Bill is an avid angler. His favorite fishing location is Willow Lake, which supports year-round sport fishing. His monthly demand function for fishing at Willow Lake is given by x = 39 - 3p, where p is the round-trip cost of driving to the lake and parking there each time he goes fishing, and x is the number of fishing trips he chooses to take to Willow Lake per month.
(a) What is the cutoff price at which Bill would stop fishing at Willow Lake altogether?
(b) If the cost of fishing is $10 per trip, how many fishing trips to Willow Lake does Bill take per month?
(c) How much money does he spend per month on fishing at Willow Lake?
(d) What is Bill's net benefit (his consumer's surplus) from being able to fish at Willow Lake for $10 per trip rather than not being able to fish there at all? Draw a diagram to explain what you calculated.
(e) What is his gross benefit from fishing at Willow Lake, given the price of $10 per trip? Draw a diagram to explain what you calculated.
(f) What would his gross and net benefits be from fishing at Willow Lake if the cost of going there was zero? Draw a diagram what you calculated.
The State Fish & Game Commission decides to stock special game fish at Willow Lake which substantially improves the quality of fishing there. As a result, Bill's demand function to fish at Willow Lake changes and becomes x = 45 - 3p. However, there is no change in the cost of fishing there.
(g) What is the cutoff price at which Bill would now stop fishing at Willow Lake altogether?
(h) With the cost of fishing still being $10 per trip, how many fishing trips to Willow Lake does Bill now take per month?
(i) What is Bill's net benefit (his consumer's surplus) from now being able to fish at Willow Lake rather than not being able to fish there at all? Draw a diagram to explain what you calculated.
(j) Would you say that Bill is worse off, better off, or neither worse nor better off from being able to fish at Willow Lake than he was before the Fish & Game Commission started stocking special game fish at Willow Lake?
(k) What is the monetary measure of the change in Bill's welfare as you described it in (j)? Use a diagram to explain what you calculated.