Consider a demand equation for a private good x of the form

where p is price, y is income, and q is a quasi-fixed quality attribute of x. Suppose we have estimated the parameters of this equation and found that α=2, β=0.65, κ=1.50 and γ=0.0002. Assume that the baseline price and quality are p=$10 and q=1, respectively, and that we are interested in examining the welfare effects for a person with income of $50,000.

(a) Compute the baseline demand level, income elasticity, ordinary demand price and quality elasticities, and choke price for this person. At the baseline, is demand more sensitive to changes in quality or price?

(b) State the indirect utility function V(p,y,q) for this demand equation. (see Eq. (14.32) in Chapter 14 and note that quality enters here via cross-product repackaging.) Use V(•) to derive the ordinary inverse demand for q function. Compute the income elasticity for the ordinary inverse demand for q at baseline conditions. How does it compare to the income elasticity for x?

(c) Consider a quality increase from q=1 to q=2. Compute the change in consumer surplus from this using the expression in Eq.
(15.10), and then using the expression in Eq. (15.13). How do they compare? Also compute the compensating and equivalent variations for the change in q. What is the percentage error when we use C rather than CV as our welfare measure?

Eq 14.32

Eq 15.10

Eq 15.13

Transcribed Image Text:

x=-Bp+kq+Yy,