Does optimal use of an input (such as labor) mean maximizing average output (per unit of input)? Explain.

Why do economists measure profit differently from accountants?

Juan Valdez owns a coffee farm in Colombia. His production function is:  f(x1​,x2​)=(x1​−1)^0.25 x2^0.5​   Assume the price of input 1 is r and the price of input 2 is w. (a)  Write down an expression for the technical rate of substitution. (b)  Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c)  Find Juan's cost function. (d)  What is the supply function of Juan's firm?

Grease Tech produces oil changes. The production of oil changes reles on both capital (K) and labor (L) and is combined in the following production function F (K, L) = KILL Take the derivative of this production function with respect to capital. What is the marginal product of capital evaluated at (le. just plug in the numbers) 64 units of capital used and 16 units of labor?

Solve the attahment.

answer question d Q5. Jason is running a cleaning business, there are available labours (L) and machines (M) for Jason to use as inputs to produce cleaning service for his clients. a) Suppose Jason must use both labours and machines without any specific ratio to complete the service for his clients, please write down the general production function formula for Jason. hint: you could use any letter if you want] b) Under the function form of a), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) equals to 2, how do you interpret it? c) Assume Jason now can use only single input, either labour or machine to complete the service, please write down the general production function formula for Jason. hint: you could use any letter if you want] d) Under the function form of c), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) is always larger than the market price ratio between labour and machine (w/r), what should Jason do? why?