Question

1. Ralf enjoys fishing. The total benefits (in dollars) he obtains from time spent fishing are given by TB = 40*ln(h), where ln( ) is the natural log function, and h is hours spent fishing. Because he has to miss work, where he earns a wage of $8 per hour, his marginal cost of time spent fishing is MC = 8.
2. 1. Solve for the optimal quantity of hours that Ralf will spend fishing and show your work.
3. 2. Generate a graph in Excel that illustrates the total benefit and total cost functions on one graph as well as the optimum that you found in part a. To generate your graph, I recommend having excel calculate the total benefit and total cost for a range of values between 0 and 10. Once you have done this, you can choose to insert a chart and by choosing the ‘scatter’ option you can generate separate lines for the total benefits and total costs. In the graph, dollars should be on the vertical axis and the quantity between 0 and 10 on the horizontal axis.

Answer 1

(a) For equilibrium quantity, MC = Marginal Benefit from fishing

i.e. MC=8= d/dh (40 ln(h))) Differentiating with respect to h)
i.e. 40/h = 8, which gives h=5

(b) See Excel graph. Additionally, a Marginal Cost and Marginal benefit graph also added. Hope this would help you appreciate the equilibrium value better!