Answer the following questions using the production function q=AK^aL^b, where A,a,b>0.
Does labor exhibit diminishing marginal product if b=1.1? Show me how you know.
Find the rate of technical substitution (RTS) for an isoquant of this production function. Show your work-b does not equal 1.1 for this part of the question. Find the RTS in terms of the parameters and variables (i.e., it won't yield a numerical answer at this stage).
Best Buy offers a protection plan for new smartphones at $132. The absolutely most expensive iPhone you can buy right now is $700. Assume for a moment you are a very cautious but forgetful person: you would never, ever drop or damage your phone, but you might lose it. How likely must you be to lose your phone for $132 to be an actuarially fair price for mobile phone insurance? [Hint: you're solving for p, the probability of losing your phone. Not losing your phone, therefore, happens 1-p percent of the time.]
If your demand for some good x is
X=.3I/P_x
a) is X a normal or inferior good? Show me how you know.
b) is good Y a substitute or complement for good X? Again, show me how you know.