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Use the following data to answer the questions below.
Using OLS, the estimated demand function (P=f(Q))(◂=▸P=f(Q)) is
Using algebra to invert the demand function, the demand function (Q=f(P))(◂=▸Q=f(P)) is
Using calculus to determine dQdP◂/▸dQdP, construct a column which calculates the point-price elasticity for each (P,Q) combination. What is the point price elasticity of demand when P=$49.80P=$49.80?
What is the point price elasticity of demand when P=$51.00P=$51.00?
To maximize total revenue, what would you recommend if the company was currently charging P=$49.15P=$49.15? If it was charging P=$51.00P=$51.00?
a. Price should be lower than both $49.15 and $51.00.
b. Price should be raised above both $49.15 and $51.00.
c. Lower the price if it is currently $49.15; raise the price if it is currently $51.00.
d. Raise the price if it is currently $49.15; lower the price if it is currently $51.00.
Use your first demand function to determine an equation for TRTR and MRMR as functions of QQ. What is total revenue when P=$52.50P=$52.50 and when P=$51.00P=$51.00?
a. At P=$52.50P=$52.50, TR=$61,487◂,▸TR=$61,487; at P=$51.00P=$51.00, TR=$62,985◂,▸TR=$62,985.
b. At P=$52.50P=$52.50, TR=$58,386◂,▸TR=$58,386; at P=$51.00P=$51.00, TR=$58,425◂,▸TR=$58,425.
c. At P=$52.50P=$52.50, TR=$34,995◂,▸TR=$34,995; at P=$51.00P=$51.00, TR=$38,163◂,▸TR=$38,163.
d. At P=$52.50P=$52.50, TR=$52,343◂,▸TR=$52,343; at P=$51.00P=$51.00, TR=$51,873◂,▸TR=$51,873.
What is the total-revenue maximizing price and quantity, and how much revenue is earned there?
a. P∗=$49.27P∗=$49.27, Q∗=1168Q∗=1168, TR∗=$57,122◂=▸TR∗=$57,122
b. P∗=$50.07P∗=$50.07, Q∗=1,167◂,▸Q∗=1,167, TR∗=$58,445◂=▸TR∗=$58,445
c. P∗=$47.54P∗=$47.54, Q∗=1263Q∗=1263, TR∗=$59,008◂=▸TR∗=$59,008
d. P∗=$51.72P∗=$51.72, Q∗=1,472◂,▸Q∗=1,472, TR∗=$59,273
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