Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the production function is q = 50K^(1/2)L^(1/2). prices of capital and labor are given as r = 2 and w = 8
a) does the production function display increasing, constant, or decreasing returns to scale? how do you know and what does this mean?
b) draw the isoquants for your firms production function using L for the x axis and K for y. how are the factors K and L?
c) derive the expansion path equation. represent it graphically. how does the expansion path change when r = 1 and w = 8?
d) find the total cost function as a function of quantity
e) represent the firms cost minimizing choice of factors to produce a given quantity q in a diagram. if q = 1000, calculate K and L