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 = 50,000 Pc = $6, and Pb = $10 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?

Explanation / Answer

Qc = 500 + 0.01 I - 100 Pc - 25 Pb

Own-price elasticity of Cashews = (Change in Qc / Change in Pc ) (Pc /Qc )

Now, to calculate( change in Qc/ Change in Pc) , take the first partial derivative of demand function with respect to Pc, we get:
Change in Qc / Change in Pc = -100

Own price elasticity of cashews = -100 (Pc / Qc)

Cross price elasticity of cashews = (change in Qc/ Change in Pb) (Pb / Qc)

To calculate (change in Qc / Change in Pb ) , take the first partial derivative of Qc with respect to Pb,we get:

Change in Qc / Change in Pb = -25

Cross price elasticity = -25 (Pb / Qc)

Income elasticity of cashews = (change in Qc / Change in I ) ( I / Qc )

To calculate (change in I / change in Qc ) , take the first partial derivative of Qc with respect to I, we get:

Change in Qc / change in I = 0.01

Income elasticity = 0.01 (I / Qc )

Assume I = 50,000 , Pc = $ 6 and Pb = $10.

Firstly , put these values in Qc , we get

Qc = 500 + 0.01 (50000) - 100(6) -25(10)

Qc = 500 + 500 -600 -250 = 150

Now, put these values in elasticities we get ,

Own price elasticity = -100 (Pc /Qc)

= -100 (6/150 )

= -4

Because own price elasticity is less than 1 . It means that demand is inelastic.

Cross price elasticity = -25 (Pb / Qc)

= -25 (10/150 )

= -1.66 .

Cross price elasticity is less than zero. Therefore, it implies that beer and cashews are complements.

Income elasticity = 0.01 (I /Qc)

= 0.01 (50000/ 150)

= 3.33

If income elastcity is greater than 1 . Then, it represents normal goods. It means cashews are a normal good.

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