Assume that a firm operates with the production function Q(K.L)=KL1/2 and assume that the price of labor w=$4 and the rental rate for capital r=$2.
a. without doing any calculations, sketch a representative LTC and LAC curve for this production function.
b. write the optimization problem of the producer for this production problem and these input price.
c. Derive the L-R expansion path for this problem given that the marginal rate of technical substitution for the production function Q (K,L)=LaKb is given by MRTS=(aK/bL)
d. Derive the equations of the LTC and LAC for this production function and the given input prices. sketch the paragraph of LTC and LAC. Do they agree with your hypothesis in part"a" above? Explain.
e. if K is held constant at K=20, calculate the equation for short-run total cost, short-run variable cost, and short run fixed cost.