In the following questions, give all your answers to two decimals.Patrice works as an economist for the Bureau of Labor Statistics (BLS). Her current project is to estimate the effect of changes inincome, prices of related goods, and the price of potatoes on the demand for beef. Patrice has the following data:Price elasticity of demand for beef-0.80Income elasticity of demand for beef+ 1.40Cross-price elasticity between beef and chicken+1.20Cross-price elasticity between beef and potatoes-0.50Suppose the price of beef rises by 8%. All else equal, the quantity of beef demanded wouldfallby%. If the price of chicken rises by 4%, the quantity of beef demanded wouldriseby%.

Answered: If the price of chicken rises by 4%,…

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter4: Demand, Supply, And Market Equilibrium

Section: Chapter Questions

Problem 7P

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Question

If the price of chicken rises by 4%, the quantity of beef demanded would
rise
by
%.

Expert Solution

Step 1

Price elasticity of demand refers to the % change in quantity demanded due to the % change in the price. It measures the responsiveness of quantity demanded towards the price change.

For a beef market, the own price elasticity of demand for beef is given as -0.80. If there is an increase in the price of beef by 8%, then the quantity demanded of beef would fall by:

$\begin{array}{rcl} E_{d} & = & \frac{% c h a n g e i n Q}{% c h a n g e i n P} \\ - 0.80 & = & \frac{% c h a n g e i n Q}{8 %} \\ % c h a n g e i n Q & = & - 0.80 * (8 %) \\ % c h a n g e i n Q & = & 0.64 \\ % c h a n g e i n Q & = & 64 % \end{array}$

The cross price elasticity between beef and chickens is +1.20. The cross price elasticity is the % change in demand for beef due to the % change in price of chicken. The positive sign implies that there is a positive relationship between the price of chicken and demand for beef. It means that an increase in price of chicken will lead to an increase in the demand for beef, which shows that the goods are substitutes.

If the price of chicken rise by 4%, then the change in quantity demanded of beef would be:

$\begin{array}{rcl} E_{c} & = & \frac{% c h a n g e i n Q o f b e e f}{% c h a n g e i n P o f c h i c k e n} \\ + 1.20 & = & \frac{% c h a n g e i n Q o f b e e f}{4 %} \\ 4.8 % & = & % c h a n g e i n Q o f b e e f \end{array}$

Thus, quantity of beef demanded will increase by 4.8%.

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