1) Consider the inverse demand function for good X below PX = 30 - 0.005X + 0.15
ID: 1137155 • Letter: 1
Question
1) Consider the inverse demand function for good X below
PX = 30 - 0.005X + 0.15PY
Where X refers to the quantity of commodity X, PX and PY are the prices of good X and Y respectively. Use the point formula to calculate all elasticities.
a) Determine the value of Q when PX = 10 and PY = 100
b) Calculate the own price elasticity of demand for good X at PX = 10 and PY = 100. [Hint: use the price of good X and the quantity calculated in Part a). Also, solve for Q before taking the coefficient of PX as the Q/PX.]
c) Interpret your answer in Part b).
d) Calculate the cross-price elasticity of demand between good X and good Y at a price, PX = 10 and PY = 100. (Hint: Use the price of Y and the quantity of X calculated in Part a). Also, solve for Q before taking the coefficient of PY as the Q/PY.]
e) Interpret your answer in Part (d).
Explanation / Answer
a) Use PX = 10 and PY = 100 in the demand function
10 = 30 – 0.005QX + 0.15*100
QX = 35/0.005 = 7000 units
b) Own price elasticity of demand for good X at PX = 10 and PY = 100 is given by ed = QX/PX * PX/QX
or ex = (-1/0.005)*10/7000 = -0.286
c) Demand for good X is inelastic because the price elasticity is less than 1 in absolute terms.
d) Cross-price elasticity of demand between good X and good Y at a price, PX = 10 and PY = 100 is given by exy = QX/PY * PY/QX = (1/0.15)*(100/7000) = 0.095
e) The cross price elasticity is positive so that the two goods X and good Y are substitutes.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.