Question

2. A firm has the following linear production function:

q = 5L + 2K

a. Does this firm’s production function exhibit diminishing returns to labor?

  

b. Does this production function exhibit diminishing returns to capital?

c. Graph the isoquant associated with q = 20.

d. What is the firm’s MRTS between K and L?

e. Does this production technology exhibit decreasing, constant, or increasing returns to scale?

Answer 1

1- diminishing returns to labour will be when the mrs is diminishing,

MRSl = Dq/DL = 5, then the mrs will not be diminishing as D(MRSl)/DL = 0

so answer is no

2- same is for capital as done above for labour

3- isoquanti is the curve that shows various combination of two inputs that a sller can use to produce a given amount of output,

so basically 20 = 5L+2K

now this is the equation of straight line, so basically this curve is going to be a downward sloping line with labour on x axis and capital on y axis, with x intercept as 4 and y intercept as 10

c- MRTSkl is the rate at which we are able to substitute one input for other such that the level of production remains the same

it is given by MPl/MPk = 2.5