A firm has estimated the following demand function for its product: Q = 100 - 5

Question

A firm has estimated the following demand function for its product:
Q = 100 - 5 P + 5 I + 15 A

Where Q is quantity demanded per month in thousands, P is product price, I is an index of consumer income, and A is advertising expenditures per month in thousands. Assume that P = $200, I = 150, and A = 30. For simplicity in calculating the results, use the point elasticity formulas to complete the calculations indicated below.

(i) Calculate quantity demanded.
(ii) Calculate the price elasticity for demand. Is demand elastic, inelastic, or unit elastic?
(iii) Calculate the income elasticity of demand. Is the good normal or inferior?
(iv) Calculate the advertising elasticity of demand.

Explanation / Answer

I use "D" to denote "change in." Elasticities are calculated at the midpoint. DQ/DY is the derivative of Q with respect to Y. So, we could find the value simply by looking at the coefficient in the equation that is given. DQ/DP=-5 DQ/DI=5 DQ/DQ=15 Price elasticity is calculated as an absolute value, so we can pretend DQ/DP=5 (i) Q = 100 - 5 P + 5 I + 15 A P= $200, I = 150, and A = 30 So, Q = 100 - 5*200 + 5*150 + 15*30 = 300 (ii) PE=DQ/DP *P/Q PE=5*(200/300) = 3.33 This good is elastic because PE>1 (iii) IE=DQ/DI * I/Q IE=5*(150/300)=2.5 This is a normal good because IE>0 (iv) AE=DQ/DA * A/Q AE=15*(30/300)=1.5

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.