Suppose the market demand for Cashews is as follows: Qc = 500 + (.01)I – 100Pc -

Question

Suppose the market demand for Cashews is as follows:

Qc = 500 + (.01)I – 100Pc - 25Pb            

Qc = Quantity of Cashews demanded                            I = Income

Pc = Price of Cashews                                                    Pb = Price of Beer

Find the own-price, cross-price, and income-elasticities of cashews as a function of prices, income and quantity. (3 pts)

Assume that Income = 40,000, Pc = $6, and Pb = $4. Solve for the elasticities above by plugging these values in. In each case, note whether elastic, inelastic, or unit elastic. Are cashews a normal or inferior good? Are beer and cashews complements, substitutes, or unrelated goods?

12. Continuing from the previous, now assume that Income rises to $50,000 and the price of beer rises to $10 (price of cashews stays the same). Are cashews still the same type (normal or inferior) of good? Solve again for the elasticities in the prior question.    (2 pts)

Explanation / Answer

(Question 1)

Plugging in given values,

Qc = 500 + (0.01 x 40,000) - (100 x 6) - (25 x 4)

Qc = 500 + 400 - 600 - 100

Qc = 200

(i) Own price elasticity = (dQc / dPc) x (Pc / Qc) = - 100 x (6 / 200) = - 3

Since absolute value of own price elasticity is higher than 1, demand is elastic.

(ii) Income elasticity = (dQc / dI) x (I / Q) = 0.01 x (40,000 / 200) = 2

Since income elasticity is positive, cashew are normal good, and since income elasticity is higher than 1, it is a luxury good.

(iii) Cross-price elasticity = (dQc / dPb) x (Pb / Qc) = - 25 x (4 / 200) = - 0.5

Since cross-price elasticity is negative, cashews and beer are complements.

NOTE: As per Chegg answering policy, 1st question is answered.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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