1. (30 marks) Given Q=2x^1/2+y^1/2. P, Wx, and Wy are prices for output, input x, and input y respectively. MPx= x^-1/2 and MPy=1/2 y^-1/2.

(a)Illustrate by example that the technology implies diminishing marginal products for input x.

(b)Show that the technology exhibits decreasing return to scale.

(c)Write out the isoquant equation for Q=100 (express y as a function of x) and illustrate it in a graph.

(d)In the short run, y=400. Find the short run demand function of x and the supply function of Q.

(e)Find the long run demand function of x and supply function of Q.

2. [3D marks] Given =2x1f1+yl. P, Wit, and W}: are prices for output, input 1:, and input 1r respectively. MPF I\": and MPFHZ V132. {a} IIEustrate by example that the technology implies diminishing marginal products for input 3:. [b] Show that the technology exhibits decreasing return to scale. {c} Write out the isoquant equation for =1 {express 1,; as a function of x} and illustrate it in a graph. [cl] In the short run, y=4DEL Find the short run demand function of x and the supply function of {1. [e] Find the long run demand function of}: and supplyfunction of [1