in eqn. (1), what are the two types of utilities from gasoline and ethanol consumption?

(2) in eqn. (1), what do the parameters θ_e and θ_g capture? What is the economic interpretation of θ_e - θ_g ?

(3) Given the utility function in eqn. (1) and budget constraint in eqn. (2), derive the househlod's optimal choice of miles if he chooses ethanol, i.e., eqn. (5). Note that v'^-1 denotes the inverse function of the first derivative of the utility function.

Question 2. Asssume that Tom's annual demand for vehicle millage traveled, VMT (in miles), can be expressed as VMT = 20000 - 1000C, where C is the per mile fuel cost in $/mile. We know that VMT is produced from the production function VMT = G * MPG where G is the amount of gasoline consumed (in gallons) and MPG (miles per gallon) is the fuel efficiency measure. Let P_g denote the gasoline price.

(i) What is the operating cost per mile? (only consider fuel cost)

(ii) Assume Tom's vehicle can drive 20 mils per gallon, i.e., MPG=20, determine Tom's gasoline demand as a function of gasoline price.

(iii) If the gas price is $2/gallon, how much gasoline will he consume?

(iv) What is the price elasticity of demand at this point?

Question 3. Answer the questions related to the article "Evidence of a shift in the short-run price elasticity of gasoline demand" by J. Hughes, C. Knittel, and D. Sperling. In Section 2, the authors estimate the following demand equation:

ln Gjt = β₀ + β₁ ln P_jt + β₂ ln Y_jt + ε_j + ε_jt

where G_jt is per capita gasoline consumption in gallons in month j and year t , P_jt is the real retail price of gasoline in month j and year t, Yjt is real per capita disposable income in month j and year t , ε_j represents unobserved demand factors that vary at the month level and ε_jt is a mean zero error term.

(i) What have the authors assumed about the price elasticity of demand when they wrote down the demand equation in this form? Remember the price elasticity of demand

E_p =  ∂G/∂P.P/G

(ii) Go to Table 1 in the paper, now assuming the author have obtained unbiased estimates of the parameters β₀ , β₁ and β₂, what do they mean (e.g., the coefficient β₁ is -0.335 in the period 1975-1980, this represents...)

(iii) What can you say about the yearly pattern of gasoline demand from the coefficients?

(iv) From the information presented in Table (1) calculate the appropriate t-statistics for each of the β's to test if it is different from 0. You will need the standard errors for each coefficient which are presented in brackets below the respective coefficient value in the table.

(v) What do the *** next to some of the entries in the table indicate?

(vi) Table (1) presents the adjusted R-squared statistics for the two regressions. What does this number mean?

Question 4. Read section 3 (except the last part on "variances") of Reiss and White (2005) and answer the following question:

(1) One of the challenges in estimating electricity demand and assessing the effect of electricity price changes is aggregation of consumption behavior over appliances. This implicitly imposes constant consumption responses for various energy-using appliances. How the authors overcome this challenge? What are the implications on price and income elasticities?

(2) Read section 6 of the paper and answer the following questions:

(i) How to interpret the result of "-22.5" (1st row; 3rd column)?

(ii) Figure 2 indicates that 44% of California households don't respond to marginal price changes. What can we say about this part of population from Table 3?

(iii) What is implied from the highly asymmetric distribution of the price elasticity in Figure 2?

(iv) How do price elasticities change with household income as presented in Table 4?

Reference for question 3:

Article - Evidence of a Shift in the Short-Run Price Elasticity of Gasoline Demand

Author(s): Jonathan E. Hughes, Christopher R. Knittel and Daniel Sperling

Source: The Energy Journal, Vol. 29, No. 1 (2008), pp. 113-134

Stable URL: http://www.jstor.org/stable/41323146

Reference for question 4:

Article - Household Electricity Demand, Revisited PETER C. REISS and MATTHEW W. WHITE

Author(s): PETER C. REISS, MATTHEW W. WHITE

Attachment:- References.rar