1. Technology of the manufacturer is described by the Cobb-Douglas production y=f(x)=Ax1^(a)x2^(b)x3^(c), where A,a,b,c>0.
a) Calculate the elasticity of production factors μi.
b) Use results of a) to calculate the scale elasticity μ.
c) What conditions must be satisfied by the production function parameters for the returns the scale to be increasing, decreasing or stable?
2. The manufacturer uses only one production factor x. During the setup phase x=a/b is used. So the production function is:
-a+bx, kai x>a/b
y= 0, kai 0
a) Draw a production function curve, find the marginal and the average product, when x>a/b. What are the returns to scale?
b) Write the cost function and draw it's curve. In the next figure draw the average and marginal cost curves. Would these graphs be affected (if so how) by the fact that the preparation would be associated with the cancellable commitment to produce/non cancellable commitment to produce?
3. Technology of the producer is described by the manufacturer's production function y=f(x)=x1^(1/2)+x2^(1/2).
a) Solve the cost minimization problem and find the cost function.
b) Find the cost elasticity, scale elasticity within the minimum cost combination of the factors x*(x1*,x2*), and the scale elasticity within randomly picked factors combination of the factors x(x1,x2), make a conclusion on the returns to scale.
4. Manufacturer's cost function is c(w,y)=(w1/a+w2/b+w3/c)y^k, where a,b,c,k>0
a) By applying Shephard lemma, find the conditional factor demands.
b) Calculate all of the conditional elasticities of demand with respect to volume of production.
c) Calculate the scale elasticity by using the cost function.
d) Calculate the Allen elasticities of substitution σ12, σ23, σ13, where σij = (ccij)/(cicj). What conclusion can be drawn about the factors of production - whether they are substitutes or complements?
5. Suppose that the manufacturer's technology is described by at least twice differentifiable quasiconvex production function. Using the comparative statics method, find the impact of w2 change to the behaviour of the producer, who minimises costs.
Attachment:- MicroAnalys.rar