John's Lawn Mowing Service is a small business that acts as a price taker. Suppose the market demand curve for mowing lawns is given by P = 40 - 0.4Q where Q is the quantity demanded in the whole market. The prevailing market price of lawn mowing is $20 per lawn. John's costs are given by TC=0.1q2+10q+50, where q is the number of lawns John chooses to cut a day.
a. How many lawns should John choose to mow in order to maximize profit?
b. Calculate John's maximum daily profit.
c. What is John's supply curve? Mathematically represent and then explain.
John pulled some political favour strings which got the local government to announce that only John can mow lawns in this state and closed down all other lawn mowing services.
d. How many lawns should John choose to mow in order to maximize profit?
e. Calculate John's maximum daily profit.
f. What is John's supply curve? Explain.
g. Draw a neat diagram showing the D and MR curves, John's MC, the price-quantity equilibrium in the market under the two cases of perfect competition and monopoly, and the change in welfare.
h. What is the change in welfare in the market (consumer surplus, producer surplus and deadweight loss) compared to the case when John was a price taker? Calculate.
Show the general steps first and then solve for particular numbers. For drawing the diagram you need the exact numbers for the intercepts and intersection of the curves.