Question

In: Economics

11. Given the demand function of McDonald’s BigMac Ln(Qm)= 3-1.5Ln(Pm)+0.4Ln(PA)+0.5Ln(Pw)+0.02Ln(I) Qm: the demand of BigMac, Pm:...

11. Given the demand function of McDonald’s BigMac

Ln(Qm)= 3-1.5Ln(Pm)+0.4Ln(PA)+0.5Ln(Pw)+0.02Ln(I)

Qm: the demand of BigMac,

Pm: the price of BigMac,

PA: the price of Arby’s sandwich

Pw: the price of Whataburger.

I: Income

What’s the own price elasticity of BigMac? Write out the formula, calculate and interpret.

What’s the cross price elasticity of demand of BigMac with respect to the price of Arby’s sandwich? Write out the formula, calculate and interpret.

What’s the cross price elasticity of BigMac with respect to the price of Whataburger? Write out the formula, calculate and interpret.

What’s the income elasticity of BigMac? Write out the formula, calculate and interpret.

If the price of Arby’s sandwich is increased by 20% , the price of Whataburger is decreased by 10%, and Income is increased by 10%. What is the aggregate effect on the demand for BigMac?

Expert Solution

11. The demand function is given as .

The own price elasticity of BM can bestated as . For , we have or or or . Hence, the own price elasticity is -1.5, ie for a unit increase in percent change in own price of BM, the quantity of BM decreases by 1.5 percent, suggesting that BM's burger is not a giffen good.

The cross price elasticity of BM demand with respect to Arby's sandwich can be stated as . For , we have or or or . Hence, the corss price elasticity of BM with respect to A's sandwich is 0.4, ie for a unit percentage increase in price of A's sandwich, the BM's demand increase by 0.4 percent, suggesting that BM's burger is a substitute to A's sandwich.

The cross price elasticity of BM's demand with respect to Whataburger can be stated as . For , we have or or or . Hence, the crossprice elasticity of BM with respect to price of Whataburger is 0.5, ie for a unit increase in percentage of price of Whataburger burger, the quantity demanded of BM's burger increases by 0.5 percent, suggesting that BM is a substitute of Whataburger.

The income elasticity of BM can be stated as . For , we have or or or . Hence, the income elasticity of BM is 0.02, ie for a unit increase in percentage of income, the demand for BM rises by 0.02%, suggesting that BM is a normal good.

The total effect on BM's burger can be stated as for , we have or or ; and for is basically the percentage change in , thus (assuming no change in price of BM) or or , ie the demand for BM rises by 3.2%. It can be seen that the change in percentage changes of the variables in this model if multiplied by their respective elasticities and aggregaated, can determine the total change in quantity.

Rahul Sunny answered 2 years ago

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